2D Models¶
Astrophysics¶
King 14 (
King_14)King 14
\(f{(x)} = k * {[}1/\sqrt{(1 + {(x/r\_c)} ^2)} - 1/\sqrt{(1 + {(r\_t/r\_c)} ^2)}{]} ^2\)
[k, r_c, r_t]
King 14 With Offset
\(f{(x)} = k * {[}1/\sqrt{(1 + {(x/r\_c)} ^2)} - 1/\sqrt{(1 + {(r\_t/r\_c)} ^2)}{]} ^2 + \text{Offset}\)
[k, r_c, r_t, Offset]
BioScience¶
Aphid Population Growth (
AphidPopulationGrowth)Aphid Population Growth
\(N{(t)} = a * \exp{(bt)} * {(1 + c * \exp{(bt)})}^{-2}\)
[a, b, c]
Aphid Population Growth With Offset
\(N{(t)} = a * \exp{(bt)} * {(1 + c * \exp{(bt)})}^{-2} + \text{Offset}\)
[a, b, c, Offset]
von Bertalanffy Growth (
BertalanffyGrowth)von Bertalanffy Growth
\(L{(t)} = L_{inf} * {(1.0 - \exp{(-K *{(t-t_{zero})})})}\)
[Linf, K, tzero]
von Bertalanffy Growth With Offset
\(L{(t)} = L_{inf} * {(1.0 - \exp{(-K *{(t-t_{zero})})})} + \text{Offset}\)
[Linf, K, tzero, Offset]
Beverton-Holt A (
BevertonHoltA)Beverton-Holt A
\(y = r / {(1 + {({(r-1)}/K)} * x)}\)
[r, K]
Beverton-Holt A With Offset
\(y = r / {(1 + {({(r-1)}/K)} * x)} + \text{Offset}\)
[r, K, Offset]
Beverton-Holt B (
BevertonHoltB)Beverton-Holt B
\(y = rx / {(1 + {({(r-1)}/K)} * x)}\)
[r, K]
Beverton-Holt B With Offset
\(y = rx / {(1 + {({(r-1)}/K)} * x)} + \text{Offset}\)
[r, K, Offset]
BioScience A (
BioScienceA)BioScience A
\(y = a * {(1.0 - {(b * c^{x})})}\)
[a, b, c]
BioScience A With Offset
\(y = a * {(1.0 - {(b * c^{x})})} + \text{Offset}\)
[a, b, c, Offset]
BioScience B (
BioScienceB)BioScience B
\(y = a * {(1.0 -{(1.0 + {(x/b)}^{c})}^{-1.0 *d})}\)
[a, b, c, d]
BioScience B With Offset
\(y = a * {(1.0 -{(1.0 + {(x/b)}^{c})}^{-1.0 *d})} + \text{Offset}\)
[a, b, c, d, Offset]
Cellular Conductance (
CellularConductance)Cellular Conductance
\(g = p3/{(1+\exp{({(v-p1)}/p2)})} + p4*\exp{({(v-45)}/p5)}\)
[p1, p2, p3, p4, p5]
Cellular Conductance With Offset
\(g = p3/{(1+\exp{({(v-p1)}/p2)})} + p4*\exp{({(v-45)}/p5)} + \text{Offset}\)
[p1, p2, p3, p4, p5, Offset]
Derek Duncan Custom Equation (
DerekDuncanCustomEquation)Derek Duncan Custom Equation
\(y = a / {(1 + \exp{(-1/b*{(x-c)})})}^{d}\)
[a, b, c, d]
Derek Duncan Custom Equation With Offset
\(y = a / {(1 + \exp{(-1/b*{(x-c)})})}^{d} + \text{Offset}\)
[a, b, c, d, Offset]
Dose-Response A (
DoseResponseA)Dose-Response A
\(y = b + {(a-b)} / {(1 + 10^{x-c})}\)
[a, b, c]
Dose-Response B (
DoseResponseB)Dose-Response B
\(y = b + {(a-b)} / {(1 + 10^{c-x})}\)
[a, b, c]
Dose-Response C (
DoseResponseC)Dose-Response C
\(y = b + {(a-b)} / {(1 + 10^{d*{(x-c)}})}\)
[a, b, c, d]
Dose-Response D (
DoseResponseD)Dose-Response D
\(y = b + {(a-b)} / {(1 + 10^{d*{(c-x)}})}\)
[a, b, c, d]
Dose-Response E (
DoseResponseE)Dose-Response E
\(y = b + {(a-b)} / {(1 + {(x/c)}^{d})}\)
[a, b, c, d]
Generalized Negative Exponential (
GeneralizedNegativeExponential)Generalized Negative Exponential
\(y = a * {(1.0 - \exp{(-bx)})}^{c}\)
[a, b, c]
Generalized Negative Exponential With Offset
\(y = a * {(1.0 - \exp{(-bx)})}^{c} + \text{Offset}\)
[a, b, c, Offset]
Generalized Product Accumulation (
GeneralizedProductAccumulation)Generalized Product Accumulation
\(y = a{(b-x)} / {(c + {(b-x)})} + d{(b-x)} + f\)
[a, b, c, d, f]
Generalized Substrate Depletion (
GeneralizedSubstrateDepletion)Generalized Substrate Depletion
\(y = ax / {(b + x)} - cx - d\)
[a, b, c, d]
High-Low Affinity (
HighLowAffinity)High-Low Affinity
\(y = abx / {(1+bx)}\)
[a, b]
High-Low Affinity With Offset
\(y = abx / {(1+bx)} + \text{Offset}\)
[a, b, Offset]
High-Low Affinity Double (
HighLowAffinityDouble)High-Low Affinity Double
\(y = abx / {(1+bx)} + cdx / {(1+dx)}\)
[a, b, c, d]
High-Low Affinity Double With Offset
\(y = abx / {(1+bx)} + cdx / {(1+dx)} + \text{Offset}\)
[a, b, c, d, Offset]
High-Low Affinity Isotope Displacement ([Hot] subsumed) (
HighLowAffinityIsotopeDisplacement)High-Low Affinity Isotope Displacement ([Hot] subsumed)
\(y = ab / {(1+bx)}\)
[a, b]
High-Low Affinity Isotope Displacement ([Hot] subsumed) With Offset
\(y = ab / {(1+bx)} + \text{Offset}\)
[a, b, Offset]
High-Low Affinity Double Isotope Displacement ([Hot] subsumed) (
HighLowAffinityIsotopeDisplacementDouble)High-Low Affinity Double Isotope Displacement ([Hot] subsumed)
\(y = ab / {(1+bx)} + cd / {(1+dx)}\)
[a, b, c, d]
High-Low Affinity Double Isotope Displacement ([Hot] subsumed) With Offset
\(y = ab / {(1+bx)} + cd / {(1+dx)} + \text{Offset}\)
[a, b, c, d, Offset]
Hyperbolic A (
HyperbolicA)Hyperbolic A
\(y = {(a + x)} / {(b + x)}\)
[a, b]
Hyperbolic A With Offset
\(y = {(a + x)} / {(b + x)} + \text{Offset}\)
[a, b, Offset]
Hyperbolic B (
HyperbolicB)Hyperbolic B
\(y = {(a + bx)} / {(c + x)}\)
[a, b, c]
Hyperbolic B With Offset
\(y = {(a + bx)} / {(c + x)} + \text{Offset}\)
[a, b, c, Offset]
Hyperbolic C (
HyperbolicC)Hyperbolic C
\(y = {(a + x)} / {(b + cx)}\)
[a, b, c]
Hyperbolic C With Offset
\(y = {(a + x)} / {(b + cx)} + \text{Offset}\)
[a, b, c, Offset]
Hyperbolic D (
HyperbolicD)Hyperbolic D
\(y = {(a + bx)} / {(c + dx)}\)
[a, b, c, d]
Hyperbolic D With Offset
\(y = {(a + bx)} / {(c + dx)} + \text{Offset}\)
[a, b, c, d, Offset]
Hyperbolic E (
HyperbolicE)Hyperbolic E
\(y = ax / {(b + x)}\)
[a, b]
Hyperbolic E With Offset
\(y = ax / {(b + x)} + \text{Offset}\)
[a, b, Offset]
Hyperbolic F (
HyperbolicF)Hyperbolic F
\(y = ax / {(b + x)} + cx\)
[a, b, c]
Hyperbolic F With Offset
\(y = ax / {(b + x)} + cx + \text{Offset}\)
[a, b, c, Offset]
Hyperbolic G (
HyperbolicG)Hyperbolic G
\(y = ax / {(b + x)} + cx / {(d + x)}\)
[a, b, c, d]
Hyperbolic G With Offset
\(y = ax / {(b + x)} + cx / {(d + x)} + \text{Offset}\)
[a, b, c, d, Offset]
Hyperbolic H (
HyperbolicH)Hyperbolic H
\(y = ax / {(b + x)} + cx / {(d + x)} + fx\)
[a, b, c, d, f]
Hyperbolic H With Offset
\(y = ax / {(b + x)} + cx / {(d + x)} + fx + \text{Offset}\)
[a, b, c, d, f, Offset]
Hyperbolic I (
HyperbolicI)Hyperbolic I
\(y = ab / {(b + x)}\)
[a, b]
Hyperbolic I With Offset
\(y = ab / {(b + x)} + \text{Offset}\)
[a, b, Offset]
Hyperbolic J (
HyperbolicJ)Hyperbolic J
\(y = x / {(a + bx)}\)
[a, b]
Hyperbolic J With Offset
\(y = x / {(a + bx)} + \text{Offset}\)
[a, b, Offset]
Hyperbolic Logistic (
HyperbolicLogistic)Hyperbolic Logistic
\(y = ax^{b} / {(c + x^{b})}\)
[a, b, c]
Hyperbolic Logistic With Offset
\(y = ax^{b} / {(c + x^{b})} + \text{Offset}\)
[a, b, c, Offset]
Jorge Rabinovich Population Growth (
JorgeRabinovichPopulationGrowth)Jorge Rabinovich Population Growth
\(Y = {(P1*CC)} / {(P1 + {(CC-P1)}*\exp{(-R*X)})}\)
[P1, CC, R]
Jorge Rabinovich Population Growth With Offset
\(Y = {(P1*CC)} / {(P1 + {(CC-P1)}*\exp{(-R*X)})} + \text{Offset}\)
[P1, CC, R, Offset]
Membrane Transport (
MembraneTransport)Membrane Transport
\(y = a{(x-b)} / {(x^{2} + cx + d)}\)
[a, b, c, d]
Membrane Transport With Offset
\(y = a{(x-b)} / {(x^{2} + cx + d)} + \text{Offset}\)
[a, b, c, d, Offset]
Michaelis-Menten (
MichaelisMenten)Michaelis-Menten
\(y = ax / {(b + x)}\)
[a, b]
Michaelis-Menten With Offset
\(y = ax / {(b + x)} + \text{Offset}\)
[a, b, Offset]
Michaelis-Menten Double (
MichaelisMentenDouble)Michaelis-Menten Double
\(y = ax / {(b + x)} + cx / {(d + x)}\)
[a, b, c, d]
Michaelis-Menten Double With Offset
\(y = ax / {(b + x)} + cx / {(d + x)} + \text{Offset}\)
[a, b, c, d, Offset]
Michaelis-Menten Isotope Displacement Double ([Hot] subsumed) (
MichaelisMentenDoubleIsotopeDisplacement)Michaelis-Menten Isotope Displacement Double ([Hot] subsumed)
\(y = a / {(b + x)} + c / {(d + x)}\)
[a, b, c, d]
Michaelis-Menten Isotope Displacement Double ([Hot] subsumed) With Offset
\(y = a / {(b + x)} + c / {(d + x)} + \text{Offset}\)
[a, b, c, d, Offset]
Michaelis-Menten Isotope Displacement ([Hot] subsumed) (
MichaelisMentenIsotopeDisplacement)Michaelis-Menten Isotope Displacement ([Hot] subsumed)
\(y = a / {(b + x)}\)
[a, b]
Michaelis-Menten Isotope Displacement ([Hot] subsumed) With Offset
\(y = a / {(b + x)} + \text{Offset}\)
[a, b, Offset]
Michaelis-Menten Product Accumulation (
MichaelisMentenProductAccumulation)Michaelis-Menten Product Accumulation
\(y = a{(b-x)} / {(c + {(b-x)})}\)
[a, b, c]
Michaelis-Menten Product Accumulation With Offset
\(y = a{(b-x)} / {(c + {(b-x)})} + \text{Offset}\)
[a, b, c, Offset]
Negative Exponential (
NegativeExponential)Negative Exponential
\(y = a * {(1.0 - \exp{(-bx)})}\)
[a, b]
Negative Exponential With Offset
\(y = a * {(1.0 - \exp{(-bx)})} + \text{Offset}\)
[a, b, Offset]
New Zealand Ecology Logistic 1 (
NewZealandEcologyLogistic1)New Zealand Ecology Logistic 1
\(n = B0 + {({(B1 - B0)} / {(1.0 + \exp{({(B2 + D)} * B3)})})}\)
[B0, B1, B2, B3]
New Zealand Ecology Logistic 2 (
NewZealandEcologyLogistic2)New Zealand Ecology Logistic 2
\(n = B0 + {({(B1 - B0)} / {(1.0 + \exp{({(B2 + D + {(B4*D^{2})})} *B3)})})}\)
[B0, B1, B2, B3, B4]
Plant Disease Exponential Model (
PlantDisease_Exponential)Plant Disease Exponential Model
\(Incidence = y0 * \exp{(r * time)}\)
[y0, r]
Plant Disease Exponential Model With Offset
\(Incidence = y0 * \exp{(r * time)} + \text{Offset}\)
[y0, r, Offset]
Plant Disease Gompertz Model (
PlantDisease_Gompertz)Plant Disease Gompertz Model
\(Incidence = \exp{(ln{(y0)} * \exp{(-r * time)})}\)
[y0, r]
Plant Disease Gompertz Model With Offset
\(Incidence = \exp{(ln{(y0)} * \exp{(-r * time)})} + \text{Offset}\)
[y0, r, Offset]
Plant Disease Logistic Model (
PlantDisease_Logistic)Plant Disease Logistic Model
\(Incidence = 1 / {(1 + {(1 - y0)} / {(y0 * \exp{(-r * time)})})}\)
[y0, r]
Plant Disease Logistic Model With Offset
\(Incidence = 1 / {(1 + {(1 - y0)} / {(y0 * \exp{(-r * time)})})} + \text{Offset}\)
[y0, r, Offset]
Plant Disease Monomolecular Model (
PlantDisease_Monomolecular)Plant Disease Monomolecular Model
\(Incidence = 1 - {({(1 - y0)} * \exp{(-r * time)})}\)
[y0, r]
Plant Disease Monomolecular Model With Offset
\(Incidence = 1 - {({(1 - y0)} * \exp{(-r * time)})} + \text{Offset}\)
[y0, r, Offset]
Plant Disease Weibull Model (
PlantDisease_Weibull)Plant Disease Weibull Model
\(Incidence = 1 - \exp{(-1.0 * {({(time - a)} / b)}^{c})}\)
[a, b, c]
Plant Disease Weibull Model With Offset
\(Incidence = 1 - \exp{(-1.0 * {({(time - a)} / b)}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Plant Disease Weibull Model Scaled (
PlantDisease_WeibullScaled)Plant Disease Weibull Model Scaled
\(y = Scale * {(1 - \exp{(-1.0 * {({(time - a)} / b)}^{c})})}\)
[a, b, c, Scale]
Plant Disease Weibull Model Scaled With Offset
\(y = Scale * {(1 - \exp{(-1.0 * {({(time - a)} / b)}^{c})})} +\text{Offset}\)
[a, b, c, Scale, Offset]
Preece And Baines Growth (
PreeceAndBaines)Preece And Baines Growth
\(y = a - 2{(a-b)} / {(\exp{(c{(x-d)})} + \exp{(f{(x-d)})})}\)
[a, b, c, d, f]
Scaled Log (
ScaledLog)Scaled Log
\(y = a * log{(x)}\)
[a]
Scaled Log With Offset
\(y = a * log{(x)} + \text{Offset}\)
[a, Offset]
Scaled Log Transform (
ScaledLog_Transform)Scaled Log Transform
\(y = a * log{(bx + c)}\)
[a, b, c]
Scaled Log Transform With Offset
\(y = a * log{(bx + c)} + \text{Offset}\)
[a, b, c, Offset]
Scaled Power (
ScaledPower)Scaled Power
\(y = a * x^{b}\)
[a, b]
Scaled Power With Offset
\(y = a * x^{b} + \text{Offset}\)
[a, b, Offset]
Scaled Power Transform (
ScaledPower_Transform)Scaled Power Transform
\(y = a * {(cx + d)}^{b}\)
[a, b, c, d]
Scaled Power Transform With Offset
\(y = a * {(cx + d)}^{b} + \text{Offset}\)
[a, b, c, d, Offset]
Standard 3-Parameter Logistic Equation (
StandardLogistic3Parameter)Standard 3-Parameter Logistic Equation
\(y = d + {(a - d)} / {(1 + {(x / c)})}\)
[a, c, d]
Standard 4-Parameter Logistic Equation (
StandardLogistic4Parameter)Standard 4-Parameter Logistic Equation
\(y = d + {(a - d)} / {(1 + {(x / c)}^{b})}\)
[a, b, c, d]
Standard 5-Parameter Logistic Equation (
StandardLogistic5Parameter)Standard 5-Parameter Logistic Equation
\(y = d + {(a - d)} / {(1 + {(x / c)}^{b} )}^{f}\)
[a, b, c, d, f]
Weibull (
Weibull)Weibull
\(y = a * {(1.0 - \exp{(-b * {(x - c)}^{d})})}\)
[a, b, c, d]
Weibull With Offset
\(y = a * {(1.0 - \exp{(-b * {(x - c)}^{d})})} + \text{Offset}\)
[a, b, c, d, Offset]
Xiaogang Peng Immunoassay (
XiaogangPengImmunoassay)Xiaogang Peng Immunoassay
\(y = K / {(1.0 + \exp{(-1.0 * {(a + blog{(x)} + cx)})})}\)
[K, a, b, c]
Xiaogang Peng Immunoassay With Offset
\(y = K / {(1.0 + \exp{(-1.0 * {(a + blog{(x)} + cx)})})} + \text{Offset}\)
[K, a, b, c, Offset]
BurkardtCollectionBased¶
Arcsin CDF Based (
arcsin_cdf)Arcsin CDF Based
\(y = a * asin{( {(bx+c)} / d)}\)
[a, b, c, d]
Arcsin CDF Based With Offset
\(y = a * asin{( {(bx+c)} / d)} + \text{Offset}\)
[a, b, c, d, Offset]
Arcsin PDF Based (
arcsin_pdf)Arcsin PDF Based
\(y = a / \sqrt{( b^{2} - x^{2})}\)
[a, b]
Arcsin PDF Based With Offset
\(y = a / \sqrt{( b^{2} - x^{2})} + \text{Offset}\)
[a, b, Offset]
Bradford CDF Based A (
bradford_cdf_a)Bradford CDF Based A
\(y = ln{(1.0+c*{(x-a)}/{(b-a)})} / ln{(c+1.0)}\)
[a, b, c]
Bradford CDF Based A With Offset
\(y = ln{(1.0+c*{(x-a)}/{(b-a)})} / ln{(c+1.0)} + \text{Offset}\)
[a, b, c, Offset]
Bradford CDF Based B (
bradford_cdf_b)Bradford CDF Based B
\(y = d * ln{(1.0+c*{(x-a)}/{(b-a)})} / ln{(c+1.0)}\)
[a, b, c, d]
Bradford CDF Based B With Offset
\(y = d * ln{(1.0+c*{(x-a)}/{(b-a)})} / ln{(c+1.0)} + \text{Offset}\)
[a, b, c, d, Offset]
Bradford PDF Based (
bradford_pdf)Bradford PDF Based
\(y = c / {({( c * {(x-a)} + b-a)} * ln{(c + 1.0)})}\)
[a, b, c]
Bradford PDF Based With Offset
\(y = c / {({( c * {(x-a)} + b-a)} * ln{(c + 1.0)})} + \text{Offset}\)
[a, b, c, Offset]
Burr CDF Based A (
burr_cdf_a)Burr CDF Based A
\(y = 1.0 / {( 1.0 + {( b / {( x-a )})}^{c})}^{d}\)
[a, b, c, d]
Burr CDF Based A With Offset
\(y = 1.0 / {( 1.0 + {( b / {( x-a )})}^{c})}^{d}+ \text{Offset}\)
[a, b, c, d, Offset]
Burr CDF Based B (
burr_cdf_b)Burr CDF Based B
\(y = f / {( 1.0 + {( b / {( x-a )})}^{c})}^{d}\)
[a, b, c, d, f]
Burr CDF Based B With Offset
\(y = f / {( 1.0 + {( b / {( x-a )})}^{c})}^{d} +\text{Offset}\)
[a, b, c, d, f, Offset]
Burr PDF Based (
burr_pdf)Burr PDF Based
\(y = {(c*d/b)} * {({(x-a)}/b)}^{(-c-1.0)} *{(1.0+{({(x-a)}/b)}^{(-c)})}^{(-d-1.0)}\)
[a, b, c, d]
Burr PDF Based With Offset
\(y = {(c*d/b)} * {({(x-a)}/b)}^{(-c-1.0)} *{(1.0+{({(x-a)}/b)}^{(-c)})}^{(-d-1.0)} + \text{Offset}\)
[a, b, c, d, Offset]
Dipole CDF Based (
dipole_cdf)Dipole CDF Based
\(y = a * arctan{(x)} + b/x\)
[a, b]
Dipole CDF Based With Offset
\(y = a * arctan{(x)} + b/x + \text{Offset}\)
[a, b, Offset]
Exponential PDF Based (
exponential_pdf)Exponential PDF Based
\(y = {(1.0/b)} * \exp{({(a-x)}/b)}\)
[a, b]
Exponential PDF Based With Offset
\(y = {(1.0/b)} * \exp{({(a-x)}/b)} + \text{Offset}\)
[a, b, Offset]
Exponential PDF Based Scaled (
exponential_pdf_scaled)Exponential PDF Based Scaled
\(y = Scale * {(1.0/b)} * \exp{({(a-x)}/b)}\)
[a, b, Scale]
Exponential PDF Based Scaled With Offset
\(y = Scale * {(1.0/b)} * \exp{({(a-x)}/b)} + \text{Offset}\)
[a, b, Scale, Offset]
Extreme Values CDF Based A (
extreme_values_cdf_a)Extreme Values CDF Based A
\(y = \exp{(-\exp{(-{({(x-a)}/b)})})}\)
[a, b]
Extreme Values CDF Based A With Offset
\(y = \exp{(-\exp{(-{({(x-a)}/b)})})} + \text{Offset}\)
[a, b, Offset]
Extreme Values CDF Based B (
extreme_values_cdf_b)Extreme Values CDF Based B
\(y = c * \exp{(-\exp{(-{({(x-a)}/b)})})}\)
[a, b, c]
Extreme Values CDF Based B With Offset
\(y = c * \exp{(-\exp{(-{({(x-a)}/b)})})} + \text{Offset}\)
[a, b, c, Offset]
Extreme Values PDF Based (
extreme_values_pdf)Extreme Values PDF Based
\(y = {(1.0/b)} * \exp{({({(a-x)}/b)}-\exp{({(a-x)}/b)})}\)
[a, b]
Extreme Values PDF Based With Offset
\(y = {(1.0/b)} * \exp{({({(a-x)}/b)}-\exp{({(a-x)}/b)})} + \text{Offset}\)
[a, b, Offset]
Fisk CDF Based A (
fisk_cdf_a)Fisk CDF Based A
\(y = 1.0 / {(1.0+{(b/{(x-a)})}^{c})}\)
[a, b, c]
Fisk CDF Based A With Offset
\(y = 1.0 / {(1.0+{(b/{(x-a)})}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Fisk CDF Based B (
fisk_cdf_b)Fisk CDF Based B
\(y = d / {(1.0+{(b/{(x-a)})}^{c})}\)
[a, b, c, d]
Fisk CDF Based B With Offset
\(y = d / {(1.0+{(b/{(x-a)})}^{c})} + \text{Offset}\)
[a, b, c, d, Offset]
Fisk PDF Based (
fisk_pdf)Fisk PDF Based
\(y = {(c/b)} * {({(x-a)}/b)}^{{(c-1.0)}} / {(1.0 +{({(x-a)}/b)}^{c})}^{2}\)
[a, b, c]
Fisk PDF Based With Offset
\(y = {(c/b)} * {({(x-a)}/b)}^{{(c-1.0)}} / {(1.0 +{({(x-a)}/b)}^{c})}^{2} + \text{Offset}\)
[a, b, c, Offset]
Folded Normal PDF Based (
folded_normal_pdf)Folded Normal PDF Based
\(y = c * {(1/b)} * cosh{(a*x/b^{2})} * \exp{(-0.5 *{(x^{2} + a^{2})}/b^{2})}\)
[a, b, c]
Folded Normal PDF Based With Offset
\(y = c * {(1/b)} * cosh{(a*x/b^{2})} * \exp{(-0.5 *{(x^{2} + a^{2})}/b^{2})} +\text{Offset}\)
[a, b, c, Offset]
Frechet CDF Based A (
frechet_cdf_a)Frechet CDF Based A
\(y = \exp{(-1.0 / x^{a})}\)
[a]
Frechet CDF Based A With Offset
\(y = \exp{(-1.0 / x^{a})} + \text{Offset}\)
[a, Offset]
Frechet CDF Based B (
frechet_cdf_b)Frechet CDF Based B
\(y = b * \exp{(-1.0 / x^{a})}\)
[a, b]
Frechet CDF Based B With Offset
\(y = b * \exp{(-1.0 / x^{a})} + \text{Offset}\)
[a, b, Offset]
Frechet PDF Based A (
frechet_pdf_a)Frechet PDF Based A
\(y = \exp{(- 1.0 / x^{a})} / x^{{( a + 1.0)}}\)
[a]
Frechet PDF Based A With Offset
\(y = \exp{(- 1.0 / x^{a})} / x^{{( a + 1.0)}} +\text{Offset}\)
[a, Offset]
Frechet PDF Based B (
frechet_pdf_b)Frechet PDF Based B
\(y = b * \exp{(- 1.0 / x^{a})} / x^{{( a +1.0)}}\)
[a, b]
Frechet PDF Based B With Offset
\(y = b * \exp{(- 1.0 / x^{a})} / x^{{( a +1.0)}} + \text{Offset}\)
[a, b, Offset]
Genlogistic CDF Based A (
genlogistic_cdf_a)Genlogistic CDF Based A
\(y = {(1.0/{(1.0+\exp{(-{(x-a)}/b)})})}^{c}\)
[a, b, c]
Genlogistic CDF Based A With Offset
\(y = {(1.0/{(1.0+\exp{(-{(x-a)}/b)})})}^{c} + \text{Offset}\)
[a, b, c, Offset]
Genlogistic CDF Based B (
genlogistic_cdf_b)Genlogistic CDF Based B
\(y = {(d/{(1.0+\exp{(-{(x-a)}/b)})})}^{c}\)
[a, b, c, d]
Genlogistic CDF Based B With Offset
\(y = {(d/{(1.0+\exp{(-{(x-a)}/b)})})}^{c} + \text{Offset}\)
[a, b, c, d, Offset]
Genlogistic PDF Based (
genlogistic_pdf)Genlogistic PDF Based
\(y = {(c/b)} * \exp{(-{({(x-a)}/b)})} /{(1.0+\exp{(-{({(x-a)}/b)})})}^{{(c+1.0)}}\)
[a, b, c]
Genlogistic PDF Based With Offset
\(y = {(c/b)} * \exp{(-{({(x-a)}/b)})} /{(1.0+\exp{(-{({(x-a)}/b)})})}^{{(c+1.0)}} + \text{Offset}\)
[a, b, c, Offset]
Gompertz CDF Based (
gompertz_cdf)Gompertz CDF Based
\(y = 1.0 - \exp{(-b * {(a^{x}-1.0)} / ln{(a)})}\)
[a, b]
Gompertz CDF Based With Offset
\(y = 1.0 - \exp{(-b * {(a^{x}-1.0)} / ln{(a)})} + \text{Offset}\)
[a, b, Offset]
Gompertz CDF Based Scaled (
gompertz_cdf_scaled)Gompertz CDF Based Scaled
\(y = Scale * {(1.0 - \exp{(-b * {(a^{x}-1.0)} / ln{(a)})})}\)
[a, b, Scale]
Gompertz CDF Based Scaled With Offset
\(y = Scale * {(1.0 - \exp{(-b * {(a^{x}-1.0)} / ln{(a)})})} +\text{Offset}\)
[a, b, Scale, Offset]
Gumbel CDF Based (
gumbel_cdf)Gumbel CDF Based
\(y = a * \exp{(-\exp{(-x)})}\)
[a]
Gumbel CDF Based With Offset
\(y = a * \exp{(-\exp{(-x)})} + \text{Offset}\)
[a, Offset]
Gumbel PDF Based (
gumbel_pdf)Gumbel PDF Based
\(y = a * \exp{(-x-\exp{(-x)})}\)
[a]
Gumbel PDF Based With Offset
\(y = a * \exp{(-x-\exp{(-x)})} + \text{Offset}\)
[a, Offset]
Half Normal PDF Based (
half_normal_pdf)Half Normal PDF Based
\(y = c * {( 1.0/b)} * \exp{(-0.5*{({(x-a)}/b)}*{({(x-a)}/b)})}\)
[a, b, c]
Half Normal PDF Based With Offset
\(y = c * {( 1.0/b)} * \exp{(-0.5*{({(x-a)}/b)}*{({(x-a)}/b)})} + \text{Offset}\)
[a, b, c, Offset]
Inverse_gaussian PDF Based A (
inverse_gaussian_pdf_a)Inverse_gaussian PDF Based A
\(y = \sqrt{(b/{(c*x^{3})})}*\exp{(-b*{(x-a)}^{2} /{(2.0*a^{2}*x)})}\)
[a, b, c]
Inverse_gaussian PDF Based A With Offset
\(y = \sqrt{(b/{(c*x^{3})})}*\exp{(-b*{(x-a)}^{2} /{(2.0*a^{2}*x)})} + \text{Offset}\)
[a, b, c, Offset]
Inverse_gaussian PDF Based B (
inverse_gaussian_pdf_b)Inverse_gaussian PDF Based B
\(y = \sqrt{(b/{(c*x^{3})})}*\exp{(-b*{(x-a)}^{2} /{(2.0*a^{2}*x)})}\)
[a, b, c, d]
Inverse_gaussian PDF Based B With Offset
\(y = \sqrt{(b/{(c*x^{3})})}*\exp{(-b*{(x-a)}^{2} /{(2.0*a^{2}*x)})} + \text{Offset}\)
[a, b, c, d, Offset]
Levy PDF Based (
levy_pdf)Levy PDF Based
\(y = b^{0.5} *\exp{(-b/{(2.0*{(x-a)})})}/\sqrt{({(x-a)}^{3})}\)
[a, b]
Levy PDF Based With Offset
\(y = b^{0.5} *\exp{(-b/{(2.0*{(x-a)})})}/\sqrt{({(x-a)}^{3})} + \text{Offset}\)
[a, b, Offset]
Levy PDF Based Scaled (
levy_pdf_scaled)Levy PDF Based Scaled
\(y = Scale * b^{0.5} *\exp{(-b/{(2.0*{(x-a)})})}/\sqrt{({(x-a)}^{3})}\)
[a, b, Scale]
Levy PDF Based Scaled With Offset
\(y = Scale * b^{0.5} *\exp{(-b/{(2.0*{(x-a)})})}/\sqrt{({(x-a)}^{3})} + \text{Offset}\)
[a, b, Scale, Offset]
Log Normal PDF Based (
log_normal_pdf)Log Normal PDF Based
\(y = \exp{(-0.5*{({(ln{(x)}-a)}/b)}^{2})} / {(b*x)}\)
[a, b]
Log Normal PDF Based With Offset
\(y = \exp{(-0.5*{({(ln{(x)}-a)}/b)}^{2})} / {(b*x)} + \text{Offset}\)
[a, b, Offset]
Logistic PDF Based (
logistic_pdf)Logistic PDF Based
\(y = \exp{({(a-x)}/b)} / {(b*{(1.0+\exp{({(a-x)}/b)})}^{2})}\)
[a, b]
Logistic PDF Based With Offset
\(y = \exp{({(a-x)}/b)} / {(b*{(1.0+\exp{({(a-x)}/b)})}^{2})} + \text{Offset}\)
[a, b, Offset]
Pareto PDF Based (
pareto_pdf)Pareto PDF Based
\(y = b * a^{b} / x^{{(b+1.0)}}\)
[a, b]
Pareto PDF Based With Offset
\(y = b * a^{b} / x^{{(b+1.0)}} + \text{Offset}\)
[a, b, Offset]
Power PDF Based (
power_pdf)Power PDF Based
\(y = {(a/b)} * {(x/b)}^{{(a-1.0)}}\)
[a, b]
Power PDF Based With Offset
\(y = {(a/b)} * {(x/b)}^{{(a-1.0)}} + \text{Offset}\)
[a, b, Offset]
Rayleigh CDF Based A (
rayleigh_cdf_a)Rayleigh CDF Based A
\(y = 1.0 - \exp{(-x^{2}/{(2.0*a^{2})})}\)
[a]
Rayleigh CDF Based A With Offset
\(y = 1.0 - \exp{(-x^{2}/{(2.0*a^{2})})} + \text{Offset}\)
[a, Offset]
Rayleigh CDF Based B (
rayleigh_cdf_b)Rayleigh CDF Based B
\(y = b * \exp{(-x^{2}/{(2.0*a^{2})})}\)
[a, b]
Rayleigh CDF Based B With Offset
\(y = b * \exp{(-x^{2}/{(2.0*a^{2})})} + \text{Offset}\)
[a, b, Offset]
Rayleigh PDF Based (
rayleigh_pdf)Rayleigh PDF Based
\(y = {(x/a^{2})} *\exp{(-x^{2}/{(2.0*a^{2})})}\)
[a]
Rayleigh PDF Based With Offset
\(y = {(x/a^{2})} *\exp{(-x^{2}/{(2.0*a^{2})})} + \text{Offset}\)
[a, Offset]
Rayleigh PDF Based Scaled (
rayleigh_pdf_scaled)Rayleigh PDF Based Scaled
\(y = Scale * {(x/a^{2})} *\exp{(-x^{2}/{(2.0*a^{2})})}\)
[a, Scale]
Rayleigh PDF Based Scaled With Offset
\(y = Scale * {(x/a^{2})} *\exp{(-x^{2}/{(2.0*a^{2})})} + \text{Offset}\)
[a, Scale, Offset]
Reciprocal CDF Based (
reciprocal_cdf)Reciprocal CDF Based
\(y = ln{(a/x)} / ln{(a/b)}\)
[a, b]
Reciprocal CDF Based With Offset
\(y = ln{(a/x)} / ln{(a/b)} + \text{Offset}\)
[a, b, Offset]
Sech CDF Based (
sech_cdf)Sech CDF Based
\(y = c * atan{(\exp{({(x-a)}/b)})}\)
[a, b, c]
Sech CDF Based With Offset
\(y = c * atan{(\exp{({(x-a)}/b)})} + \text{Offset}\)
[a, b, c, Offset]
Weibull CDF Based A (
weibull_cdf_a)Weibull CDF Based A
\(y = 1.0 / \exp{({({(x-a)}/b)}^{c})}\)
[a, b, c]
Weibull CDF Based A With Offset
\(y = 1.0 / \exp{({({(x-a)}/b)}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Weibull CDF Based B (
weibull_cdf_b)Weibull CDF Based B
\(y = d / \exp{({({(x-a)}/b)}^{c})}\)
[a, b, c, d]
Weibull CDF Based B With Offset
\(y = d / \exp{({({(x-a)}/b)}^{c})} + \text{Offset}\)
[a, b, c, d, Offset]
Weibull PDF Based (
weibull_pdf)Weibull PDF Based
\(y = {(c/b)} * {({(x-a)}/b)}^{{(c-1.0)}} /\exp{({({(x-a)}/b)}^{c})}\)
[a, b, c]
Weibull PDF Based With Offset
\(y = {(c/b)} * {({(x-a)}/b)}^{{(c-1.0)}} /\exp{({({(x-a)}/b)}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Engineering¶
Dispersion Optical (
DispersionOptical)Dispersion Optical
\(n^{2}{(x)} = A1 + A2*x^{2} +A3/x^{2} + A4/x^{4}\)
[A1, A2, A3, A4]
Dispersion Optical Square Root (
DispersionOpticalSqrt)Dispersion Optical Square Root
\(n = {(A1 + A2*x^{2} + A3/x^{2} +A4/x^{4})}^{0.5}\)
[A1, A2, A3, A4]
Electron Beam Lithography Point Spread (
ElectronBeamLithographyPointSpread)Electron Beam Lithography Point Spread
\(y = a*\exp{(-b*x)} + c*\exp{(-{(x-d)}^{2} /f^{2})} + g*\exp{(-{(x-h)}^{2} /i^{2})} + j*\exp{(-{(x-k)}^{2} /l^{2})}\)
[a, b, c, d, f, g, h, i, j, k, l]
Electron Beam Lithography Point Spread With Offset
\(y = a*\exp{(-b*x)} + c*\exp{(-{(x-d)}^{2} /f^{2})} + g*\exp{(-{(x-h)}^{2} /i^{2})} + j*\exp{(-{(x-k)}^{2} /l^{2})} + \text{Offset}\)
[a, b, c, d, f, g, h, i, j, k, l, Offset]
Extended Steinhart-Hart (
Extended_Steinhart_Hart)Extended Steinhart-Hart
\(1/T = A + Bln{(R)} + C{(ln{(R)})}^{2} +D{(ln{(R)})}^{3}\)
[A, B, C, D]
Graeme Paterson Electric Motor (
GraemePatersonElectricMotor)Graeme Paterson Electric Motor
\(y = A*\exp{(-b*t)}*cos{(omega*t + phi)} + A2*\exp{(-b2*t)}\)
[A, b, omega, phi, A2, b2]
Graeme Paterson Electric Motor With Offset
\(y = A*\exp{(-b*t)}*cos{(omega*t + phi)} + A2*\exp{(-b2*t)} + \text{Offset}\)
[A, b, omega, phi, A2, b2, Offset]
Klimpel Kinetics Flotation A (
KlimpelFlotationA)Klimpel Kinetics Flotation A
\(y = a * {(1 - {(1 - \exp{(-b*x)})} / {(b*x)})}\)
[a, b]
Klimpel Kinetics Flotation A With Offset
\(y = a * {(1 - {(1 - \exp{(-b*x)})} / {(b*x)})} + \text{Offset}\)
[a, b, Offset]
Maxwell - Wiechert 1 (
MaxwellWiechert_1)Maxwell - Wiechert 1
\(y = a1*\exp{(-X/Tau1)}\)
[a1, Tau1]
Maxwell - Wiechert 1 With Offset
\(y = a1*\exp{(-X/Tau1)} + \text{Offset}\)
[a1, Tau1, Offset]
Maxwell - Wiechert 2 (
MaxwellWiechert_2)Maxwell - Wiechert 2
\(y = a1*\exp{(-X/Tau1)} + a2*\exp{(-X/Tau2)}\)
[a1, Tau1, a2, Tau2]
Maxwell - Wiechert 2 With Offset
\(y = a1*\exp{(-X/Tau1)} + a2*\exp{(-X/Tau2)} + \text{Offset}\)
[a1, Tau1, a2, Tau2, Offset]
Maxwell - Wiechert 3 (
MaxwellWiechert_3)Maxwell - Wiechert 3
\(y = a1*\exp{(-X/Tau1)} + a2*\exp{(-X/Tau2)} + a3*\exp{(-X/Tau3)}\)
[a1, Tau1, a2, Tau2, a3, Tau3]
Maxwell - Wiechert 3 With Offset
\(y = a1*\exp{(-X/Tau1)} + a2*\exp{(-X/Tau2)} + a3*\exp{(-X/Tau3)} + \text{Offset}\)
[a1, Tau1, a2, Tau2, a3, Tau3, Offset]
Maxwell - Wiechert 4 (
MaxwellWiechert_4)Maxwell - Wiechert 4
\(y = a1*\exp{(-X/Tau1)} + a2*\exp{(-X/Tau2)} + a3*\exp{(-X/Tau3)} +a4*\exp{(-X/Tau4)}\)
[a1, Tau1, a2, Tau2, a3, Tau3, a4, Tau4]
Maxwell - Wiechert 4 With Offset
\(y = a1*\exp{(-X/Tau1)} + a2*\exp{(-X/Tau2)} + a3*\exp{(-X/Tau3)} +a4*\exp{(-X/Tau4)} + \text{Offset}\)
[a1, Tau1, a2, Tau2, a3, Tau3, a4, Tau4, Offset]
Modified Arps Well Production (
ModifiedArpsWellProduction)Modified Arps Well Production
\(y = {(qi\_x/{({(1.0-b\_x)}*Di\_x)})} *{(1.0-{({(1.0+b\_x*Di\_x*x)}^{(1.0-1.0/b\_x)})})}\)
[qi_x, b_x, Di_x]
Modified Arps Well Production With Offset
\(y = {(qi\_x/{({(1.0-b\_x)}*Di\_x)})} *{(1.0-{({(1.0+b\_x*Di\_x*x)}^{(1.0-1.0/b\_x)})})} + \text{Offset}\)
[qi_x, b_x, Di_x, Offset]
Ramberg-Osgood (
Ramberg_Osgood)Ramberg-Osgood
\(y = {(Stress / Youngs\_Modulus)} + {(Stress/K)}^{{(1.0/n)}}\)
[Youngs_Modulus, K, n]
Ramberg-Osgood With Offset
\(y = {(Stress / Youngs\_Modulus)} + {(Stress/K)}^{{(1.0/n)}} +\text{Offset}\)
[Youngs_Modulus, K, n, Offset]
Reciprocal Extended Steinhart-Hart (
Reciprocal_Extended_Steinhart_Hart)Reciprocal Extended Steinhart-Hart
\(T = 1.0 / {(A + Bln{(R)} + C{(ln{(R)})}^{2} +D{(ln{(R)})}^{3})}\)
[A, B, C, D]
Reciprocal Extended Steinhart-Hart With Offset
\(T = 1.0 / {(A + Bln{(R)} + C{(ln{(R)})}^{2} +D{(ln{(R)})}^{3})} + \text{Offset}\)
[A, B, C, D, Offset]
Reciprocal Steinhart-Hart (
Reciprocal_Steinhart_Hart)Reciprocal Steinhart-Hart
\(T = 1.0 / {(A + Bln{(R)} + C{(ln{(R)})}^{3})}\)
[A, B, C]
Reciprocal Steinhart-Hart With Offset
\(T = 1.0 / {(A + Bln{(R)} + C{(ln{(R)})}^{3})} + \text{Offset}\)
[A, B, C, Offset]
Sellmeier Optical (
SellmeierOptical)Sellmeier Optical
\(n^{2}{(x)} = 1 + {(B1x^{2})}/{(x^{2}-C1)} + {(B2x^{2})}/{(x^{2}-C2)} + {(B3x^{2})}/{(x^{2}-C3)}\)
[B1, C1, B2, C2, B3, C3]
Sellmeier Optical With Offset
\(n^{2}{(x)} = 1 + {(B1x^{2})}/{(x^{2}-C1)} + {(B2x^{2})}/{(x^{2}-C2)} + {(B3x^{2})}/{(x^{2}-C3)} + \text{Offset}\)
[B1, C1, B2, C2, B3, C3, Offset]
Sellmeier Optical Square Root (
SellmeierOpticalSqrt)Sellmeier Optical Square Root
\(n = {(1 + {(B1 x^{2})}/{(x^{2}-C1)} + {(B2x^{2})}/{(x^{2}-C2)} + {(B3x^{2})}/{(x^{2}-C3)})}^{0.5}\)
[B1, C1, B2, C2, B3, C3]
Sellmeier Optical Square Root With Offset
\(n = {(1 + {(B1 x^{2})}/{(x^{2}-C1)} + {(B2x^{2})}/{(x^{2}-C2)} + {(B3x^{2})}/{(x^{2}-C3)})}^{0.5} +\text{Offset}\)
[B1, C1, B2, C2, B3, C3, Offset]
Steinhart-Hart (
Steinhart_Hart)Steinhart-Hart
\(1/T = A + Bln{(R)} + C{(ln{(R)})}^{3}\)
[A, B, C]
VanDeemter Chromatography (
VanDeemterChromatography)VanDeemter Chromatography
\(y = a + b/x + cx\)
[a, b, c]
Exponential¶
Asymptotic Exponential A (
AsymptoticExponentialA)Asymptotic Exponential A
\(y = 1.0 - a^{x}\)
[a]
Asymptotic Exponential A With Offset
\(y = 1.0 - a^{x} + \text{Offset}\)
[a, Offset]
Asymptotic Exponential A Transform (
AsymptoticExponentialA_Transform)Asymptotic Exponential A Transform
\(y = 1.0 - a^{bx + c}\)
[a, b, c]
Asymptotic Exponential A Transform With Offset
\(y = 1.0 - a^{bx + c} + \text{Offset}\)
[a, b, c, Offset]
Asymptotic Exponential B (
AsymptoticExponentialB)Asymptotic Exponential B
\(y = a * {(1.0 - \exp{(bx)})}\)
[a, b]
Asymptotic Exponential B With Offset
\(y = a * {(1.0 - \exp{(bx)})} + \text{Offset}\)
[a, b, Offset]
Bruno Torremans Quadruple Exponential (
BrunoTorremansQuadrupleExponential)Bruno Torremans Quadruple Exponential
\(y = \text{Offset} - R1 * \exp{(-x/T1)} + R2 * \exp{(-x/T2)} + R3 * \exp{(-x/T3)} + R4 *\exp{(-x/T4)}\)
[R1, R2, R3, R4, T1, T2, T3, T4, Offset]
Double Asymptotic Exponential B (
DoubleAsymptoticExponentialB)Double Asymptotic Exponential B
\(y = a * {(1.0 - \exp{(bx)})} + c * {(1.0 - \exp{(dx)})}\)
[a, b, c, d]
Double Asymptotic Exponential B With Offset
\(y = a * {(1.0 - \exp{(bx)})} + c * {(1.0 - \exp{(dx)})} + \text{Offset}\)
[a, b, c, d, Offset]
Double Exponential (
DoubleExponential)Double Exponential
\(y = a * \exp{(bx)} + c * \exp{(dx)}\)
[a, b, c, d]
Double Exponential With Offset
\(y = a * \exp{(bx)} + c * \exp{(dx)} + \text{Offset}\)
[a, b, c, d, Offset]
Exponential (
Exponential)Exponential
\(y = a * \exp{(bx)}\)
[a, b]
Exponential With Offset
\(y = a * \exp{(bx)} + \text{Offset}\)
[a, b, Offset]
Hocket-Sherby (
Hocket_Sherby)Hocket-Sherby
\(y = b - {(b-a)} * \exp{(-c * {(x^{d})})}\)
[a, b, c, d]
Hoerl (
Hoerl)Hoerl
\(y = x^{a} * \exp{(x)}\)
[a]
Hoerl With Offset
\(y = x^{a} * \exp{(x)} + \text{Offset}\)
[a, Offset]
Hoerl Transform (
Hoerl_Transform)Hoerl Transform
\(y = {(bx + c)}^{a} * \exp{(bx + c)}\)
[a, b, c]
Hoerl Transform With Offset
\(y = {(bx + c)}^{a} * \exp{(bx + c)} + \text{Offset}\)
[a, b, c, Offset]
Inverted Exponential (
InvExponential)Inverted Exponential
\(y = a * \exp{(b/x)}\)
[a, b]
Inverted Exponential With Offset
\(y = a * \exp{(b/x)} + \text{Offset}\)
[a, b, Offset]
Inverted Offset Exponential (
InvertedOffsetExponential)Inverted Offset Exponential
\(y = a * \exp{(b/{(x+c)})}\)
[a, b, c]
Inverted Offset Exponential With Offset
\(y = a * \exp{(b/{(x+c)})} + \text{Offset}\)
[a, b, c, Offset]
Jonathan Litz Custom Exponential (
JonathanLitzCustomExponential)Jonathan Litz Custom Exponential
\(y = a + b * x + c * \exp{(-d * x)} - c * x * \exp{(-d * x)}\)
[a, b, c, d]
Lake Nganoke Samples Exponential (
LakeNganokeSamplesExponential)Lake Nganoke Samples Exponential
\(y = C/{(1.0 + \exp{({(x-A)}/B)})} + D * \exp{({(x-B)}/E)}\)
[A, B, C, D, E]
Lake Nganoke Samples Exponential With Offset
\(y = C/{(1.0 + \exp{({(x-A)}/B)})} + D * \exp{({(x-B)}/E)} + \text{Offset}\)
[A, B, C, D, E, Offset]
Offset Exponential (
OffsetExponential)Offset Exponential
\(y = a * \exp{(bx + c)}\)
[a, b, c]
Offset Exponential With Offset
\(y = a * \exp{(bx + c)} + \text{Offset}\)
[a, b, c, Offset]
Scaled Exponential (
ScaledExponential)Scaled Exponential
\(y = a * \exp{(x)}\)
[a]
Scaled Exponential With Offset
\(y = a * \exp{(x)} + \text{Offset}\)
[a, Offset]
Shifted Exponential (
ShiftedExponential)Shifted Exponential
\(y = a * \exp{(x + b)}\)
[a, b]
Shifted Exponential With Offset
\(y = a * \exp{(x + b)} + \text{Offset}\)
[a, b, Offset]
Simple Exponential (
SimpleExponential)Simple Exponential
\(y = a^{x}\)
[a]
Simple Exponential With Offset
\(y = a^{x} + \text{Offset}\)
[a, Offset]
Steve Battison Exponential A (
SteveBattisonExponentialA)Steve Battison Exponential A
\(y = \exp{({(a + bx)} / {(c + dx)})}\)
[a, b, c, d]
Steve Battison Exponential A With Offset
\(y = \exp{({(a + bx)} / {(c + dx)})} + \text{Offset}\)
[a, b, c, d, Offset]
Steve Battison Exponential B (
SteveBattisonExponentialB)Steve Battison Exponential B
\(y = a * \exp{({(b + cx)} / {(d + fx)})}\)
[a, b, c, d, f]
Steve Battison Exponential B With Offset
\(y = a * \exp{({(b + cx)} / {(d + fx)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Stirling (
Stirling)Stirling
\(y = a * {(\exp{(bx)} - 1.0)} / b\)
[a, b]
Stirling With Offset
\(y = a * {(\exp{(bx)} - 1.0)} / b + \text{Offset}\)
[a, b, Offset]
Triple Exponential (
TripleExponential)Triple Exponential
\(y = a * \exp{(bx)} + c * \exp{(dx)} + f * \exp{(gx)}\)
[a, b, c, d, f, g]
Triple Exponential With Offset
\(y = a * \exp{(bx)} + c * \exp{(dx)} + f * \exp{(gx)} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Standard Vapor Pressure (
VaporPressure)Standard Vapor Pressure
\(y = \exp{(a + {(b/x)} + c*ln{(x)})}\)
[a, b, c]
Standard Vapor Pressure With Offset
\(y = \exp{(a + {(b/x)} + c*ln{(x)})} + \text{Offset}\)
[a, b, c, Offset]
FourierSeries¶
1 Term (Scaled X) (
ScaledX_1Term)1 Term (Scaled X)
\(y = a0 + a1*sin{(c1*x)}+b1*cos{(c1*x)}\)
[a0, a1, b1, c1]
1 Term Standard (
Standard_1Term)1 Term Standard
\(y = a0 + a1*sin{(x)}+b1*cos{(x)}\)
[a0, a1, b1]
2 Term Standard (
Standard_2Term)2 Term Standard
\(y = a0 + a1*sin{(x)}+b1*cos{(x)} + a2*sin{(2x)}+b2*cos{(2x)}\)
[a0, a1, b1, a2, b2]
3 Term Standard (
Standard_3Term)3 Term Standard
\(y = a0 + a1*sin{(x)}+b1*cos{(x)} + a2*sin{(2x)}+b2*cos{(2x)} +a3*sin{(3x)}+b3*cos{(3x)}\)
[a0, a1, b1, a2, b2, a3, b3]
4 Term Standard (
Standard_4Term)4 Term Standard
\(y = a0 + a1*sin{(x)}+b1*cos{(x)} + a2*sin{(2x)}+b2*cos{(2x)} +a3*sin{(3x)}+b3*cos{(3x)} + a4*sin{(4x)}+b4*cos{(4x)}\)
[a0, a1, b1, a2, b2, a3, b3, a4, b4]
LegendrePolynomial¶
Legendre Polynomial G - Eighth Degree (
EighthDegreeLegendrePolynomial)Legendre Polynomial G - Eighth Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4} + gP_{5} + hP_{6} +iP_{7} + jP_{8}\)
[a, b, c, d, f, g, h, i, j]
Legendre Polynomial D - Fifth Degree (
FifthDegreeLegendrePolynomial)Legendre Polynomial D - Fifth Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4} + gP_{5}\)
[a, b, c, d, f, g]
Legendre Polynomial C - Fourth Degree (
FourthDegreeLegendrePolynomial)Legendre Polynomial C - Fourth Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4}\)
[a, b, c, d, f]
Gamma Ray Angular Distribution (degrees) A (
GammaRayAngularDistributionDegreesA)Gamma Ray Angular Distribution (degrees) A
\(y = A0 + A2 * P_{2}{(cos{(theta)})}\)
[A0, A2]
Gamma Ray Angular Distribution (degrees) B (
GammaRayAngularDistributionDegreesB)Gamma Ray Angular Distribution (degrees) B
\(y = A0 + A2 * P_{2}{(cos{(theta)})} + A4 *P_{4}{(cos{(theta)})}\)
[A0, A2, A4]
Gamma Ray Angular Distribution (radians) A (
GammaRayAngularDistributionRadiansA)Gamma Ray Angular Distribution (radians) A
\(y = A0 + A2 * P_{2}{(cos{(theta)})}\)
[A0, A2]
Gamma Ray Angular Distribution (radians) B (
GammaRayAngularDistributionRadiansB)Gamma Ray Angular Distribution (radians) B
\(y = A0 + A2 * P_{2}{(cos{(theta)})} + A4 *P_{4}{(cos{(theta)})}\)
[A0, A2, A4]
Legendre Polynomial H - Ninth Degree (
NinthDegreeLegendrePolynomial)Legendre Polynomial H - Ninth Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4} + gP_{5} + hP_{6} +iP_{7} + jP_{8} + kP_{9}\)
[a, b, c, d, f, g, h, i, j, k]
Legendre Polynomial A - Second Degree (
SecondDegreeLegendrePolynomial)Legendre Polynomial A - Second Degree
\(y = a + bx + cP_{2}\)
[a, b, c]
Legendre Polynomial F - Seventh Degree (
SeventhDegreeLegendrePolynomial)Legendre Polynomial F - Seventh Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4} + gP_{5} + hP_{6} +iP_{7}\)
[a, b, c, d, f, g, h, i]
Legendre Polynomial E - Sixth Degree (
SixthDegreeLegendrePolynomial)Legendre Polynomial E - Sixth Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4} + gP_{5} + hP_{6}\)
[a, b, c, d, f, g, h]
Legendre Polynomial I - Tenth Degree (
TenthDegreeLegendrePolynomial)Legendre Polynomial I - Tenth Degree
\(y = a + bx + cP_{2} + dP_{3} +fP_{4} + gP_{5} + hP_{6} +iP_{7} + jP_{8} + kP_{9} +mP_{10}\)
[a, b, c, d, f, g, h, i, j, k, m]
Legendre Polynomial B - Third Degree (
ThirdDegreeLegendrePolynomial)Legendre Polynomial B - Third Degree
\(y = a + bx + cP_{2} + dP_{3}\)
[a, b, c, d]
Logarithmic¶
Base 10 Logarithmic (
Base10Logarithmic)Base 10 Logarithmic
\(y = a + b*log_{10}{(x)}\)
[a, b]
Bradley (
Bradley)Bradley
\(y = a * ln{(-b * ln{(x)})}\)
[a, b]
Bradley With Offset
\(y = a * ln{(-b * ln{(x)})} + \text{Offset}\)
[a, b, Offset]
Bradley Transform (
BradleyTransform)Bradley Transform
\(y = a * ln{(-b * ln{(cx + d)})}\)
[a, b, c, d]
Bradley Transform With Offset
\(y = a * ln{(-b * ln{(cx + d)})} + \text{Offset}\)
[a, b, c, d, Offset]
Crystal Resonator Ageing MIL-PRF-55310E (
CrystalResonatorAgeing)Crystal Resonator Ageing MIL-PRF-55310E
\(y = A{(ln{(Bt + 1)})} + f0\)
[A, B, f0]
Cubic Logarithmic (
CubicLogarithmic)Cubic Logarithmic
\(y = a + b*ln{(x)} + c*ln{(x)}^{2} +d*ln{(x)}^{3}\)
[a, b, c, d]
Cubic Logarithmic Scaled (
CubicLogarithmicScaled)Cubic Logarithmic Scaled
\(y = a + b*ln{(f*x)} + c*ln{(f*x)}^{2} +d*ln{(f*x)}^{3}\)
[a, b, c, d, f]
Cubic Logarithmic Transform (
CubicLogarithmicTransform)Cubic Logarithmic Transform
\(y = a + b*ln{(f*x+g)} + c*ln{(f*x+g)}^{2} +d*ln{(f*x+g)}^{3}\)
[a, b, c, d, f, g]
Linear Logarithmic (
LinearLogarithmic)Linear Logarithmic
\(y = a + b*ln{(x)}\)
[a, b]
Linear Logarithmic Scaled (
LinearLogarithmicScaled)Linear Logarithmic Scaled
\(y = a + b*ln{(cx)}\)
[a, b, c]
Linear Logarithmic Shifted (
LinearLogarithmicShifted)Linear Logarithmic Shifted
\(y = a + b*ln{(c+x)}\)
[a, b, c]
Linear Logarithmic Transform (
LinearLogarithmicTransform)Linear Logarithmic Transform
\(y = a + b*ln{(cx+d)}\)
[a, b, c, d]
Quadratic Logarithmic (
QuadraticLogarithmic)Quadratic Logarithmic
\(y = a + b*ln{(x)} + c*ln{(x)}^{2}\)
[a, b, c]
Quadratic Logarithmic Scaled (
QuadraticLogarithmicScaled)Quadratic Logarithmic Scaled
\(y = a + b*ln{(dx)} + c*ln{(dx)}^{2}\)
[a, b, c, d]
Quadratic Logarithmic Transform (
QuadraticLogarithmicTransform)Quadratic Logarithmic Transform
\(y = a + b*ln{(dx+f)} + c*ln{(dx+f)}^{2}\)
[a, b, c, d, f]
Quartic Logarithmic (
QuarticLogarithmic)Quartic Logarithmic
\(y = a + b*ln{(x)} + c*ln{(x)}^{2} +d*ln{(x)}^{3} + f*ln{(x)}^{4}\)
[a, b, c, d, f]
Quartic Logarithmic Scaled (
QuarticLogarithmicScaled)Quartic Logarithmic Scaled
\(y = a + b*ln{(h*x)} + c*ln{(h*x)}^{2} +d*ln{(h*x)}^{3} + f*ln{(h*x)}^{4}\)
[a, b, c, d, f, g]
Quartic Logarithmic Transform (
QuarticLogarithmicTransform)Quartic Logarithmic Transform
\(y = a + b*ln{(g*x+h)} + c*ln{(g*x+h)}^{2} +d*ln{(g*x+h)}^{3} + f*ln{(g*x+h)}^{4}\)
[a, b, c, d, f, g, h]
Quintic Logarithmic (
QuinticLogarithmic)Quintic Logarithmic
\(y = a + b*ln{(x)} + c*ln{(x)}^{2} +d*ln{(x)}^{3} + f*ln{(x)}^{4} +g*ln{(x)}^{5}\)
[a, b, c, d, f, g]
Quintic Logarithmic Scaled (
QuinticLogarithmicScaled)Quintic Logarithmic Scaled
\(y = a + b*ln{(h*x)} + c*ln{(h*x)}^{2} +d*ln{(h*x)}^{3} + f*ln{(h*x)}^{4} +g*ln{(h*x)}^{4}\)
[a, b, c, d, f, g, h]
Quintic Logarithmic Transform (
QuinticLogarithmicTransform)Quintic Logarithmic Transform
\(y = a + b*ln{(h*x+i)} + c*ln{(h*x+i)}^{2} +d*ln{(h*x+i)}^{3} + f*ln{(h*x+i)}^{4} +g*ln{(h*x+i)}^{5}\)
[a, b, c, d, f, g, h, i]
Miscellaneous¶
Arrhenius Rate Constant Law (
ArrheniusRateConstantLaw)Arrhenius Rate Constant Law
\(y = a * \exp{(-b/x)}\)
[a, b]
Arrhenius Rate Constant Law With Offset
\(y = a * \exp{(-b/x)} + \text{Offset}\)
[a, b, Offset]
Arrhenius Rate Constant Law Stretched (
ArrheniusRateConstantLawStretched)Arrhenius Rate Constant Law Stretched
\(y = a * \exp{(-pow{(b/x, c)})}\)
[a, b, c]
Arrhenius Rate Constant Law Stretched With Offset
\(y = a * \exp{(-pow{(b/x, c)})} + \text{Offset}\)
[a, b, c, Offset]
Bleasdale-Nelder (
Bleasdale_Nelder)Bleasdale-Nelder
\(y = {(a + bx)}^{-c}\)
[a, b, c]
Bleasdale-Nelder With Offset
\(y = {(a + bx)}^{-c} + \text{Offset}\)
[a, b, c, Offset]
Catenary (
Catenary)Catenary
\(y = a * cosh{(x / a)}\)
[a]
Catenary With Offset
\(y = a * cosh{(x / a)} + \text{Offset}\)
[a, Offset]
Catenary Transform (
CatenaryTransform)Catenary Transform
\(y = a * cosh{({(bx + c)} / a)}\)
[a, b, c]
Catenary Transform With Offset
\(y = a * cosh{({(bx + c)} / a)} + \text{Offset}\)
[a, b, c, Offset]
Cissoid Of Diocles (
CissoidOfDiocles)Cissoid Of Diocles
\(y = a{(x^{3} / {(2b-x)})}^{0.5}\)
[a, b]
Cissoid Of Diocles With Offset
\(y = a{(x^{3} / {(2b-x)})}^{0.5} + \text{Offset}\)
[a, b, Offset]
Cissoid Of Diocles Transform (
CissoidOfDioclesTransform)Cissoid Of Diocles Transform
\(y = a{({(x*c-d)}^{3} / {(2b-{(x*c-d)})})}^{0.5}\)
[a, b, c, d]
Cissoid Of Diocles Transform With Offset
\(y = a{({(x*c-d)}^{3} / {(2b-{(x*c-d)})})}^{0.5} +\text{Offset}\)
[a, b, c, d, Offset]
Combined Power And Exponential (
CombinedPowerAndExponential)Combined Power And Exponential
\(y = ax^{b} * \exp{(cx)}\)
[a, b, c]
Combined Power And Exponential With Offset
\(y = ax^{b} * \exp{(cx)} + \text{Offset}\)
[a, b, c, Offset]
David Rodbard NIH (
DavidRodbardNIH)David Rodbard NIH
\(y = d + {(a - d)} / {(1.0 + {(x/c)}^{b})}\)
[a, b, c, d]
Double Langmuir Probe Characteristic (
DoubleLangmuirProbeCharacteristic)Double Langmuir Probe Characteristic
\(y = a * tanh{(bx+c)}\)
[a, b, c]
Double Langmuir Probe Characteristic With Offset
\(y = a * tanh{(bx+c)} + \text{Offset}\)
[a, b, c, Offset]
Double Rectangular Hyperbola A (
DoubleRectangularHyperbolaA)Double Rectangular Hyperbola A
\(y = ax/{(b+x)} + cx/{(d+x)}\)
[a, b, c, d]
Double Rectangular Hyperbola A With Offset
\(y = ax/{(b+x)} + cx/{(d+x)} + \text{Offset}\)
[a, b, c, d, Offset]
Double Rectangular Hyperbola B (
DoubleRectangularHyperbolaB)Double Rectangular Hyperbola B
\(y = ax/{(b+x)} + cx/{(d+x)} + fx\)
[a, b, c, d, f]
Double Rectangular Hyperbola B With Offset
\(y = ax/{(b+x)} + cx/{(d+x)} + fx + \text{Offset}\)
[a, b, c, d, f, Offset]
Figure Eight Curve (
FigureEight)Figure Eight Curve
\(y = a{(x^{2} -{(x^{4}/b^{2})})}^{0.5}\)
[a, b]
Figure Eight Curve With Offset
\(y = a{(x^{2} -{(x^{4}/b^{2})})}^{0.5} +\text{Offset}\)
[a, b, Offset]
Figure Eight Curve Transform (
FigureEightTransform)Figure Eight Curve Transform
\(y = a{({(cx+d)}^{2} -{({(cx+d)}^{4}/b^{2})})}^{0.5}\)
[a, b, c, d]
Figure Eight Curve Transform With Offset
\(y = a{({(cx+d)}^{2} -{({(cx+d)}^{4}/b^{2})})}^{0.5} +\text{Offset}\)
[a, b, c, d, Offset]
Gunary (
Gunary)Gunary
\(y = x / {(a + bx + cx^{0.5})}\)
[a, b, c]
Gunary With Offset
\(y = x / {(a + bx + cx^{0.5})} + \text{Offset}\)
[a, b, c, Offset]
Hyperbola A Modified (
HyperbolaA_Modified)Hyperbola A Modified
\(y = ax/{(1+bx)}\)
[a, b]
Hyperbola A Modified With Offset
\(y = ax/{(1+bx)} + \text{Offset}\)
[a, b, Offset]
Hyperbola B Modified (
HyperbolaB_Modified)Hyperbola B Modified
\(y = x/{(a+bx)}\)
[a, b]
Hyperbola B Modified With Offset
\(y = x/{(a+bx)} + \text{Offset}\)
[a, b, Offset]
Hyperbolic Decay (
HyperbolicDecay)Hyperbolic Decay
\(y = ab/{(b+x)}\)
[a, b]
Hyperbolic Decay With Offset
\(y = ab/{(b+x)} + \text{Offset}\)
[a, b, Offset]
Karplus NMR Spectroscopy (
KarplusNMRSpectroscopy)Karplus NMR Spectroscopy
\(J{(da)} = Acos^{2}{(da)} + Bcos{(da)} + C\)
[A, B, C]
Karplus NMR Spectroscopy Scaled (
KarplusNMRSpectroscopyScaled)Karplus NMR Spectroscopy Scaled
\(J{(da)} = Acos^{2}{(s * da)} + Bcos{(s * da)} + C\)
[A, B, C, s]
Lame’s Cubic (
LamesCubic)Lame’s Cubic
\(y = {(a^{3} - x^{3})}^{1/3}\)
[a]
Lame’s Cubic With Offset
\(y = {(a^{3} - x^{3})}^{1/3} +\text{Offset}\)
[a, Offset]
Lame’s Cubic Transform (
LamesCubicTransform)Lame’s Cubic Transform
\(y = {(a^{3} - {(bx +c)}^{3})}^{1/3}\)
[a, b, c]
Lame’s Cubic Transform With Offset
\(y = {(a^{3} - {(bx +c)}^{3})}^{1/3} + \text{Offset}\)
[a, b, c, Offset]
Miscellaneous 1 (
Misc1)Miscellaneous 1
\(y = 1.0 + a{(1.0 - \exp{(bx)})}\)
[a, b]
Miscellaneous 1 With Offset
\(y = 1.0 + a{(1.0 - \exp{(bx)})} + \text{Offset}\)
[a, b, Offset]
Morse Potential (
MorsePotential)Morse Potential
\(V = D*{(\exp{(-2*m*{(x-u)})} - 2*\exp{(-m*{(x-u)})})} + offset\)
[D, m, u, offset]
Nelson-Siegel (
NelsonSiegel)Nelson-Siegel
\(y{(m)} = B0 + B1*{({(1-\exp{(-m/t)})}/{(m/t)})} + B2*{({({(1-\exp{(-m/t)})}/{(m/t)})} -\exp{(-m/t)})}\)
[B0, B1, B2, t]
Nelson-Siegel-Svensson (
NelsonSiegelSvensson)Nelson-Siegel-Svensson
\(y{(m)} = B0 + B1*{({(1-\exp{(-m/t)})}/{(m/t)})} + B2*{({({(1-\exp{(-m/t)})}/{(m/t)})} -\exp{(-m/t)})} + B3*{({({(1-\exp{(-m/t2)})}/{(m/t2)})} - \exp{(-m/t2)})}\)
[B0, B1, B2, B3, t, t2]
Niele’s Semi-cubical Parabola (
NielesSemicubicalParabola)Niele’s Semi-cubical Parabola
\(y = {(ax^{2})}^{1.0/3.0}\)
[a]
Niele’s Semi-cubical Parabola With Offset
\(y = {(ax^{2})}^{1.0/3.0} + \text{Offset}\)
[a, Offset]
Niele’s Semi-cubical Parabola Transform (
NielesSemicubicalParabolaTransform)Niele’s Semi-cubical Parabola Transform
\(y = {(a{(b*x+c)}^{2})}^{1.0/3.0}\)
[a, b, c]
Niele’s Semi-cubical Parabola Transform With Offset
\(y = {(a{(b*x+c)}^{2})}^{1.0/3.0} + \text{Offset}\)
[a, b, c, Offset]
Pareto A (
ParetoA)Pareto A
\(y = 1 - x^{-a}\)
[a]
Pareto A With Offset
\(y = 1 - x^{-a} + \text{Offset}\)
[a, Offset]
Pareto B (
ParetoB)Pareto B
\(y = a{(1 - x^{-b})}\)
[a, b]
Pareto B With Offset
\(y = a{(1 - x^{-b})} + \text{Offset}\)
[a, b, Offset]
Pareto C (
ParetoC)Pareto C
\(y = 1.0 - {(1.0 / {(1 + ax)}^{b})}\)
[a, b]
Pareto C With Offset
\(y = 1.0 - {(1.0 / {(1 + ax)}^{b})} + \text{Offset}\)
[a, b, Offset]
Pareto D (
ParetoD)Pareto D
\(y = 1.0 - {(1.0 / x^{a})}\)
[a]
Pareto D With Offset
\(y = 1.0 - {(1.0 / x^{a})} + \text{Offset}\)
[a, Offset]
Pear-shaped Quartic (
PearShapedQuartic)Pear-shaped Quartic
\(y = a{(x^{3}{(b-x)} /c^{2})}^{0.5}\)
[a, b, c]
Pear-shaped Quartic With Offset
\(y = a{(x^{3}{(b-x)} /c^{2})}^{0.5} + \text{Offset}\)
[a, b, c, Offset]
Pear-shaped Quartic Transform (
PearShapedQuarticTransform)Pear-shaped Quartic Transform
\(y = a{({(dx+f)}^{3}{(b-{(dx+f)})} /c^{2})}^{0.5}\)
[a, b, c, d, f]
Pear-shaped Quartic Transform With Offset
\(y = a{({(dx+f)}^{3}{(b-{(dx+f)})} /c^{2})}^{0.5} + \text{Offset}\)
[a, b, c, d, f, Offset]
Physicist Peter’s Custom Equation (
PhysicistPeterCustomEquation)Physicist Peter’s Custom Equation
\(y = A + B*{(X-C)} + 0.5*G*{(X-C)}^2\)
[A, B, C, G]
Physicist Peter’s Pendulum Traversal (
PhysicistPeterPendulumTraversal)Physicist Peter’s Pendulum Traversal
\(y = a*{(x + b)}^{1/2}\)
[a, b]
Physicist Peter’s Pendulum Traversal With Offset
\(y = a*{(x + b)}^{1/2} + \text{Offset}\)
[a, b, Offset]
Polytrope (
Polytrope)Polytrope
\(y = a / x^{b}\)
[a, b]
Polytrope With Offset
\(y = a / x^{b} + \text{Offset}\)
[a, b, Offset]
Polytrope Transform (
PolytropeTransform)Polytrope Transform
\(y = a / {(cx + d)}^{b}\)
[a, b, c, d]
Polytrope Transform With Offset
\(y = a / {(cx + d)}^{b} + \text{Offset}\)
[a, b, c, d, Offset]
Pursuit Curve (
PursuitCurve)Pursuit Curve
\(y = ax^{2} - log{(x)}\)
[a]
Pursuit Curve With Offset
\(y = ax^{2} - log{(x)} + \text{Offset}\)
[a, Offset]
Pursuit Curve Transform (
PursuitCurve_Transform)Pursuit Curve Transform
\(y = a{(bx + c)}^{2} - log{(bx + c)}\)
[a, b, c]
Pursuit Curve Transform With Offset
\(y = a{(bx + c)}^{2} - log{(bx + c)} + \text{Offset}\)
[a, b, c, Offset]
Rectangular Hyperbola A (
RectangularHyperbolaA)Rectangular Hyperbola A
\(y = ax/{(b+x)}\)
[a, b]
Rectangular Hyperbola A With Offset
\(y = ax/{(b+x)} + \text{Offset}\)
[a, b, Offset]
Rectangular Hyperbola B (
RectangularHyperbolaB)Rectangular Hyperbola B
\(y = ax/{(b+x)} + cx\)
[a, b, c]
Rectangular Hyperbola B With Offset
\(y = ax/{(b+x)} + cx + \text{Offset}\)
[a, b, c, Offset]
Serpentine (
Serpentine)Serpentine
\(y = ax / {(1.0 + bx^{2})}\)
[a, b]
Serpentine With Offset
\(y = ax / {(1.0 + bx^{2})} + \text{Offset}\)
[a, b, Offset]
Shifted Reciprocal (
ShiftedReciprocal)Shifted Reciprocal
\(y = 1.0 / {(a - x)}\)
[a]
Shifted Reciprocal With Offset
\(y = 1.0 / {(a - x)} + \text{Offset}\)
[a, Offset]
Square Modified (
Square_Modified)Square Modified
\(y = x^{2} - ax\)
[a]
Square Modified With Offset
\(y = x^{2} - ax + \text{Offset}\)
[a, Offset]
Square Modified Transform (
Square_Modified_Transform)Square Modified Transform
\(y = {(bx + c)}^{2} - a{(bx + c)}\)
[a, b, c]
Square Modified Transform With Offset
\(y = {(bx + c)}^{2} - a{(bx + c)} + \text{Offset}\)
[a, b, c, Offset]
Timothy Strobel’s Custom Equation (
TimothyStrobelCustomEquation)Timothy Strobel’s Custom Equation
\(y ={(A-B*X^C)}*{(1-{(0.5+{(arctan{({(X-D)}/E)})}/pi)})}+{(F-G*X^H)}*{(0.5+{(arctan{({(X-D)}/E)})}/pi)}\)
[A, B, C, D, E, F, G, H]
Timothy Strobel’s Custom Equation With Offset
\(y ={(A-B*X^C)}*{(1-{(0.5+{(arctan{({(X-D)}/E)})}/pi)})}+{(F-G*X^H)}*{(0.5+{(arctan{({(X-D)}/E)})}/pi)}+ \text{Offset}\)
[A, B, C, D, E, F, G, H, Offset]
Transition State Rate Constant Law (
TransitionStateRateConstantLaw)Transition State Rate Constant Law
\(y = ax^{b} * \exp{(-c/x)}\)
[a, b, c]
Transition State Rate Constant Law With Offset
\(y = ax^{b} * \exp{(-c/x)} + \text{Offset}\)
[a, b, c, Offset]
Trisectrix Of Maclaurin (
TrisectrixOfMaclaurin)Trisectrix Of Maclaurin
\(y = a{(x^{2}{(3b-x)} / {(b+x)})}^{0.5}\)
[a, b]
Trisectrix Of Maclaurin With Offset
\(y = a{(x^{2}{(3b-x)} / {(b+x)})}^{0.5} + \text{Offset}\)
[a, b, Offset]
Trisectrix Of Maclaurin Transform (
TrisectrixOfMaclaurinTransform)Trisectrix Of Maclaurin Transform
\(y = a{({(cx+d)}^{2}{(3b-{(cx+d)})} /{(b+{(cx+d)})})}^{0.5}\)
[a, b, c, d]
Trisectrix Of Maclaurin Transform With Offset
\(y = a{({(cx+d)}^{2}{(3b-{(cx+d)})} /{(b+{(cx+d)})})}^{0.5} + \text{Offset}\)
[a, b, c, d, Offset]
Witch Of Maria Agnesi A (
WitchOfAgnesiA)Witch Of Maria Agnesi A
\(y = 8a^{3} / {(x^{2} +4a^{2})}\)
[a]
Witch Of Maria Agnesi A With Offset
\(y = 8a^{3} / {(x^{2} +4a^{2})} + \text{Offset}\)
[a, Offset]
Witch Of Maria Agnesi B (
WitchOfAgnesiB)Witch Of Maria Agnesi B
\(y = a^{3} / {(x^{2} + a^{2})}\)
[a]
Witch Of Maria Agnesi B With Offset
\(y = a^{3} / {(x^{2} + a^{2})}+ \text{Offset}\)
[a, Offset]
Witch Of Maria Agnesi C (
WitchOfAgnesiC)Witch Of Maria Agnesi C
\(y = a^{3} / {({(x * b + c)}^{2} +a^{2})}\)
[a, b, c]
Witch Of Maria Agnesi C With Offset
\(y = a^{3} / {({(x * b + c)}^{2} +a^{2})} + \text{Offset}\)
[a, b, c, Offset]
NIST¶
NIST Bennett5 (
NIST_Bennett5)NIST Bennett5
\(y = a * {(b+x)}^{-1/c}\)
[a, b, c]
NIST Bennett5 With Offset
\(y = a * {(b+x)}^{-1/c} + \text{Offset}\)
[a, b, c, Offset]
NIST BoxBOD (
NIST_BoxBOD)NIST BoxBOD
\(y = a * {(1.0-\exp{(-b*x)})}\)
[a, b]
NIST BoxBOD With Offset
\(y = a * {(1.0-\exp{(-b*x)})} + \text{Offset}\)
[a, b, Offset]
NIST Chwirut (
NIST_Chwirut)NIST Chwirut
\(y = \exp{(-a*x)} / {(b + c*x)}\)
[a, b, c]
NIST Chwirut With Offset
\(y = \exp{(-a*x)} / {(b + c*x)} + \text{Offset}\)
[a, b, c, Offset]
NIST DanWood (
NIST_DanWood)NIST DanWood
\(y = a*x^{b}\)
[a, b]
NIST DanWood With Offset
\(y = a*x^{b} + \text{Offset}\)
[a, b, Offset]
NIST ENSO (
NIST_ENSO)NIST ENSO
\(y = a + b*cos{(2*pi*x/12)} + c*sin{(2*pi*x/12)} + f*cos{(2*pi*x/d)} +g*sin{(2*pi*x/d)} + i*cos{(2*pi*x/h)} + j*sin{(2*pi*x/h)}\)
[a, b, c, d, f, g, h, i, j]
NIST Eckerle4 (
NIST_Eckerle4)NIST Eckerle4
\(y = {(a/b)} * \exp{(-0.5*{({(x-c)}/b)}^{2})}\)
[a, b, c]
NIST Eckerle4 With Offset
\(y = {(a/b)} * \exp{(-0.5*{({(x-c)}/b)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
NIST Gauss (
NIST_Gauss)NIST Gauss
\(y = a*\exp{(-b*x)} + c*\exp{(-{(x-d)}^{2} /f^{2})} + g*\exp{(-{(x-h)}^{2} /i^{2})}\)
[a, b, c, d, f, g, h, i]
NIST Gauss With Offset
\(y = a*\exp{(-b*x)} + c*\exp{(-{(x-d)}^{2} /f^{2})} + g*\exp{(-{(x-h)}^{2} /i^{2})} + \text{Offset}\)
[a, b, c, d, f, g, h, i, Offset]
NIST Hahn (
NIST_Hahn)NIST Hahn
\(y = {(a + b*x + c*x^{2} + d*x^{3})} / {(1.0 +f*x + g*x^{2} + h*x^{3})}\)
[a, b, c, d, f, g, h]
NIST Hahn With Offset
\(y = {(a + b*x + c*x^{2} + d*x^{3})} / {(1.0 +f*x + g*x^{2} + h*x^{3})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
NIST Kirby (
NIST_Kirby)NIST Kirby
\(y = {(a + b*x + c*x^{2})} / {(1.0 + d*x +f*x^{2})}\)
[a, b, c, d, f]
NIST Kirby With Offset
\(y = {(a + b*x + c*x^{2})} / {(1.0 + d*x +f*x^{2})} + \text{Offset}\)
[a, b, c, d, f, Offset]
NIST Lanczos (
NIST_Lanczos)NIST Lanczos
\(y = a*\exp{(-b*x)} + c*\exp{(-d*x)} + f*\exp{(-g*x)}\)
[a, b, c, d, f, g]
NIST Lanczos With Offset
\(y = a*\exp{(-b*x)} + c*\exp{(-d*x)} + f*\exp{(-g*x)} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
NIST MGH09 (
NIST_MGH09)NIST MGH09
\(y = a * {(x^{2} + b*x)} / {(x^{2} + c*x + d)}\)
[a, b, c, d]
NIST MGH09 With Offset
\(y = a * {(x^{2} + b*x)} / {(x^{2} + c*x + d)}+ \text{Offset}\)
[a, b, c, d, Offset]
NIST MGH10 (
NIST_MGH10)NIST MGH10
\(y = a * \exp{(b/{(x+c)})}\)
[a, b, c]
NIST MGH10 With Offset
\(y = a * \exp{(b/{(x+c)})} + \text{Offset}\)
[a, b, c, Offset]
NIST MGH17 (
NIST_MGH17)NIST MGH17
\(y = a + b*\exp{(-x*d)} + c*\exp{(-x*f)}\)
[a, b, c, d, f]
NIST Misra1a (
NIST_Misra1a)NIST Misra1a
\(y = a * {(1.0 - \exp{(-b*x)})}\)
[a, b]
NIST Misra1a With Offset
\(y = a * {(1.0 - \exp{(-b*x)})} + \text{Offset}\)
[a, b, Offset]
NIST Misra1b (
NIST_Misra1b)NIST Misra1b
\(y = a * {(1.0 - {(1.0+b*x/2.0)}^{-2.0})}\)
[a, b]
NIST Misra1b With Offset
\(y = a * {(1.0 - {(1.0+b*x/2.0)}^{-2.0})} + \text{Offset}\)
[a, b, Offset]
NIST Misra1c (
NIST_Misra1c)NIST Misra1c
\(y = a * {(1.0 - {(1.0 + 2.0*b*x)}^{-0.5})}\)
[a, b]
NIST Misra1c With Offset
\(y = a * {(1.0 - {(1.0 + 2.0*b*x)}^{-0.5})} + \text{Offset}\)
[a, b, Offset]
NIST Misra1d (
NIST_Misra1d)NIST Misra1d
\(y = a * b * x * {(1.0 + b*x)}^{-1.0}\)
[a, b]
NIST Misra1d With Offset
\(y = a * b * x * {(1.0 + b*x)}^{-1.0} + \text{Offset}\)
[a, b, Offset]
NIST Rat42 (
NIST_Rat42)NIST Rat42
\(y = a / {(1.0 + \exp{(b - c*x)})}\)
[a, b, c]
NIST Rat42 With Offset
\(y = a / {(1.0 + \exp{(b - c*x)})} + \text{Offset}\)
[a, b, c, Offset]
NIST Rat43 (
NIST_Rat43)NIST Rat43
\(y = a / {({(1.0 + \exp{(b - c*x)})}^{{(1.0/d)}})}\)
[a, b, c, d]
NIST Rat43 With Offset
\(y = a / {({(1.0 + \exp{(b - c*x)})}^{{(1.0/d)}})} + \text{Offset}\)
[a, b, c, d, Offset]
NIST Roszman (
NIST_Roszman)NIST Roszman
\(y = a - bx - {(arctan{(c/{(x-d)})} / pi)}\)
[a, b, c, d]
NIST Thurber (
NIST_Thurber)NIST Thurber
\(y = {(a + bx + cx^{2} + dx^{3})} / {(1.0 + fx+ gx^{2} + hx^{3})}\)
[a, b, c, d, f, g, h]
NIST Thurber With Offset
\(y = {(a + bx + cx^{2} + dx^{3})} / {(1.0 + fx+ gx^{2} + hx^{3})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Optical¶
CAUCHY (
Cauchy)CAUCHY
\(n = A + B/x^{2} + C/x^{4}\)
[A, B, C]
CONRADY1 (
Conrady1)CONRADY1
\(n = A + B/x + C/x^{3.5}\)
[A, B, C]
CONRADY2 (
Conrady2)CONRADY2
\(n = A + B/x^{2} + C/x^{3.5}\)
[A, B, C]
HARTMANN1 (
Hartmann1)HARTMANN1
\(n = A + B/{(C - x)}\)
[A, B, C]
HARTMANN2 (
Hartmann2)HARTMANN2
\(n = A + B/{(C - x)}^{2}\)
[A, B, C]
HARTMANN3a (
Hartmann3a)HARTMANN3a
\(n = A + B/{(C - x)}^{1.2}\)
[A, B, C]
HARTMANN3b (
Hartmann3b)HARTMANN3b
\(n = A/{(x - B)}^{1.2}\)
[A, B]
HARTMANN3b With Offset
\(n = A/{(x - B)}^{1.2} + \text{Offset}\)
[A, B, Offset]
HARTMANN4 (
Hartmann4)HARTMANN4
\(n = A + B/{(C - x)} + D/{(E - x)}\)
[A, B, C, D, E]
HERZBRGR2X2 (
Herzberger2X2)HERZBRGR2X2
\(n = A + Bx^{2} + C / {(x^{2} - 0.028)} + D /{(x^{2} - 0.028)}^{2}\)
[A, B, C, D]
HERZBRGR3X2 (
Herzberger3X2)HERZBRGR3X2
\(n = A + Bx^{2} + Cx^{4} + D /{(x^{2} - 0.028)} + E / {(x^{2} -0.028)}^{2}\)
[A, B, C, D, E]
HERZBRGR3X3 (
Herzberger3X3)HERZBRGR3X3
\(n = A + Bx^{2} + Cx^{4} + D /{(x^{2} - 0.028)} + E / {(x^{2} -0.028)}^{2} + F / {(x^{2} -0.028)}^{4}\)
[A, B, C, D, E, F]
HERZBRGR4X2 (
Herzberger4X2)HERZBRGR4X2
\(n = A + Bx^{2} + Cx^{4} +Dx^{6} + E / {(x^{2} - 0.028)} + F /{(x^{2} - 0.028)}^{2}\)
[A, B, C, D, E, F]
HERZBRGR5X2 (
Herzberger5X2)HERZBRGR5X2
\(n = A + Bx^{2} + Cx^{4} +Dx^{6} + Ex^{8} + F /{(x^{2} - 0.028)} + G / {(x^{2} -0.028)}^{2}\)
[A, B, C, D, E, F, G]
HERZBRGRJK (
HerzbergerJK)HERZBRGRJK
\(n = A + Bx^{2} + Cx^{4} +Dx^{6} + E / {(x^{2} - J)} + F /{(x^{2} - K)}^{2}\)
[A, B, C, D, E, F, J, K]
HoO1 (
HoO1)HoO1
\(n^{2} = A + Bx^{2} + C /{(x^{2} - D^{2})}\)
[A, B, C, D]
HoO2 (
HoO2)HoO2
\(n^{2} = A + Bx^{2} + Cx^{2}/ {(x^{2} - D^{2})}\)
[A, B, C, D]
KINGSLAKE1 (
Kingslake1)KINGSLAKE1
\(n^{2} = A + B/{(x^{2}-C^{2})}+ D/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
KINGSLAKE2 (
Kingslake2)KINGSLAKE2
\(n^{2} = A + B/{(x^{2}-C^{2})}+ D/{(x^{2}-E^{2})} +F/{(x^{2}-G^{2})}\)
[A, B, C, D, E, F, G]
MISC01 (
Misc01)MISC01
\(n^{2} = A + B/{(x^{2}-C^{2})}\)
[A, B, C]
MISC02 (
Misc02)MISC02
\(n^{2} = A + Bx^{2} +C/{(x^{2}-D^{2})}\)
[A, B, C, D]
MISC03 (
Misc03)MISC03
\(n^{2} = A + B/x^{2} +Cx^{2}/{(x^{2}-D^{2})}\)
[A, B, C, D]
MISC04 (
Misc04)MISC04
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/x^{2} +Ex^{2}/{(x^{2}-F+{(Gx^{2}/{(x^{2}-F)})})}\)
[A, B, C, D, E, F, G]
SCHOTT2X3 (
Schott2X3)SCHOTT2X3
\(n^{2} = A + Bx^{2} +C/x^{2} + D/x^{4} + E/x^{6}\)
[A, B, C, D, E]
SCHOTT2X4 (
Schott2X4)SCHOTT2X4
\(n^{2} = A + Bx^{2} +C/x^{2} + D/x^{4} + E/x^{6}+ F/x^{8}\)
[A, B, C, D, E, F]
SCHOTT2X5 (
Schott2X5)SCHOTT2X5
\(n^{2} = A + Bx^{2} +C/x^{2} + D/x^{4} + E/x^{6}+ F/x^{8} + G/x^{10}\)
[A, B, C, D, E, F, G]
SCHOTT2X6 (
Schott2X6)SCHOTT2X6
\(n^{2} = A + Bx^{2} +C/x^{2} + D/x^{4} + E/x^{6}+ F/x^{8} + G/x^{10} +H/x^{12}\)
[A, B, C, D, E, F, G, H]
SCHOTT3X3 (
Schott3X3)SCHOTT3X3
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/x^{2} + E/x^{4} +F/x^{6}\)
[A, B, C, D, E, F]
SCHOTT3X4 (
Schott3X4)SCHOTT3X4
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/x^{2} + E/x^{4} +F/x^{6} + G/x^{8}\)
[A, B, C, D, E, F, G]
SCHOTT3X5 (
Schott3X5)SCHOTT3X5
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/x^{2} + E/x^{4} +F/x^{6} + G/x^{8} +H/x^{10}\)
[A, B, C, D, E, F, G, H]
SCHOTT4X4 (
Schott4X4)SCHOTT4X4
\(n^{2} = A + Bx^{2} + Cx^{4}+ Dx^{6} + E/x^{2} +F/x^{4} + G/x^{6} + H/x^{8}\)
[A, B, C, D, E, F, G, H]
SCHOTT5X5 (
Schott5X5)SCHOTT5X5
\(n^{2} = A + Bx^{2} + Cx^{4}+ Dx^{6} + Ex^{8} + F/x^{2}+ G/x^{4} + H/x^{6} +J/x^{8} + K/x^{10}\)
[A, B, C, D, E, F, G, H, J, K]
SELL1T (
Sell1T)SELL1T
\(n^{2} = 1 + Ax^{2} / {(x^{2}- B^{2})}\)
[A, B]
SELL1TA (
Sell1TA)SELL1TA
\(n^{2} = A + Bx^{2} / {(x^{2}- C^{2})}\)
[A, B, C]
SELL2T (
Sell2T)SELL2T
\(n^{2} = 1 +Ax^{2}/{(x^{2}-B^{2})} +Cx^{2}/{(x^{2}-D^{2})}\)
[A, B, C, D]
SELL2TA (
Sell2TA)SELL2TA
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELL3T (
Sell3T)SELL3T
\(n^{2} = 1 +Ax^{2}/{(x^{2}-B^{2})} +Cx^{2}/{(x^{2}-D^{2})} +Ex^{2}/{(x^{2}-F^{2})}\)
[A, B, C, D, E, F]
SELL3TA (
Sell3TA)SELL3TA
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})} +Fx^{2}/{(x^{2}-G^{2})}\)
[A, B, C, D, E, F, G]
SELL4T (
Sell4T)SELL4T
\(n^{2} = 1 +Ax^{2}/{(x^{2}-B^{2})} +Cx^{2}/{(x^{2}-D^{2})} +Ex^{2}/{(x^{2}-F^{2})} +Gx^{2}/{(x^{2}-H^{2})}\)
[A, B, C, D, E, F, G, H]
SELL4TA (
Sell4TA)SELL4TA
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})} +Fx^{2}/{(x^{2}-G^{2})} +Hx^{2}/{(x^{2}-J^{2})}\)
[A, B, C, D, E, F, G, H, J]
SELL5T (
Sell5T)SELL5T
\(n^{2} = 1 +Ax^{2}/{(x^{2}-B^{2})} +Cx^{2}/{(x^{2}-D^{2})} +Ex^{2}/{(x^{2}-F^{2})} +Gx^{2}/{(x^{2}-H^{2})} +Jx^{2}/{(x^{2}-K^{2})}\)
[A, B, C, D, E, F, G, H, J, K]
SELL5TA (
Sell5TA)SELL5TA
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})} +Fx^{2}/{(x^{2}-G^{2})} +Hx^{2}/{(x^{2}-J^{2})} +Kx^{2}/{(x^{2}-M^{2})}\)
[A, B, C, D, E, F, G, H, J, K, M]
SELL6TA (
Sell6TA)SELL6TA
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})} +Fx^{2}/{(x^{2}-G^{2})} +Hx^{2}/{(x^{2}-J^{2})} +Kx^{2}/{(x^{2}-M^{2})} +Nx^{2}/{(x^{2}-P^{2})}\)
[A, B, C, D, E, F, G, H, J, K, M, N, P]
SELL7TA (
Sell7TA)SELL7TA
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})} +Fx^{2}/{(x^{2}-G^{2})} +Hx^{2}/{(x^{2}-J^{2})} +Kx^{2}/{(x^{2}-M^{2})} +Nx^{2}/{(x^{2}-P^{2})} +Qx^{2}/{(x^{2}-R^{2})}\)
[A, B, C, D, E, F, G, H, J, K, M, N, P, Q, R]
SELLMOD1 (
Sellmod1)SELLMOD1
\(n^{2} = A + Bx + Cx^{2} +Dx^{2}/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELLMOD1A (
Sellmod1A)SELLMOD1A
\(n^{2} = A + Bx + Cx^{2} +D/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELLMOD2 (
Sellmod2)SELLMOD2
\(n^{2} = A + Bx + Cx^{4} +Dx^{2}/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELLMOD2A (
Sellmod2A)SELLMOD2A
\(n^{2} = A + Bx + Cx^{4} +D/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELLMOD3 (
Sellmod3)SELLMOD3
\(n^{2} ={(Ax^{2}+B)}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELLMOD3 With Offset
\(n^{2} ={(Ax^{2}+B)}/{(x^{2}-C^{2})} +Dx^{2}/{(x^{2}-E^{2})} +\text{Offset}\)
[A, B, C, D, E, Offset]
SELLMOD4 (
Sellmod4)SELLMOD4
\(n^{2} = A + Bx^{2} +C/x^{2} +Dx^{2}/{(x^{2}-E^{2})} +Fx^{2}/{(x^{2}-G^{2})}\)
[A, B, C, D, E, F, G]
SELLMOD4A (
Sellmod4A)SELLMOD4A
\(n^{2} = A + Bx^{2} +C/x^{2} + D/{(x^{2}-E^{2})} +F/{(x^{2}-G^{2})}\)
[A, B, C, D, E, F, G]
SELLMOD5 (
Sellmod5)SELLMOD5
\(n^{2} = A + Bx^{2} +Cx^{2}/{(x^{2}-D^{2})} +Ex^{2}/{(x^{2}-F^{2})}\)
[A, B, C, D, E, F]
SELLMOD6 (
Sellmod6)SELLMOD6
\(n^{2} = A +Bx^{2}/{(x^{2}-C^{2})} +D/{(x^{2}-E^{2})}\)
[A, B, C, D, E]
SELLMOD7 (
Sellmod7)SELLMOD7
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/x^{6} +Ex^{2}/{(x^{2}-F^{2})}\)
[A, B, C, D, E, F]
SELLMOD7A (
Sellmod7A)SELLMOD7A
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/x^{6} + E/{(x^{2}-F^{2})}\)
[A, B, C, D, E, F]
SELLMOD8 (
Sellmod8)SELLMOD8
\(n^{2} = A + Bx^{2} + Cx^{4}+ D/{(x^{2}-E^{2})} +F/{(x^{2}-G^{2})}\)
[A, B, C, D, E, F, G]
SELLMOD9 (
Sellmod9)SELLMOD9
\(n^{2} = A + B/x^{2} +C/x^{4} + D/x^{6} +Ex^{2}/{(x^{2}-F^{2})}\)
[A, B, C, D, E, F]
Peak¶
Arnold Cohen Log-Normal Peak Shifted (
ArnoldCohenLogNormalShifted)Arnold Cohen Log-Normal Peak Shifted
\(y = a * {(\exp{(-0.5 * {({(ln{(x-f)}-b)}/c)}^{2})})} / {(d * {(x-g)})}\)
[a, b, c, d, f, g]
Arnold Cohen Log-Normal Peak Shifted With Offset
\(y = a * {(\exp{(-0.5 * {({(ln{(x-f)}-b)}/c)}^{2})})} / {(d * {(x-g)})} +\text{Offset}\)
[a, b, c, d, f, g, Offset]
Arnold Cohen Two-Parameter Log-Normal Peak Shifted (
ArnoldCohenTwoParameterLogNormalShifted)Arnold Cohen Two-Parameter Log-Normal Peak Shifted
\(y = \exp{(-0.5 * {({(ln{(x-d)}-b)}/c)}^{2})} / {(\sqrt{(2*pi)} * c *{(x-f)})}\)
[b, c, d, f]
Arnold Cohen Two-Parameter Log-Normal Peak Shifted With Offset
\(y = \exp{(-0.5 * {({(ln{(x-d)}-b)}/c)}^{2})} / {(\sqrt{(2*pi)} * c *{(x-f)})} + \text{Offset}\)
[b, c, d, f, Offset]
Box Lucas A (
BoxLucasA)Box Lucas A
\(y = a * {(1.0 - b^{x})}\)
[a, b]
Box Lucas A With Offset
\(y = a * {(1.0 - b^{x})} + \text{Offset}\)
[a, b, Offset]
Box Lucas A Shifted (
BoxLucasAShifted)Box Lucas A Shifted
\(y = a * {(1.0 - b^{x-c})}\)
[a, b, c]
Box Lucas A Shifted With Offset
\(y = a * {(1.0 - b^{x-c})} + \text{Offset}\)
[a, b, c, Offset]
Box Lucas B (
BoxLucasB)Box Lucas B
\(y = a * {(1.0 - \exp{(-bx)})}\)
[a, b]
Box Lucas B With Offset
\(y = a * {(1.0 - \exp{(-bx)})} + \text{Offset}\)
[a, b, Offset]
Box Lucas B Shifted (
BoxLucasBShifted)Box Lucas B Shifted
\(y = a * {(1.0 - \exp{(-b{(x-c)})})}\)
[a, b, c]
Box Lucas B Shifted With Offset
\(y = a * {(1.0 - \exp{(-b{(x-c)})})} + \text{Offset}\)
[a, b, c, Offset]
Box Lucas C (
BoxLucasC)Box Lucas C
\(y = {(a / {(a-b)})} * {(\exp{(-bx)} - \exp{(-ax)})}\)
[a, b]
Box Lucas C With Offset
\(y = {(a / {(a-b)})} * {(\exp{(-bx)} - \exp{(-ax)})} + \text{Offset}\)
[a, b, Offset]
Box Lucas C shifted (
BoxLucasCShifted)Box Lucas C shifted
\(y = {(a / {(a-b)})} * {(\exp{(-b{(x-c)})} - \exp{(-a{(x-c)})})}\)
[a, b, c]
Box Lucas C shifted With Offset
\(y = {(a / {(a-b)})} * {(\exp{(-b{(x-c)})} - \exp{(-a{(x-c)})})} + \text{Offset}\)
[a, b, c, Offset]
Extreme Value 4 Parameter Peak (
ExtremeValue4ParameterPeak)Extreme Value 4 Parameter Peak
\(y = a * \exp{(-x + b + c - c*d*\exp{(-1.0 * {({(x + c*ln{(d)} - b)} / c)})} /{(c*d)})}\)
[a, b, c, d]
Extreme Value 4 Parameter Peak With Offset
\(y = a * \exp{(-x + b + c - c*d*\exp{(-1.0 * {({(x + c*ln{(d)} - b)} / c)})} /{(c*d)})} + \text{Offset}\)
[a, b, c, d, Offset]
Extreme Value Area (
ExtremeValueArea)Extreme Value Area
\(y = {(a/c)} * \exp{(-\exp{(-{({(x-b)}/c)})}-{({(x-b)}/c)})}\)
[a, b, c]
Extreme Value Area With Offset
\(y = {(a/c)} * \exp{(-\exp{(-{({(x-b)}/c)})}-{({(x-b)}/c)})} + \text{Offset}\)
[a, b, c, Offset]
Extreme Value Peak (
ExtremeValuePeak)Extreme Value Peak
\(y = a * \exp{(-\exp{(-{({(x-b)}/c)})}-{({(x-b)}/c)}+1.0)}\)
[a, b, c]
Extreme Value Peak With Offset
\(y = a * \exp{(-\exp{(-{({(x-b)}/c)})}-{({(x-b)}/c)}+1.0)} + \text{Offset}\)
[a, b, c, Offset]
Gaussian Area (
GaussianArea)Gaussian Area
\(y = {(a / {(pow{(2*pi, 0.5)} * c)})} * \exp{(-0.5 *{({(x-b)}/c)}^{2})}\)
[a, b, c]
Gaussian Area With Offset
\(y = {(a / {(pow{(2*pi, 0.5)} * c)})} * \exp{(-0.5 *{({(x-b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Gaussian Peak (
GaussianPeak)Gaussian Peak
\(y = a * \exp{(-0.5 * {({(x-b)}/c)}^{2})}\)
[a, b, c]
Gaussian Peak With Offset
\(y = a * \exp{(-0.5 * {({(x-b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Gaussian Peak Modified (
GaussianPeak_Modified)Gaussian Peak Modified
\(y = a * \exp{(-0.5 * {({(x-b)}/c)}^{d})}\)
[a, b, c, d]
Gaussian Peak Modified With Offset
\(y = a * \exp{(-0.5 * {({(x-b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Hamilton (
Hamilton)Hamilton
\(Vb = Gb * {(I/mu)}^{ln{(mu/I)}/{(B*B)}} +{(Vb_{max} * I)}/{(I + sigma\_b)}\)
[Gb, mu, B, Vbmax, sigma_b]
Hamilton With Offset
\(Vb = Gb * {(I/mu)}^{ln{(mu/I)}/{(B*B)}} +{(Vb_{max} * I)}/{(I + sigma\_b)} + \text{Offset}\)
[Gb, mu, B, Vbmax, sigma_b, Offset]
Laplace Area (
LaplaceArea)Laplace Area
\(y = {(a / {(pow{(2.0, 0.5)} * c)})} * \exp{({(-1.0 * pow{(2.0, 0.5)} * abs{(x-b)})}/c)}\)
[a, b, c]
Laplace Area With Offset
\(y = {(a / {(pow{(2.0, 0.5)} * c)})} * \exp{({(-1.0 * pow{(2.0, 0.5)} * abs{(x-b)})}/c)}+ \text{Offset}\)
[a, b, c, Offset]
Laplace Peak (
LaplacePeak)Laplace Peak
\(y = a * \exp{({(-1.0 * pow{(2.0, 0.5)} * abs{(x-b)})}/c)}\)
[a, b, c]
Laplace Peak With Offset
\(y = a * \exp{({(-1.0 * pow{(2.0, 0.5)} * abs{(x-b)})}/c)} + \text{Offset}\)
[a, b, c, Offset]
Log-Normal 4 Parameter (
LogNormal4Parameter)Log-Normal 4 Parameter
\(y = a * \exp{(-1.0 * {(ln{(2)} * ln{({({({(x-b)} * {(d^{2}-1)})} /{(c*d)})} + 1.0)}^{2})} / ln{(d)}^{2})}\)
[a, b, c, d]
Log-Normal 4 Parameter With Offset
\(y = a * \exp{(-1.0 * {(ln{(2)} * ln{({({({(x-b)} * {(d^{2}-1)})} /{(c*d)})} + 1.0)}^{2})} / ln{(d)}^{2})} + \text{Offset}\)
[a, b, c, d, Offset]
Log-Normal Peak A (
LogNormalA)Log-Normal Peak A
\(y = a * \exp{(-0.5 * {({(ln{(x)}-b)}/c)}^{2})}\)
[a, b, c]
Log-Normal Peak A With Offset
\(y = a * \exp{(-0.5 * {({(ln{(x)}-b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Log-Normal Peak A Shifted (
LogNormalAShifted)Log-Normal Peak A Shifted
\(y = a * \exp{(-0.5 * {({(ln{(x-d)}-b)}/c)}^{2})}\)
[a, b, c, d]
Log-Normal Peak A Shifted With Offset
\(y = a * \exp{(-0.5 * {({(ln{(x-d)}-b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, d, Offset]
Log-Normal Peak A Modified (
LogNormalA_Modified)Log-Normal Peak A Modified
\(y = a * \exp{(-0.5 * {({(ln{(x)}-b)}/c)}^{d})}\)
[a, b, c, d]
Log-Normal Peak A Modified With Offset
\(y = a * \exp{(-0.5 * {({(ln{(x)}-b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Log-Normal Peak A Modified Shifted (
LogNormalA_ModifiedShifted)Log-Normal Peak A Modified Shifted
\(y = a * \exp{(-0.5 * {({(ln{(x-f)}-b)}/c)}^{d})}\)
[a, b, c, d, f]
Log-Normal Peak A Modified Shifted With Offset
\(y = a * \exp{(-0.5 * {({(ln{(x-f)}-b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Log-Normal Peak B (
LogNormalB)Log-Normal Peak B
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{2})}\)
[a, b, c]
Log-Normal Peak B With Offset
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Log-Normal Peak B Shifted (
LogNormalBShifted)Log-Normal Peak B Shifted
\(y = a * \exp{(-0.5 * {(ln{({(x-d/b)})}/c)}^{2})}\)
[a, b, c, d]
Log-Normal Peak B Shifted With Offset
\(y = a * \exp{(-0.5 * {(ln{({(x-d/b)})}/c)}^{2})} + \text{Offset}\)
[a, b, c, d, Offset]
Log-Normal Peak B Modified (
LogNormalB_Modified)Log-Normal Peak B Modified
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{d})}\)
[a, b, c, d]
Log-Normal Peak B Modified With Offset
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Log-Normal Peak B Modified Shifted (
LogNormalB_ModifiedShifted)Log-Normal Peak B Modified Shifted
\(y = a * \exp{(-0.5 * {(ln{({(x-f)}/b)}/c)}^{d})}\)
[a, b, c, d, f]
Log-Normal Peak B Modified Shifted With Offset
\(y = a * \exp{(-0.5 * {(ln{({(x-f)}/b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Logistic Area (
LogisticArea)Logistic Area
\(y = a * \exp{(-1.0 * {(x-b)} / c)} / {(c * {(1.0 + \exp{(-1.0 * {(x-b)} /c)})}^{2})}\)
[a, b, c]
Logistic Area With Offset
\(y = a * \exp{(-1.0 * {(x-b)} / c)} / {(c * {(1.0 + \exp{(-1.0 * {(x-b)} /c)})}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Logistic Peak (
LogisticPeak)Logistic Peak
\(y = 4a * \exp{(-1.0 * {(x-b)} / c)} / {(1.0 + \exp{(-1.0 * {(x-b)} /c)})}^{2}\)
[a, b, c]
Logistic Peak With Offset
\(y = 4a * \exp{(-1.0 * {(x-b)} / c)} / {(1.0 + \exp{(-1.0 * {(x-b)} /c)})}^{2} + \text{Offset}\)
[a, b, c, Offset]
Lorentzian Modified Peak A (
LorentzianModifiedPeakA)Lorentzian Modified Peak A
\(y = 1.0 / {(1.0 + {(x-a)}^{b})}\)
[a, b]
Lorentzian Modified Peak A With Offset
\(y = 1.0 / {(1.0 + {(x-a)}^{b})} + \text{Offset}\)
[a, b, Offset]
Lorentzian Modified Peak B (
LorentzianModifiedPeakB)Lorentzian Modified Peak B
\(y = 1.0 / {(a + {(x-b)}^{c})}\)
[a, b, c]
Lorentzian Modified Peak B With Offset
\(y = 1.0 / {(a + {(x-b)}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Lorentzian Modified Peak C (
LorentzianModifiedPeakC)Lorentzian Modified Peak C
\(y = a / {(b + {(x-c)}^{d})}\)
[a, b, c, d]
Lorentzian Modified Peak C With Offset
\(y = a / {(b + {(x-c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Lorentzian Modified Peak D (
LorentzianModifiedPeakD)Lorentzian Modified Peak D
\(y = 1.0 / {(1.0 + {({(x-a)}/b)}^{c})}\)
[a, b, c]
Lorentzian Modified Peak D With Offset
\(y = 1.0 / {(1.0 + {({(x-a)}/b)}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Lorentzian Modified Peak E (
LorentzianModifiedPeakE)Lorentzian Modified Peak E
\(y = 1.0 / {(a + {({(x-b)}/c)}^{d})}\)
[a, b, c, d]
Lorentzian Modified Peak E With Offset
\(y = 1.0 / {(a + {({(x-b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Lorentzian Modified Peak F (
LorentzianModifiedPeakF)Lorentzian Modified Peak F
\(y = a / {(b + {({(x-c)}/d)}^{f})}\)
[a, b, c, d, f]
Lorentzian Modified Peak F With Offset
\(y = a / {(b + {({(x-c)}/d)}^{f})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Lorentzian Modified Peak G (
LorentzianModifiedPeakG)Lorentzian Modified Peak G
\(y = a / {(1.0 + {({(x-b)}/c)}^{d})}\)
[a, b, c, d]
Lorentzian Modified Peak G With Offset
\(y = a / {(1.0 + {({(x-b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Lorentzian Peak A (
LorentzianPeakA)Lorentzian Peak A
\(y = 1.0 / {(1.0 + {(x-a)}^{2})}\)
[a]
Lorentzian Peak A With Offset
\(y = 1.0 / {(1.0 + {(x-a)}^{2})} + \text{Offset}\)
[a, Offset]
Lorentzian Peak B (
LorentzianPeakB)Lorentzian Peak B
\(y = 1.0 / {(a + {(x-b)}^{2})}\)
[a, b]
Lorentzian Peak B With Offset
\(y = 1.0 / {(a + {(x-b)}^{2})} + \text{Offset}\)
[a, b, Offset]
Lorentzian Peak C (
LorentzianPeakC)Lorentzian Peak C
\(y = a / {(b + {(x-c)}^{2})}\)
[a, b, c]
Lorentzian Peak C With Offset
\(y = a / {(b + {(x-c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Lorentzian Peak D (
LorentzianPeakD)Lorentzian Peak D
\(y = 1.0 / {(1.0 + {({(x-a)}/b)}^{2})}\)
[a, b]
Lorentzian Peak D With Offset
\(y = 1.0 / {(1.0 + {({(x-a)}/b)}^{2})} + \text{Offset}\)
[a, b, Offset]
Lorentzian Peak E (
LorentzianPeakE)Lorentzian Peak E
\(y = 1.0 / {(a + {({(x-b)}/c)}^{2})}\)
[a, b, c]
Lorentzian Peak E With Offset
\(y = 1.0 / {(a + {({(x-b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Lorentzian Peak F (
LorentzianPeakF)Lorentzian Peak F
\(y = a / {(b + {({(x-c)}/d)}^{2})}\)
[a, b, c, d]
Lorentzian Peak F With Offset
\(y = a / {(b + {({(x-c)}/d)}^{2})} + \text{Offset}\)
[a, b, c, d, Offset]
Lorentzian Peak G (
LorentzianPeakG)Lorentzian Peak G
\(y = a / {(1.0 + {({(x-b)}/c)}^{2})}\)
[a, b, c]
Lorentzian Peak G With Offset
\(y = a / {(1.0 + {({(x-b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Pseudo-Voight Peak (
PseudoVoight)Pseudo-Voight Peak
\(y = a * {(d * {(1/{(1+{({(x-b)}/c)}^{2})})} + {(1-d)} * \exp{(-0.5 *{({(x-b)}/c)}^{2})})}\)
[a, b, c, d]
Pseudo-Voight Peak With Offset
\(y = a * {(d * {(1/{(1+{({(x-b)}/c)}^{2})})} + {(1-d)} * \exp{(-0.5 *{({(x-b)}/c)}^{2})})} + \text{Offset}\)
[a, b, c, d, Offset]
Pseudo-Voight Peak Modified (
PseudoVoight_Modified)Pseudo-Voight Peak Modified
\(y = a * {(d * {(1/{(1+{({(x-b)}/c)}^{f})})} + {(1-d)} * \exp{(-0.5 *{({(x-b)}/c)}^{g})})}\)
[a, b, c, d, f, g]
Pseudo-Voight Peak Modified With Offset
\(y = a * {(d * {(1/{(1+{({(x-b)}/c)}^{f})})} + {(1-d)} * \exp{(-0.5 *{({(x-b)}/c)}^{g})})} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Pulse Peak (
Pulse)Pulse Peak
\(y = 4a * \exp{(-{(x-b)}/c)} * {(1.0 - \exp{(-{(x-b)}/c)})}\)
[a, b, c]
Pulse Peak With Offset
\(y = 4a * \exp{(-{(x-b)}/c)} * {(1.0 - \exp{(-{(x-b)}/c)})} + \text{Offset}\)
[a, b, c, Offset]
UVED Fruit Growth Rate (
UVEDFruitGrowthRate)UVED Fruit Growth Rate
\(y ={({(t/5)}^{{(a-1)}}*{(1-t/5)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}\)
[a, b]
UVED Fruit Growth Rate With Offset
\(y ={({(t/5)}^{{(a-1)}}*{(1-t/5)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}+ \text{Offset}\)
[a, b, Offset]
UVED Fruit Growth Rate B (
UVEDFruitGrowthRateB)UVED Fruit Growth Rate B
\(y = c *{({(t/5)}^{{(a-1)}}*{(1-t/5)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}\)
[a, b, c]
UVED Fruit Growth Rate B With Offset
\(y = c *{({(t/5)}^{{(a-1)}}*{(1-t/5)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}+ \text{Offset}\)
[a, b, c, Offset]
UVED Fruit Growth Rate Scaled (
UVEDFruitGrowthRateScaled)UVED Fruit Growth Rate Scaled
\(y ={(c*t)}^{{(a-1)}}*{(1-{(c*t)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}\)
[a, b, c]
UVED Fruit Growth Rate Scaled With Offset
\(y ={(c*t)}^{{(a-1)}}*{(1-{(c*t)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}+ \text{Offset}\)
[a, b, c, Offset]
UVED Fruit Growth Rate Scaled B (
UVEDFruitGrowthRateScaledB)UVED Fruit Growth Rate Scaled B
\(y = d *{(c*t)}^{{(a-1)}}*{(1-{(c*t)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}\)
[a, b, c, d]
UVED Fruit Growth Rate Scaled B With Offset
\(y = d *{(c*t)}^{{(a-1)}}*{(1-{(c*t)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}+ \text{Offset}\)
[a, b, c, d, Offset]
UVED Fruit Growth Rate Transform (
UVEDFruitGrowthRateTransform)UVED Fruit Growth Rate Transform
\(y ={(c*t+d)}^{{(a-1)}}*{(1-{(c*t+d)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}\)
[a, b, c, d]
UVED Fruit Growth Rate Transform With Offset
\(y ={(c*t+d)}^{{(a-1)}}*{(1-{(c*t+d)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}+ \text{Offset}\)
[a, b, c, d, Offset]
UVED Fruit Growth Rate Transform B (
UVEDFruitGrowthRateTransformB)UVED Fruit Growth Rate Transform B
\(y = f *{(c*t+d)}^{{(a-1)}}*{(1-{(c*t+d)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}\)
[a, b, c, d, f]
UVED Fruit Growth Rate Transform B With Offset
\(y = f *{(c*t+d)}^{{(a-1)}}*{(1-{(c*t+d)}^{{(b-1)}})}/{({({(a-1)}/{(a+b-2)})}^{{(a-1)}}*{({(b-1)}/{(a+b-2)})}^{{(b-1)}})}+ \text{Offset}\)
[a, b, c, d, f, Offset]
Weibull Peak (
WeibullPeak)Weibull Peak
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{2})}\)
[a, b, c]
Weibull Peak With Offset
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, Offset]
Weibull Peak Shifted (
WeibullPeakShifted)Weibull Peak Shifted
\(y = a * \exp{(-0.5 * {(ln{({(x-d)}/b)}/c)}^{2})}\)
[a, b, c, d]
Weibull Peak Shifted With Offset
\(y = a * \exp{(-0.5 * {(ln{({(x-d)}/b)}/c)}^{2})} + \text{Offset}\)
[a, b, c, d, Offset]
Weibull Peak Modified (
WeibullPeak_Modified)Weibull Peak Modified
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{d})}\)
[a, b, c, d]
Weibull Peak Modified With Offset
\(y = a * \exp{(-0.5 * {(ln{(x/b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, Offset]
Weibull Peak Modified Shifted (
WeibullPeak_ModifiedShifted)Weibull Peak Modified Shifted
\(y = a * \exp{(-0.5 * {(ln{({(x-f)}/b)}/c)}^{d})}\)
[a, b, c, d, f]
Weibull Peak Modified Shifted With Offset
\(y = a * \exp{(-0.5 * {(ln{({(x-f)}/b)}/c)}^{d})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Polyfunctional¶
User-Selectable Polyfunctional (
UserSelectablePolyfunctional)User-Selectable Polyfunctional
\(y = user-selectable function\)
[]
Polynomial¶
3rd Order (Cubic) (
Cubic)3rd Order (Cubic)
\(y = a + bx + cx^{2} + dx^{3}\)
[a, b, c, d]
1st Order (Linear) (
Linear)1st Order (Linear)
\(y = a + bx\)
[a, b]
Marc Plante’s Custom Quadratic (
MarcPlanteQuadratic)Marc Plante’s Custom Quadratic
\(y = {(-b + {(b^{2} - 4 a {(c - x)})}^{0.5})} / 2/ a\)
[a, b, c]
Marc Plante’s Custom Quadratic With Offset
\(y = {(-b + {(b^{2} - 4 a {(c - x)})}^{0.5})} / 2/ a + \text{Offset}\)
[a, b, c, Offset]
2nd Order (Quadratic) (
Quadratic)2nd Order (Quadratic)
\(y = a + bx + cx^{2}\)
[a, b, c]
4th Order (Quartic) (
Quartic)4th Order (Quartic)
\(y = a + bx + cx^{2} + dx^{3} +fx^{4}\)
[a, b, c, d, f]
5th Order (Quintic) (
Quintic)5th Order (Quintic)
\(y = a + bx + cx^{2} + dx^{3} +fx^{4} + gx^{5}\)
[a, b, c, d, f, g]
User-Customizable Polynomial (
UserCustomizablePolynomial)User-Customizable Polynomial
\(y = user-customizable polynomial\)
[]
User-Selectable Polynomial (
UserSelectablePolynomial)User-Selectable Polynomial
\(y = user-selectable polynomial\)
Power¶
Geometric Modified (
Geometric_Modified)Geometric Modified
\(y = a * x^{{(b/x)}}\)
[a, b]
Geometric Modified With Offset
\(y = a * x^{{(b/x)}} + \text{Offset}\)
[a, b, Offset]
Power A Modified (
PowerA_Modified)Power A Modified
\(y = a * b^{x}\)
[a, b]
Power A Modified With Offset
\(y = a * b^{x} + \text{Offset}\)
[a, b, Offset]
Power A Modified Transform (
PowerA_Modified_Transform)Power A Modified Transform
\(y = a * b^{cx + d}\)
[a, b, c, d]
Power A Modified Transform With Offset
\(y = a * b^{cx + d} + \text{Offset}\)
[a, b, c, d, Offset]
Power B Modified (
PowerB_Modified)Power B Modified
\(y = a^{ln{(x)}}\)
[a]
Power B Modified With Offset
\(y = a^{ln{(x)}} + \text{Offset}\)
[a, Offset]
Power B Modified Transform (
PowerB_Modified_Transform)Power B Modified Transform
\(y = a^{ln{(bx + c)}}\)
[a, b, c]
Power B Modified Transform With Offset
\(y = a^{ln{(bx + c)}} + \text{Offset}\)
[a, b, c, Offset]
Power C Modified (
PowerC_Modified)Power C Modified
\(y = {(a + x)}^{b}\)
[a, b]
Power C Modified With Offset
\(y = {(a + x)}^{b} + \text{Offset}\)
[a, b, Offset]
Power C Modified Transform (
PowerC_Modified_Transform)Power C Modified Transform
\(y = {(a + bx)}^{c}\)
[a, b, c]
Power C Modified Transform With Offset
\(y = {(a + bx)}^{c} + \text{Offset}\)
[a, b, c, Offset]
Power Law With Exponential Cutoff (
PowerLawExponentialCutoff)Power Law With Exponential Cutoff
\(p{(k)} = C * k^{{(-T)}} * \exp{(-k/K)}\)
[C, T, K]
Power Law With Exponential Cutoff With Offset
\(p{(k)} = C * k^{{(-T)}} * \exp{(-k/K)} + \text{Offset}\)
[C, T, K, Offset]
Root (
PowerRoot)Root
\(y = a^{{(1.0/x)}}\)
[a]
Root With Offset
\(y = a^{{(1.0/x)}} + \text{Offset}\)
[a, Offset]
Simple Power (
SimplePower)Simple Power
\(y = x^{a}\)
[a]
Simple Power With Offset
\(y = x^{a} + \text{Offset}\)
[a, Offset]
Standard Geometric (
StandardGeometric)Standard Geometric
\(y = a * x^{bx}\)
[a, b]
Standard Geometric With Offset
\(y = a * x^{bx} + \text{Offset}\)
[a, b, Offset]
Standard Power (
StandardPower)Standard Power
\(y = a * x^{b}\)
[a, b]
Standard Power With Offset
\(y = a * x^{b} + \text{Offset}\)
[a, b, Offset]
X Shifted Power (
XShiftedPower)X Shifted Power
\(y = a * {(x-b)}^{c}\)
[a, b, c]
X Shifted Power With Offset
\(y = a * {(x-b)}^{c} + \text{Offset}\)
[a, b, c, Offset]
Rational¶
User-Selectable Rational (
UserSelectableRational)User-Selectable Rational
\(y = user-selectable rational\)
[]
User-Selectable Rational With Offset
\(y = user-selectable rational + \text{Offset}\)
[Offset]
Sigmoidal¶
BET Sigmoidal A (
BET_Sigmoidal_A)BET Sigmoidal A
\(y = x / {(a + bx - {(a+b)}x^{2})}\)
[a, b]
BET Sigmoidal A With Offset
\(y = x / {(a + bx - {(a+b)}x^{2})} + \text{Offset}\)
[a, b, Offset]
BET Sigmoidal B (
BET_Sigmoidal_B)BET Sigmoidal B
\(y = abx / {(1.0 + {(b-2.0)}x - {(b-1.0)}x^{2})}\)
[a, b]
BET Sigmoidal B With Offset
\(y = abx / {(1.0 + {(b-2.0)}x - {(b-1.0)}x^{2})} + \text{Offset}\)
[a, b, Offset]
Boltzmann Sigmoid A (
BoltzmannSigmoidA)Boltzmann Sigmoid A
\(y = {(a - b)} / {(1.0 + \exp{({(x-c)}/d)})} + b\)
[a, b, c, d]
Boltzmann Sigmoid B (
BoltzmannSigmoidB)Boltzmann Sigmoid B
\(y = {(a - b)} / {(1.0 + \exp{({(x-c)}/{(dx)})})} + b\)
[a, b, c, d]
Chapman (
Chapman)Chapman
\(y = a * {(1.0 - \exp{(-bx)})}^{c}\)
[a, b, c]
Chapman With Offset
\(y = a * {(1.0 - \exp{(-bx)})}^{c} + \text{Offset}\)
[a, b, c, Offset]
Don Levin Sigmoid (
DonLevinSigmoid)Don Levin Sigmoid
\(y = a1 / {(1.0 + \exp{(-{(x-b1)}/c1)})} + a2 / {(1.0 + \exp{(-{(x-b2)}/c2)})} + a3 /{(1.0 + \exp{(-{(x-b3)}/c3)})}\)
[a1, b1, c1, a2, b2, c2, a3, b3, c3]
Don Levin Sigmoid With Offset
\(y = a1 / {(1.0 + \exp{(-{(x-b1)}/c1)})} + a2 / {(1.0 + \exp{(-{(x-b2)}/c2)})} + a3 /{(1.0 + \exp{(-{(x-b3)}/c3)})} + \text{Offset}\)
[a1, b1, c1, a2, b2, c2, a3, b3, c3, Offset]
Five-Parameter Logistic (
FiveParameterLogistic)Five-Parameter Logistic
\(y = d + {(a-d)} / {(1.0 + {(x/c)}^{b})}^{f}\)
[a, b, c, d, f]
Four-Parameter Logistic (
FourParameterLogistic)Four-Parameter Logistic
\(y = d + {(a-d)} / {(1.0 + {(x/c)}^{b})}\)
[a, b, c, d]
Generalised Logistic (
GeneralisedLogistic)Generalised Logistic
\(y = A + C / {(1 + T * \exp{(-B * {(x - M)})})}^{1/T}\)
[A, C, M, B, T]
Gompertz A (
GompertzA)Gompertz A
\(y = a * \exp{(-\exp{(b - cx)})}\)
[a, b, c]
Gompertz A With Offset
\(y = a * \exp{(-\exp{(b - cx)})} + \text{Offset}\)
[a, b, c, Offset]
Gompertz B (
GompertzB)Gompertz B
\(y = a * \exp{(-\exp{({(x-b)}/c)})}\)
[a, b, c]
Gompertz B With Offset
\(y = a * \exp{(-\exp{({(x-b)}/c)})} + \text{Offset}\)
[a, b, c, Offset]
Gompertz C (
GompertzC)Gompertz C
\(y = a * \exp{(b * \exp{(c * x)})}\)
[a, b, c]
Gompertz C With Offset
\(y = a * \exp{(b * \exp{(c * x)})} + \text{Offset}\)
[a, b, c, Offset]
Hill (
Hill)Hill
\(y = ax^{b} / {(c^{b} +x^{b})}\)
[a, b, c]
Hill With Offset
\(y = ax^{b} / {(c^{b} +x^{b})} + \text{Offset}\)
[a, b, c, Offset]
JJacquelin Generalised Logistic (
JJacquelinGeneralisedLogistic)JJacquelin Generalised Logistic
\(y = L / {(1.0 + {(b * \exp{(-k*t)})} + {(c * \exp{(h*t)})})}\)
[L, b, k, c, h]
JJacquelin Generalised Logistic With Offset
\(y = L / {(1.0 + {(b * \exp{(-k*t)})} + {(c * \exp{(h*t)})})} + \text{Offset}\)
[L, b, k, c, h, Offset]
Janoschek Growth (
Janoschek)Janoschek Growth
\(w = a - {(1.0 - \exp{(-b * t^{c})})}\)
[a, b, c]
Janoschek Growth Modified (
Janoschek_Modified)Janoschek Growth Modified
\(w = a - {(a - w0)} * {(1.0 - \exp{(-b * t^{c})})}\)
[a, b, c, w0]
Logistic A (
LogisticA)Logistic A
\(y = a / {(1.0 + b*\exp{(-cx)})}\)
[a, b, c]
Logistic A With Offset
\(y = a / {(1.0 + b*\exp{(-cx)})} + \text{Offset}\)
[a, b, c, Offset]
Logistic B (
LogisticB)Logistic B
\(y = a / {(1.0 + {(x/b)}^{c})}\)
[a, b, c]
Logistic B With Offset
\(y = a / {(1.0 + {(x/b)}^{c})} + \text{Offset}\)
[a, b, c, Offset]
Lomolino (
Lomolino)Lomolino
\(y = a / {(1.0 + b^{ln{(c/x)}})}\)
[a, b, c]
Lomolino With Offset
\(y = a / {(1.0 + b^{ln{(c/x)}})} + \text{Offset}\)
[a, b, c, Offset]
Magnetic Saturation (
MagneticSaturation)Magnetic Saturation
\(y = ax * {(1.0 + b*\exp{(cx)})}\)
[a, b, c]
Magnetic Saturation With Offset
\(y = ax * {(1.0 + b*\exp{(cx)})} + \text{Offset}\)
[a, b, c, Offset]
Morgan-Mercer-Flodin (MMF) (
MorganMercerFlodin)Morgan-Mercer-Flodin (MMF)
\(y = {(a * b + c * x^{d})} / {(b + x^{d})}\)
[a, b, c, d]
Morgan-Mercer-Flodin (MMF) With Offset
\(y = {(a * b + c * x^{d})} / {(b + x^{d})} +\text{Offset}\)
[a, b, c, d, Offset]
Peters-Baskin Step-Stool: y (1) (
PetersBaskin_Y)Peters-Baskin Step-Stool: y (1)
\(y = ln{(c + \exp{(b*d*x)})} / d\)
[b, c, d]
Peters-Baskin Step-Stool: y (1) With Offset
\(y = ln{(c + \exp{(b*d*x)})} / d + \text{Offset}\)
[b, c, d, Offset]
Peters-Baskin Step-Stool: yI (2) (
PetersBaskin_YI)Peters-Baskin Step-Stool: yI (2)
\(yI = ln{(\exp{(b2*c1*d1)} + \exp{(b2*d1*x)})} / d1\)
[b2, c1, d1]
Peters-Baskin Step-Stool: yI (2) With Offset
\(yI = ln{(\exp{(b2*c1*d1)} + \exp{(b2*d1*x)})} / d1 + \text{Offset}\)
[b2, c1, d1, Offset]
Peters-Baskin Step-Stool: yII (3) (
PetersBaskin_YII)Peters-Baskin Step-Stool: yII (3)
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\)
[b2, c1, d1, b1]
Peters-Baskin Step-Stool: yII (3) With Offset
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1 + \text{Offset}\)
[b2, c1, d1, b1, Offset]
Peters-Baskin Step-Stool: yIII (6) (
PetersBaskin_YIII)Peters-Baskin Step-Stool: yIII (6)
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\\L = ln{( \exp{(b2*c1*d1)} + \exp{(b2*c2*d1)} )}\\yIII = yII - ln{( \exp{(d2*{(b1*c1 + L/d1)})} + \exp{(d2*yII)} )} / d2\)
[b2, c1, d1, b1, c2, d2]
Peters-Baskin Step-Stool: yIII (6) With Offset
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\\L = ln{( \exp{(b2*c1*d1)} + \exp{(b2*c2*d1)} )}\\yIII = yII - ln{( \exp{(d2*{(b1*c1 + L/d1)})} + \exp{(d2*yII)} )} / d2 + \text{Offset}\)
[b2, c1, d1, b1, c2, d2, Offset]
Peters-Baskin Step-Stool: yIV (9) (
PetersBaskin_YIV)Peters-Baskin Step-Stool: yIV (9)
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\\L = ln{( \exp{(b2*c1*d1)} + \exp{(b2*c2*d1)} )}\\yIII = yII - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII)} )} / d2\\yII,0 = ln{(\exp{(b2*c1*d1)} + 1.0 )} / d1\\yIII,0 = yII,0 - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII,0)} )} / d2\\yIV = yIII - yIII,0\)
[b2, c1, d1, b1, c2, d2]
Peters-Baskin Step-Stool: yIV (9) With Offset
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\\L = ln{( \exp{(b2*c1*d1)} + \exp{(b2*c2*d1)} )}\\yIII = yII - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII)} )} / d2\\yII,0 = ln{(\exp{(b2*c1*d1)} + 1.0 )} / d1\\yIII,0 = yII,0 - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII,0)} )} / d2\\yIV = yIII - yIII,0 + \text{Offset}\)
[b2, c1, d1, b1, c2, d2, Offset]
Peters-Baskin Step-Stool: yV (10) (
PetersBaskin_YV)Peters-Baskin Step-Stool: yV (10)
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\\L = ln{( \exp{(b2*c1*d1)} + \exp{(b2*c2*d1)} )}\\yIII = yII - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII)} )} / d2\\yII,0 = ln{(\exp{(b2*c1*d1)} + 1.0 )} / d1\\yIII,0 = yII,0 - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII,0)} )} / d2\\yIV = yIII - yIII,0 + q\)
[b2, c1, d1, b1, c2, d2, q]
Peters-Baskin Step-Stool: yV (10) Scaled (
PetersBaskin_YV_Scaled)Peters-Baskin Step-Stool: yV (10) Scaled
\(K = ln{( \exp{(b2*c1*d1)} + \exp{(b2*d1*x)} )}\\yII = b1*x + K/d1\\L = ln{( \exp{(b2*c1*d1)} + \exp{(b2*c2*d1)} )}\\yIII = yII - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII)} )} / d2\\yII,0 = ln{(\exp{(b2*c1*d1)} + 1.0 )} / d1\\yIII,0 = yII,0 - ln{( \exp{(d2*{(b1*c2 + L/d1)})} + \exp{(d2*yII,0)} )} / d2\\yIV = scale * {(yIII - yIII,0 )}+ q\)
[b2, c1, d1, b1, c2, d2, q, scale]
Richards (
Richards)Richards
\(y = 1.0 / {(a + b * e^{{(c*x)}})}^{d}\)
[a, b, c, d]
Richards With Offset
\(y = 1.0 / {(a + b * e^{{(c*x)}})}^{d} + \text{Offset}\)
[a, b, c, d, Offset]
Sigmoid A (
SigmoidA)Sigmoid A
\(y = 1.0 / {(1.0 + \exp{(-a{(x-b)})})}\)
[a, b]
Sigmoid A With Offset
\(y = 1.0 / {(1.0 + \exp{(-a{(x-b)})})} + \text{Offset}\)
[a, b, Offset]
Sigmoid A Modified (
SigmoidA_Modified)Sigmoid A Modified
\(y = 1.0 / {(1.0 + \exp{(-a{(x-b)})})}^{c}\)
[a, b, c]
Sigmoid A Modified With Offset
\(y = 1.0 / {(1.0 + \exp{(-a{(x-b)})})}^{c} + \text{Offset}\)
[a, b, c, Offset]
Sigmoid B (
SigmoidB)Sigmoid B
\(y = a / {(1.0 + \exp{(-{(x-b)}/c)})}\)
[a, b, c]
Sigmoid B With Offset
\(y = a / {(1.0 + \exp{(-{(x-b)}/c)})} + \text{Offset}\)
[a, b, c, Offset]
Sigmoid B Modified (
SigmoidB_Modified)Sigmoid B Modified
\(y = a / {(1.0 + \exp{(-{(x-b)}/c)})}^{d}\)
[a, b, c, d]
Sigmoid B Modified With Offset
\(y = a / {(1.0 + \exp{(-{(x-b)}/c)})}^{d} + \text{Offset}\)
[a, b, c, d, Offset]
Weibull (
Weibull)Weibull
\(y = a - b*\exp{(-cx^{d})}\)
[a, b, c, d]
Weibull CDF (
WeibullCDF)Weibull CDF
\(y = 1.0 - \exp{(-{(x/b)}^{a})}\)
[a, b]
Weibull CDF With Offset
\(y = 1.0 - \exp{(-{(x/b)}^{a})} + \text{Offset}\)
[a, b, Offset]
Weibull CDF Scaled (
WeibullCDF_scaled)Weibull CDF Scaled
\(y = Scale * {(1.0 - \exp{(-{(x/b)}^{a})})}\)
[a, b, Scale]
Weibull CDF Scaled With Offset
\(y = Scale * {(1.0 - \exp{(-{(x/b)}^{a})})} + \text{Offset}\)
[a, b, Scale, Offset]
Weibull PDF (
WeibullPDF)Weibull PDF
\(y = {(a/b)} * {(x/b)}^{{(a-1.0)}} *\exp{(-{(x/b)}^{a})}\)
[a, b]
Weibull PDF With Offset
\(y = {(a/b)} * {(x/b)}^{{(a-1.0)}} *\exp{(-{(x/b)}^{a})} + \text{Offset}\)
[a, b, Offset]
Simple¶
Simple Equation 01 (
SimpleEquation_01)Simple Equation 01
\(y = a\)
[a]
Simple Equation 02 (
SimpleEquation_02)Simple Equation 02
\(y = a/pow{(x,-2.0)}\)
[a]
Simple Equation 02 With Offset
\(y = a/pow{(x,-2.0)} + \text{Offset}\)
[a, Offset]
Simple Equation 03 (
SimpleEquation_03)Simple Equation 03
\(y = a*pow{(ln{(x)},b)}\)
[a, b]
Simple Equation 03 With Offset
\(y = a*pow{(ln{(x)},b)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 04 (
SimpleEquation_04)Simple Equation 04
\(y = a*pow{(x,3.0)}\)
[a]
Simple Equation 04 With Offset
\(y = a*pow{(x,3.0)} + \text{Offset}\)
[a, Offset]
Simple Equation 05 (
SimpleEquation_05)Simple Equation 05
\(y = a*pow{(x,4.0)}\)
[a]
Simple Equation 05 With Offset
\(y = a*pow{(x,4.0)} + \text{Offset}\)
[a, Offset]
Simple Equation 06 (
SimpleEquation_06)Simple Equation 06
\(y = x/{(a+b*pow{(x,2.0)})}\)
[a, b]
Simple Equation 06 With Offset
\(y = x/{(a+b*pow{(x,2.0)})} + \text{Offset}\)
[a, b, Offset]
Simple Equation 07 (
SimpleEquation_07)Simple Equation 07
\(y = a * pow{(b,x)} * pow{(x,c)}\)
[a, b, c]
Simple Equation 07 With Offset
\(y = a * pow{(b,x)} * pow{(x,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 08 (
SimpleEquation_08)Simple Equation 08
\(y = a*pow{(b,1.0/x)}*pow{(x,c)}\)
[a, b, c]
Simple Equation 08 With Offset
\(y = a*pow{(b,1.0/x)}*pow{(x,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 09 (
SimpleEquation_09)Simple Equation 09
\(y = a*\exp{(pow{(x-b,2.0)}/c)}\)
[a, b, c]
Simple Equation 09 With Offset
\(y = a*\exp{(pow{(x-b,2.0)}/c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 10 (
SimpleEquation_10)Simple Equation 10
\(y = a*\exp{(pow{(ln{(x)}-b,2.0)}/c)}\)
[a, b, c]
Simple Equation 10 With Offset
\(y = a*\exp{(pow{(ln{(x)}-b,2.0)}/c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 13 (
SimpleEquation_13)Simple Equation 13
\(y = a*pow{(x/b,c)}*\exp{(x/b)}\)
[a, b, c]
Simple Equation 13 With Offset
\(y = a*pow{(x/b,c)}*\exp{(x/b)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 14 (
SimpleEquation_14)Simple Equation 14
\(y = a*pow{(x,b+c*x)}\)
[a, b, c]
Simple Equation 14 With Offset
\(y = a*pow{(x,b+c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 15 (
SimpleEquation_15)Simple Equation 15
\(y = a*pow{(x,b+c/x)}\)
[a, b, c]
Simple Equation 15 With Offset
\(y = a*pow{(x,b+c/x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 16 (
SimpleEquation_16)Simple Equation 16
\(y = a*pow{(x,b+c*ln{(x)})}\)
[a, b, c]
Simple Equation 16 With Offset
\(y = a*pow{(x,b+c*ln{(x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 17 (
SimpleEquation_17)Simple Equation 17
\(y = a*pow{(x,b*x+c*pow{(x,2.0)})}\)
[a, b, c]
Simple Equation 17 With Offset
\(y = a*pow{(x,b*x+c*pow{(x,2.0)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 18 (
SimpleEquation_18)Simple Equation 18
\(y = a*\exp{(b*x+c*pow{(x,0.5)})}\)
[a, b, c]
Simple Equation 18 With Offset
\(y = a*\exp{(b*x+c*pow{(x,0.5)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 19 (
SimpleEquation_19)Simple Equation 19
\(y = a*\exp{(b/x+c*x)}\)
[a, b, c]
Simple Equation 19 With Offset
\(y = a*\exp{(b/x+c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 20 (
SimpleEquation_20)Simple Equation 20
\(y = {(a+x)}/{(b+c*x)}\)
[a, b, c]
Simple Equation 20 With Offset
\(y = {(a+x)}/{(b+c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 21 (
SimpleEquation_21)Simple Equation 21
\(y = {(a+x)}/{(b+c*pow{(x,2.0)})}\)
[a, b, c]
Simple Equation 21 With Offset
\(y = {(a+x)}/{(b+c*pow{(x,2.0)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 22 (
SimpleEquation_22)Simple Equation 22
\(y = a*{(\exp{(b*x)}-\exp{(c*x)})}\)
[a, b, c]
Simple Equation 22 With Offset
\(y = a*{(\exp{(b*x)}-\exp{(c*x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 23 (
SimpleEquation_23)Simple Equation 23
\(y = a*\exp{(b*\exp{(c*x)})}\)
[a, b, c]
Simple Equation 23 With Offset
\(y = a*\exp{(b*\exp{(c*x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 24 (
SimpleEquation_24)Simple Equation 24
\(y = a/{(1.0 + b * \exp{(c*x)})}\)
[a, b, c]
Simple Equation 24 With Offset
\(y = a/{(1.0 + b * \exp{(c*x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 25 (
SimpleEquation_25)Simple Equation 25
\(y = a/{(b+pow{(x,c)})}\)
[a, b, c]
Simple Equation 25 With Offset
\(y = a/{(b+pow{(x,c)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 26 (
SimpleEquation_26)Simple Equation 26
\(y = a/pow{(1.0 + b * pow{(x,c)},2.0)}\)
[a, b, c]
Simple Equation 26 With Offset
\(y = a/pow{(1.0 + b * pow{(x,c)},2.0)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 27 (
SimpleEquation_27)Simple Equation 27
\(y = pow{(a+b*x,c)}\)
[a, b, c]
Simple Equation 27 With Offset
\(y = pow{(a+b*x,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 28 (
SimpleEquation_28)Simple Equation 28
\(y = \exp{(a+b/x+c*ln{(x)})}\)
[a, b, c]
Simple Equation 28 With Offset
\(y = \exp{(a+b/x+c*ln{(x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 29 (
SimpleEquation_29)Simple Equation 29
\(y = a*\exp{(b*pow{(x,c)})}\)
[a, b, c]
Simple Equation 29 With Offset
\(y = a*\exp{(b*pow{(x,c)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 30 (
SimpleEquation_30)Simple Equation 30
\(y = a*pow{(x,b*pow{(x,c)})}\)
[a, b, c]
Simple Equation 30 With Offset
\(y = a*pow{(x,b*pow{(x,c)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 31 (
SimpleEquation_31)Simple Equation 31
\(y = a*ln{(x+b)}\)
[a, b]
Simple Equation 31 With Offset
\(y = a*ln{(x+b)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 32 (
SimpleEquation_32)Simple Equation 32
\(y = a/x+b*pow{(x,c)}\)
[a, b, c]
Simple Equation 32 With Offset
\(y = a/x+b*pow{(x,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 33 (
SimpleEquation_33)Simple Equation 33
\(y = a/x+b*\exp{(c/x)}\)
[a, b, c]
Simple Equation 33 With Offset
\(y = a/x+b*\exp{(c/x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 34 (
SimpleEquation_34)Simple Equation 34
\(y = a/x+b*\exp{(c*x)}\)
[a, b, c]
Simple Equation 34 With Offset
\(y = a/x+b*\exp{(c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 35 (
SimpleEquation_35)Simple Equation 35
\(y = a*\exp{(b*x)}/x\)
[a, b]
Simple Equation 35 With Offset
\(y = a*\exp{(b*x)}/x + \text{Offset}\)
[a, b, Offset]
Simple Equation 36 (
SimpleEquation_36)Simple Equation 36
\(y = a*\exp{(b/x)}/x\)
[a, b]
Simple Equation 36 With Offset
\(y = a*\exp{(b/x)}/x + \text{Offset}\)
[a, b, Offset]
Simple Equation 37 (
SimpleEquation_37)Simple Equation 37
\(y = a*pow{(x,b)}*ln{(x)}\)
[a, b]
Simple Equation 37 With Offset
\(y = a*pow{(x,b)}*ln{(x)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 38 (
SimpleEquation_38)Simple Equation 38
\(y = a*pow{(x,b)}/ln{(x)}\)
[a, b]
Simple Equation 38 With Offset
\(y = a*pow{(x,b)}/ln{(x)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 39 (
SimpleEquation_39)Simple Equation 39
\(y = a*pow{(x,b)}*ln{(x+c)}\)
[a, b, c]
Simple Equation 39 With Offset
\(y = a*pow{(x,b)}*ln{(x+c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 40 (
SimpleEquation_40)Simple Equation 40
\(y = a*pow{(ln{(x+b)},c)}\)
[a, b, c]
Simple Equation 40 With Offset
\(y = a*pow{(ln{(x+b)},c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 41 (
SimpleEquation_41)Simple Equation 41
\(y = a*pow{(x,b/x)}+c*x\)
[a, b, c]
Simple Equation 41 With Offset
\(y = a*pow{(x,b/x)}+c*x + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 42 (
SimpleEquation_42)Simple Equation 42
\(y = a*pow{(x,b/x)}+c*ln{(x)}\)
[a, b, c]
Simple Equation 42 With Offset
\(y = a*pow{(x,b/x)}+c*ln{(x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Reciprocal (
SimpleReciprocalA)Simple Reciprocal
\(y = a / x\)
[a]
Simple Reciprocal With Offset
\(y = a / x + \text{Offset}\)
[a, Offset]
Spline¶
Spline (
Spline)Spline
\(y = B-Spline Interpolation Curve\)
Trigonometric¶
Great Circle [Degrees] (
GreatCircleDegrees)Great Circle [Degrees]
\(latitude = arctan{(A*cos{({(B + longitude)} / 57.2957795131)})} *57.2957795131\)
[A, B]
Great Circle [radians] (
GreatCircleRadians)Great Circle [radians]
\(latitude = arctan{(A*cos{(B + longitude)})}\)
[A, B]
Hyperbolic Cosine [radians] (
HyperbolicCosine)Hyperbolic Cosine [radians]
\(y = amplitude * cosh{(pi * {(x - center)} / width)}\)
[amplitude, center, width]
Hyperbolic Cosine [radians] With Offset
\(y = amplitude * cosh{(pi * {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Hyperbolic Cosine [radians] (Nyquist Limited) (
HyperbolicCosine_NyquistLimited)Hyperbolic Cosine [radians] (Nyquist Limited)
\(y = amplitude * cosh{(pi * {(x - center)} / width)}\)
[amplitude, center, width]
Hyperbolic Cosine [radians] (Nyquist Limited) With Offset
\(y = amplitude * cosh{(pi * {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Cardinal Sine (sinc) [radians] (
Sinc)Cardinal Sine (sinc) [radians]
\(y = amplitude * sin{(pi * {(x - center)} / width)} / {(pi * {(x - center)} /width)}\)
[amplitude, center, width]
Cardinal Sine (sinc) [radians] With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)} / {(pi * {(x - center)} /width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Cardinal Sine (sinc) Squared [radians] (
SincSquared)Cardinal Sine (sinc) Squared [radians]
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2} / {(pi* {(x - center)} / width)}\)
[amplitude, center, width]
Cardinal Sine (sinc) Squared [radians] With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2} / {(pi* {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Cardinal Sine (sinc) Squared [radians] (Nyquist Limited) (
SincSquared_NyquistLimited)Cardinal Sine (sinc) Squared [radians] (Nyquist Limited)
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2} / {(pi* {(x - center)} / width)}\)
[amplitude, center, width]
Cardinal Sine (sinc) Squared [radians] (Nyquist Limited) With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2} / {(pi* {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Cardinal Sine (sinc) [radians] (Nyquist Limited) (
Sinc_NyquistLimited)Cardinal Sine (sinc) [radians] (Nyquist Limited)
\(y = amplitude * sin{(pi * {(x - center)} / width)} / {(pi * {(x - center)} /width)}\)
[amplitude, center, width]
Cardinal Sine (sinc) [radians] (Nyquist Limited) With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)} / {(pi * {(x - center)} /width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Sine [radians] (
Sine)Sine [radians]
\(y = amplitude * sin{(pi * {(x - center)} / width)}\)
[amplitude, center, width]
Sine [radians] With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Sine Squared [radians] (
SineSquared)Sine Squared [radians]
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2}\)
[amplitude, center, width]
Sine Squared [radians] With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2} +\text{Offset}\)
[amplitude, center, width, Offset]
Sine Squared [radians] (Nyquist Limited) (
SineSquared_NyquistLimited)Sine Squared [radians] (Nyquist Limited)
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2}\)
[amplitude, center, width]
Sine Squared [radians] (Nyquist Limited) With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)}^{2} +\text{Offset}\)
[amplitude, center, width, Offset]
Sine [radians] (Nyquist Limited) (
Sine_NyquistLimited)Sine [radians] (Nyquist Limited)
\(y = amplitude * sin{(pi * {(x - center)} / width)}\)
[amplitude, center, width]
Sine [radians] (Nyquist Limited) With Offset
\(y = amplitude * sin{(pi * {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Tangent [radians] (
Tangent)Tangent [radians]
\(y = amplitude * tan{(pi * {(x - center)} / width)}\)
[amplitude, center, width]
Tangent [radians] With Offset
\(y = amplitude * tan{(pi * {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Tangent [radians] (Nyquist Limited) (
Tangent_NyquistLimited)Tangent [radians] (Nyquist Limited)
\(y = amplitude * tan{(pi * {(x - center)} / width)}\)
[amplitude, center, width]
Tangent [radians] (Nyquist Limited) With Offset
\(y = amplitude * tan{(pi * {(x - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
UserDefinedFunction¶
User Defined Function (
UserDefinedFunction)User Defined Function
\(y = User Defined Function\)
YieldDensity¶
Bleasdale (
Bleasdale)Bleasdale
\(y = 1.0 / {(a + bx)}^{{(-1.0/c)}}\)
[a, b, c]
Bleasdale With Offset
\(y = 1.0 / {(a + bx)}^{{(-1.0/c)}} + \text{Offset}\)
[a, b, c, Offset]
Extended Holliday (
ExtendedHolliday)Extended Holliday
\(y = a / {(a + bx + cx^{2})}\)
[a, b, c]
Extended Holliday With Offset
\(y = a / {(a + bx + cx^{2})} + \text{Offset}\)
[a, b, c, Offset]
Harris (
Harris)Harris
\(y = 1.0 / {(a + bx^{c})}\)
[a, b, c]
Harris With Offset
\(y = 1.0 / {(a + bx^{c})} + \text{Offset}\)
[a, b, c, Offset]
Holliday (
Holliday)Holliday
\(y = 1.0 / {(a + bx + cx^{2})}\)
[a, b, c]
Holliday With Offset
\(y = 1.0 / {(a + bx + cx^{2})} + \text{Offset}\)
[a, b, c, Offset]
Inverse Bleasdale (
InverseBleasdale)Inverse Bleasdale
\(y = x / {(a + bx)}^{{(-1.0/c)}}\)
[a, b, c]
Inverse Bleasdale With Offset
\(y = x / {(a + bx)}^{{(-1.0/c)}} + \text{Offset}\)
[a, b, c, Offset]
InverseHarris (
InverseHarris)InverseHarris
\(y = x / {(a + bx^{c})}\)
[a, b, c]
InverseHarris With Offset
\(y = x / {(a + bx^{c})} + \text{Offset}\)
[a, b, c, Offset]
Nelder (
Nelder)Nelder
\(y = {(a + x)} / {(b + c{(a + x)} + d{(a + x)}^{2})}\)
[a, b, c, d]
Nelder With Offset
\(y = {(a + x)} / {(b + c{(a + x)} + d{(a + x)}^{2})} + \text{Offset}\)
[a, b, c, d, Offset]
3D Models¶
BioScience¶
Chen-Clayton (
ChenClayton)Chen-Clayton
\(r.h.{(T_{k},M)} = \exp{(-{(C1/T^{C2})} *\exp{(-C3*T^{C4}*M)})}\)
[C1, C2, C3, C4]
Chen-Clayton With Offset
\(r.h.{(T_{k},M)} = \exp{(-{(C1/T^{C2})} *\exp{(-C3*T^{C4}*M)})} + \text{Offset}\)
[C1, C2, C3, C4, Offset]
Chen-Clayton Scaled (
ChenClayton_scaled)Chen-Clayton Scaled
\(z = Scale * \exp{(-{(C1/T^{C2})} *\exp{(-C3*T^{C4}*M)})}\)
[C1, C2, C3, C4, Scale]
Chen-Clayton Scaled With Offset
\(z = Scale * \exp{(-{(C1/T^{C2})} *\exp{(-C3*T^{C4}*M)})} + \text{Offset}\)
[C1, C2, C3, C4, Scale, Offset]
High-Low Affinity Double Isotope Displacement (y = [Hot]) (
HighLowAffinityDoubleIsotopeDisplacement)High-Low Affinity Double Isotope Displacement (y = [Hot])
\(z = aby / {(1+b{(x+y)})} + cdy / {(1+d{(x+y)})}\)
[a, b, c, d]
High-Low Affinity Double Isotope Displacement (y = [Hot]) With Offset
\(z = aby / {(1+b{(x+y)})} + cdy / {(1+d{(x+y)})} + \text{Offset}\)
[a, b, c, d, Offset]
High-Low Affinity Isotope Displacement (y = [Hot]) (
HighLowAffinityIsotopeDisplacement)High-Low Affinity Isotope Displacement (y = [Hot])
\(z = aby / {(1+b{(x+y)})}\)
[a, b]
High-Low Affinity Isotope Displacement (y = [Hot]) With Offset
\(z = aby / {(1+b{(x+y)})} + \text{Offset}\)
[a, b, Offset]
Logistic Growth (
LogisticGrowth)Logistic Growth
\(z = a / {(1 + \exp{(-{(b + cx + dy + fxy)})})} + g\)
[a, b, c, d, f, g]
Michaelis-Menten Double Isotope Displacement (y = [Hot]) (
MichaelisMentenDoubleIsotopeDisplacement)Michaelis-Menten Double Isotope Displacement (y = [Hot])
\(z = ay / {(b + x + y)} + cy / {(d + x + y)}\)
[a, b, c, d]
Michaelis-Menten Double Isotope Displacement (y = [Hot]) With Offset
\(z = ay / {(b + x + y)} + cy / {(d + x + y)} + \text{Offset}\)
[a, b, c, d, Offset]
Michaelis-Menten Isotope Displacement (y = [Hot]) (
MichaelisMentenIsotopeDisplacement)Michaelis-Menten Isotope Displacement (y = [Hot])
\(z = ay / {(b + x + y)}\)
[a, b]
Michaelis-Menten Isotope Displacement (y = [Hot]) With Offset
\(z = ay / {(b + x + y)} + \text{Offset}\)
[a, b, Offset]
Modified Chung-Pfost (
ModifiedChungPfost)Modified Chung-Pfost
\(r.h.{(T,M)} = \exp{(-{(C1/{(T+C2)})} * \exp{(-C3*M)})}\)
[C1, C2, C3]
Modified Chung-Pfost With Offset
\(r.h.{(T,M)} = \exp{(-{(C1/{(T+C2)})} * \exp{(-C3*M)})} + \text{Offset}\)
[C1, C2, C3, Offset]
Modified Halsey (
ModifiedHalsey)Modified Halsey
\(r.h.{(T,M)} = \exp{(-\exp{(C1 + C2*T)} * M^{-C3})}\)
[C1, C2, C3]
Modified Halsey With Offset
\(r.h.{(T,M)} = \exp{(-\exp{(C1 + C2*T)} * M^{-C3})} + \text{Offset}\)
[C1, C2, C3, Offset]
Modified Halsey Scaled (
ModifiedHalsey_scaled)Modified Halsey Scaled
\(z = Scale * \exp{(-\exp{(C1 + C2*T)} * M^{-C3})}\)
[C1, C2, C3, Scale]
Modified Halsey Scaled With Offset
\(z = Scale * \exp{(-\exp{(C1 + C2*T)} * M^{-C3})} + \text{Offset}\)
[C1, C2, C3, Scale, Offset]
Modified Henderson (
ModifiedHenderson)Modified Henderson
\(r.h.{(T,M)} = 1 - \exp{(-C1 * {(T + C2)} * M^{C3})}\)
[C1, C2, C3]
Modified Henderson With Offset
\(r.h.{(T,M)} = 1 - \exp{(-C1 * {(T + C2)} * M^{C3})} + \text{Offset}\)
[C1, C2, C3, Offset]
Strohman-Yoerger (
StrohmanYoerger)Strohman-Yoerger
\(r.h.{(P_{s},M)} = \exp{(C1*\exp{(-C2*M)}*ln{(P_{s})} -C3*\exp{(-C4*M)})}\)
[C1, C2, C3, C4]
Strohman-Yoerger With Offset
\(r.h.{(P_{s},M)} = \exp{(C1*\exp{(-C2*M)}*ln{(P_{s})} -C3*\exp{(-C4*M)})} + \text{Offset}\)
[C1, C2, C3, C4, Offset]
EnzymeKinetics¶
Competitive Inhibition A (
CompetitiveInhibitionA)Competitive Inhibition A
\(z = ax / {(b{(1 + y/c)} + x)}\)
[a, b, c]
Competitive Inhibition A With Offset
\(z = ax / {(b{(1 + y/c)} + x)} + \text{Offset}\)
[a, b, c, Offset]
Competitive Inhibition B (
CompetitiveInhibitionB)Competitive Inhibition B
\(z = ay / {(b{(1 + x/c)} + y)}\)
[a, b, c]
Competitive Inhibition B With Offset
\(z = ay / {(b{(1 + x/c)} + y)} + \text{Offset}\)
[a, b, c, Offset]
Competitive Inhibition C (
CompetitiveInhibitionC)Competitive Inhibition C
\(z = axy / {(b{(1 + x/c)} + y)}\)
[a, b, c]
Competitive Inhibition C With Offset
\(z = axy / {(b{(1 + x/c)} + y)} + \text{Offset}\)
[a, b, c, Offset]
Inhibition By Competing Substrate A (
InhibitionByCompetingSubstrateA)Inhibition By Competing Substrate A
\(z = {(ax/b)} / {(1 + x/b + y/c)}\)
[a, b, c]
Inhibition By Competing Substrate A With Offset
\(z = {(ax/b)} / {(1 + x/b + y/c)} + \text{Offset}\)
[a, b, c, Offset]
Inhibition By Competing Substrate B (
InhibitionByCompetingSubstrateB)Inhibition By Competing Substrate B
\(z = {(ay/b)} / {(1 + y/b + x/c)}\)
[a, b, c]
Inhibition By Competing Substrate B With Offset
\(z = {(ay/b)} / {(1 + y/b + x/c)} + \text{Offset}\)
[a, b, c, Offset]
Inhibition By Competing Substrate C (
InhibitionByCompetingSubstrateC)Inhibition By Competing Substrate C
\(z = {(axy/b)} / {(1 + y/b + x/c)}\)
[a, b, c]
Inhibition By Competing Substrate C With Offset
\(z = {(axy/b)} / {(1 + y/b + x/c)} + \text{Offset}\)
[a, b, c, Offset]
Michaelis Menten Product Inhibition (
MichaelisMentenProductInhibition)Michaelis Menten Product Inhibition
\(z = {(ax/b - cy/d)} / {(1 + x/b + y/d)}\)
[a, b, c, d]
Michaelis Menten Product Inhibition With Offset
\(z = {(ax/b - cy/d)} / {(1 + x/b + y/d)} + \text{Offset}\)
[a, b, c, d, Offset]
Mixed Inhibition A (
MixedInhibitionA)Mixed Inhibition A
\(z = ax / {(b{(1 + y/c)} + x{(1 + y/d)})}\)
[a, b, c, d]
Mixed Inhibition A With Offset
\(z = ax / {(b{(1 + y/c)} + x{(1 + y/d)})} + \text{Offset}\)
[a, b, c, d, Offset]
Mixed Inhibition B (
MixedInhibitionB)Mixed Inhibition B
\(z = ay / {(b{(1 + x/c)} + y{(1 + x/d)})}\)
[a, b, c, d]
Mixed Inhibition B With Offset
\(z = ay / {(b{(1 + x/c)} + y{(1 + x/d)})} + \text{Offset}\)
[a, b, c, d, Offset]
Noncompetitive Inhibition A (
NoncompetitiveInhibitionA)Noncompetitive Inhibition A
\(z = ax / {({(b + x)}{(1 + y/c)})}\)
[a, b, c]
Noncompetitive Inhibition A With Offset
\(z = ax / {({(b + x)}{(1 + y/c)})} + \text{Offset}\)
[a, b, c, Offset]
Noncompetitive Inhibition B (
NoncompetitiveInhibitionB)Noncompetitive Inhibition B
\(z = ay / {({(b + y)}{(1 + x/c)})}\)
[a, b, c]
Noncompetitive Inhibition B With Offset
\(z = ay / {({(b + y)}{(1 + x/c)})} + \text{Offset}\)
[a, b, c, Offset]
Ping Pong Bi Bi A (
PingPongBiBiA)Ping Pong Bi Bi A
\(z = ax / {(bx + cy + xy)}\)
[a, b, c]
Ping Pong Bi Bi A With Offset
\(z = ax / {(bx + cy + xy)} + \text{Offset}\)
[a, b, c, Offset]
Ping Pong Bi Bi B (
PingPongBiBiB)Ping Pong Bi Bi B
\(z = ay / {(by + cx + xy)}\)
[a, b, c]
Ping Pong Bi Bi B With Offset
\(z = ay / {(by + cx + xy)} + \text{Offset}\)
[a, b, c, Offset]
Ping Pong Bi Bi C (
PingPongBiBiC)Ping Pong Bi Bi C
\(z = axy / {(by + cx + xy)}\)
[a, b, c]
Ping Pong Bi Bi C With Offset
\(z = axy / {(by + cx + xy)} + \text{Offset}\)
[a, b, c, Offset]
Uncompetitive Inhibition A (
UncompetitiveInhibitionA)Uncompetitive Inhibition A
\(z = ax / {(b + x{(1 + y/c)})}\)
[a, b, c]
Uncompetitive Inhibition A With Offset
\(z = ax / {(b + x{(1 + y/c)})} + \text{Offset}\)
[a, b, c, Offset]
Uncompetitive Inhibition B (
UncompetitiveInhibitionB)Uncompetitive Inhibition B
\(z = ay / {(b + y{(1 + x/c)})}\)
[a, b, c]
Uncompetitive Inhibition B With Offset
\(z = ay / {(b + y{(1 + x/c)})} + \text{Offset}\)
[a, b, c, Offset]
Exponential¶
Full Cubic Exponential (
FullCubicExponential)Full Cubic Exponential
\(z = a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}^{2} +f*\exp{(y)}^{2} + g*\exp{(x)}^{3} +h*\exp{(y)}^{3} + i*\exp{(x)}*\exp{(y)} +j*\exp{(x)}^{2}*\exp{(y)} + k*\exp{(x)}*\exp{(y)}^{2}\)
[a, b, c, d, f, g, h, i, j, k]
Transform Full Cubic Exponential (
FullCubicExponentialTransform)Transform Full Cubic Exponential
\(z = a + b*\exp{(m*x+n)} + c*\exp{(o*y+p)} + d*\exp{(m*x+n)}^{2} +f*\exp{(o*y+p)}^{2} + g*\exp{(m*x+n)}^{3} +h*\exp{(o*y+p)}^{3} + i*\exp{(m*x+n)}*\exp{(o*y+p)} +j*\exp{(m*x+n)}^{2}*\exp{(o*y+p)} +k*\exp{(m*x+n)}*\exp{(o*y+p)}^{2}\)
[a, b, c, d, f, g, h, i, j, k, m, n, o, p]
Full Quadratic Exponential (
FullQuadraticExponential)Full Quadratic Exponential
\(z = a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}^{2} +f*\exp{(y)}^{2} + g*\exp{(x)}*\exp{(y)}\)
[a, b, c, d, f, g]
Transform Full Quadratic Exponential (
FullQuadraticExponentialTransform)Transform Full Quadratic Exponential
\(z = a + b*\exp{(h*x+i)} + c*\exp{(j*y+k)} + d*\exp{(h*x+i)}^{2} +e*\exp{(j*y+k)}^{2} + f*\exp{(h*x+i)}*\exp{(j*y+k)}\)
[a, b, c, d, f, g, h, i, j, k]
Linear Exponential (
LinearExponential)Linear Exponential
\(z = a + b*\exp{(x)} + c*\exp{(y)}\)
[a, b, c]
Transform Linear Exponential (
LinearExponentialTransform)Transform Linear Exponential
\(z = a + b*\exp{(d*x+f)} + c*\exp{(g*y+h)}\)
[a, b, c, d, f, g, h]
Simplified Cubic Exponential (
SimplifiedCubicExponential)Simplified Cubic Exponential
\(z = a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}^{2} +e*\exp{(y)}^{2} + f*\exp{(x)}^{3} +g*\exp{(y)}^{3}\)
[a, b, c, d, f, g, h]
Transform Simplified Cubic Exponential (
SimplifiedCubicExponentialTransform)Transform Simplified Cubic Exponential
\(z = a + b*\exp{(i*x+j)} + c*\exp{(k*y+m)} + d*\exp{(i*x+j)}^{2} +f*\exp{(k*y+m)}^{2} + g*\exp{(i*x+j)}^{3} +h*\exp{(k*y+m)}^{3}\)
[a, b, c, d, f, g, h, i, j, k, m]
Simplified Quadratic Exponential (
SimplifiedQuadraticExponential)Simplified Quadratic Exponential
\(z = a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}^{2} +f*\exp{(y)}^{2}\)
[a, b, c, d, f]
Transform Simplified Quadratic Exponential (
SimplifiedQuadraticExponentialTransform)Transform Simplified Quadratic Exponential
\(z = a + b*\exp{(g*x+h)} + c*\exp{(i*y+j)} + d*\exp{(g*x+h)}^{2} +f*\exp{(i*y+j)}^{2}\)
[a, b, c, d, f, g, h, i, j]
Logarithmic¶
Full Cubic Logarithmic (
FullCubicLogarithmic)Full Cubic Logarithmic
\(z = a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}^{2} +f*ln{(y)}^{2} + g*ln{(x)}^{3} +h*ln{(y)}^{3} + i*ln{(x)}*ln{(y)} +j*ln{(x)}^{2}*ln{(y)} + k*ln{(x)}*ln{(y)}^{2}\)
[a, b, c, d, f, g, h, i, j, k]
Transform Full Cubic Logarithmic (
FullCubicLogarithmicTransform)Transform Full Cubic Logarithmic
\(z = a + b*ln{(m*x+n)} + c*ln{(o*y+p)} + d*ln{(m*x+n)}^{2} +f*ln{(o*y+p)}^{2} + g*ln{(m*x+n)}^{3} +h*ln{(o*y+p)}^{3} + i*ln{(m*x+n)}*ln{(o*y+p)} +j*ln{(m*x+n)}^{2}*ln{(o*y+p)} +k*ln{(m*x+n)}*ln{(o*y+p)}^{2}\)
[a, b, c, d, f, g, h, i, j, k, m, n, o, p]
Full Quadratic Logarithmic (
FullQuadraticLogarithmic)Full Quadratic Logarithmic
\(z = a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}^{2} +f*ln{(y)}^{2} + g*ln{(x)}*ln{(y)}\)
[a, b, c, d, f, g]
Transform Full Quadratic Logarithmic (
FullQuadraticLogarithmicTransform)Transform Full Quadratic Logarithmic
\(z = a + b*ln{(h*x+i)} + c*ln{(j*y+k)} + d*ln{(h*x+i)}^{2} +f*ln{(j*y+k)}^{2} + g*ln{(h*x+i)}*ln{(j*y+k)}\)
[a, b, c, d, f, g, h, i, j, k]
Linear Logarithmic (
LinearLogarithmic)Linear Logarithmic
\(z = a + b*ln{(x)} + c*ln{(y)}\)
[a, b, c]
Transform Linear Logarithmic (
LinearLogarithmicTransform)Transform Linear Logarithmic
\(z = a + b*ln{(d*x+f)} + c*ln{(g*y+h)}\)
[a, b, c, d, f, g, h]
Simplified Cubic Logarithmic (
SimplifiedCubicLogarithmic)Simplified Cubic Logarithmic
\(z = a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}^{2} +f*ln{(y)}^{2} + g*ln{(x)}^{3} +h*ln{(y)}^{3}\)
[a, b, c, d, f, g, h]
Transform Simplified Cubic Logarithmic (
SimplifiedCubicLogarithmicTransform)Transform Simplified Cubic Logarithmic
\(z = a + b*ln{(i*x+j)} + c*ln{(k*y+m)} + d*ln{(i*x+j)}^{2} +f*ln{(k*y+m)}^{2} + g*ln{(i*x+j)}^{3} +h*ln{(k*y+m)}^{3}\)
[a, b, c, d, f, g, h, i, j, k, m]
Simplified Quadratic Logarithmic (
SimplifiedQuadraticLogarithmic)Simplified Quadratic Logarithmic
\(z = a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}^{2} +f*ln{(y)}^{2}\)
[a, b, c, d, f]
Transform Simplified Quadratic Logarithmic (
SimplifiedQuadraticLogarithmicTransform)Transform Simplified Quadratic Logarithmic
\(z = a + b*ln{(g*x+h)} + c*ln{(i*y+j)} + d*ln{(g*x+h)}^{2} +f*ln{(i*y+j)}^{2}\)
[a, b, c, d, f, g, h, i, j]
Miscellaneous¶
Gary Cler’s Custom Equation Transform (
GaryCler_Transform)Gary Cler’s Custom Equation Transform
\(z = a * {(dx + f)}^{b} * {(gy + h)}^{c}\)
[a, b, c, d, f, g, h]
Gary Cler’s Custom Equation Transform With Offset
\(z = a * {(dx + f)}^{b} * {(gy + h)}^{c} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Gaussian Curvature Of Paraboloid (
GaussianCurvatureOfParaboloid)Gaussian Curvature Of Paraboloid
\(z = 4a^{2} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{2}\)
[a]
Gaussian Curvature Of Paraboloid With Offset
\(z = 4a^{2} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{2} +\text{Offset}\)
[a, Offset]
Gaussian Curvature Of Paraboloid Scaled (
GaussianCurvatureOfParaboloid_scaled)Gaussian Curvature Of Paraboloid Scaled
\(z = Scale * 4a^{2} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{2}\)
[a, Scale]
Gaussian Curvature Of Paraboloid Scaled With Offset
\(z = Scale * 4a^{2} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{2} +\text{Offset}\)
[a, Scale, Offset]
Gaussian Curvature Of Richmond’s Minimal Surface (
GaussianCurvatureOfRichmondsMinimalSurface)Gaussian Curvature Of Richmond’s Minimal Surface
\(z = -1.0 * a * {(x^{2} +y^{2})}^{3} / {(b + {(x^{2} +y^{2})}^{2})}^{4}\)
[a, b]
Gaussian Curvature Of Richmond’s Minimal Surface With Offset
\(z = -1.0 * a * {(x^{2} +y^{2})}^{3} / {(b + {(x^{2} +y^{2})}^{2})}^{4} + \text{Offset}\)
[a, b, Offset]
Gaussian Curvature Of Whitney’s Umbrella A (
GaussianCurvatureOfWhitneysUmbrellaA)Gaussian Curvature Of Whitney’s Umbrella A
\(z = -1.0 * a * y^{2} / {(x^{2} + a *{(y^{2} + y^{4})})}^{2}\)
[a]
Gaussian Curvature Of Whitney’s Umbrella A With Offset
\(z = -1.0 * a * y^{2} / {(x^{2} + a *{(y^{2} + y^{4})})}^{2} +\text{Offset}\)
[a, Offset]
Gaussian Curvature Of Whitney’s Umbrella B (
GaussianCurvatureOfWhitneysUmbrellaB)Gaussian Curvature Of Whitney’s Umbrella B
\(z = -1.0 * a * x^{2} / {(y^{2} + a *{(x^{2} + x^{4})})}^{2}\)
[a]
Gaussian Curvature Of Whitney’s Umbrella B With Offset
\(z = -1.0 * a * x^{2} / {(y^{2} + a *{(x^{2} + x^{4})})}^{2} +\text{Offset}\)
[a, Offset]
Liping Zheng’s core loss coefficients (
LipingZheng)Liping Zheng’s core loss coefficients
\(z = ax^{2}y + bx^{2}y^{2} +cx^{1.5}y^{1.5}\)
[a, b, c]
Liping Zheng’s core loss coefficients With Offset
\(z = ax^{2}y + bx^{2}y^{2} +cx^{1.5}y^{1.5} + \text{Offset}\)
[a, b, c, Offset]
Mean Curvature Of Paraboloid (
MeanCurvatureOfParaboloid)Mean Curvature Of Paraboloid
\(z = 2 * {(a + 2a^{3} * {(x^{2} +y^{2})})} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{1.5}\)
[a]
Mean Curvature Of Paraboloid With Offset
\(z = 2 * {(a + 2a^{3} * {(x^{2} +y^{2})})} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{1.5} +\text{Offset}\)
[a, Offset]
Mean Curvature Of Paraboloid Scaled (
MeanCurvatureOfParaboloid_scaled)Mean Curvature Of Paraboloid Scaled
\(z = Scale * {(a + 2a^{3} * {(x^{2} +y^{2})})} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{1.5}\)
[a, Scale]
Mean Curvature Of Paraboloid Scaled With Offset
\(z = Scale * {(a + 2a^{3} * {(x^{2} +y^{2})})} / {(1 + 4a^{2} *{(x^{2} + y^{2})})}^{1.5} +\text{Offset}\)
[a, Scale, Offset]
Mean Curvature Of Whitney’s Umbrella A (
MeanCurvatureOfWhitneysUmbrellaA)Mean Curvature Of Whitney’s Umbrella A
\(z = -1.0 * x * {(a + b * y^{2})} / {(x^{2} +a * {(y^{2} + y^{4})})}^{1.5}\)
[a, b]
Mean Curvature Of Whitney’s Umbrella A With Offset
\(z = -1.0 * x * {(a + b * y^{2})} / {(x^{2} +a * {(y^{2} + y^{4})})}^{1.5}+ \text{Offset}\)
[a, b, Offset]
Mean Curvature Of Whitney’s Umbrella B (
MeanCurvatureOfWhitneysUmbrellaB)Mean Curvature Of Whitney’s Umbrella B
\(z = -1.0 * y * {(a + b * x^{2})} / {(y^{2} +a * {(x^{2} + x^{4})})}^{1.5}\)
[a, b]
Mean Curvature Of Whitney’s Umbrella B With Offset
\(z = -1.0 * y * {(a + b * x^{2})} / {(y^{2} +a * {(x^{2} + x^{4})})}^{1.5}+ \text{Offset}\)
[a, b, Offset]
Menn’s Surface A (
MennSurfaceA)Menn’s Surface A
\(z = ax^{4} + bx^{2}y -cy^{2}\)
[a, b, c]
Menn’s Surface A With Offset
\(z = ax^{4} + bx^{2}y -cy^{2} + \text{Offset}\)
[a, b, c, Offset]
Menn’s Surface B (
MennSurfaceB)Menn’s Surface B
\(z = ay^{4} + by^{2}x -cx^{2}\)
[a, b, c]
Menn’s Surface B With Offset
\(z = ay^{4} + by^{2}x -cx^{2} + \text{Offset}\)
[a, b, c, Offset]
Monkey Saddle A (
MonkeySaddleA)Monkey Saddle A
\(z = ax^{3} - bxy^{2}\)
[a, b]
Monkey Saddle A With Offset
\(z = ax^{3} - bxy^{2} + \text{Offset}\)
[a, b, Offset]
Monkey Saddle B (
MonkeySaddleB)Monkey Saddle B
\(z = ay^{3} - byx^{2}\)
[a, b]
Monkey Saddle B With Offset
\(z = ay^{3} - byx^{2} + \text{Offset}\)
[a, b, Offset]
Monkey Saddle Transform A (
MonkeySaddle_TransformA)Monkey Saddle Transform A
\(z = a{(cx + d)}^{3} - b{(cx + d)}{(fy + g)}^{2}\)
[a, b, c, d, f, g]
Monkey Saddle Transform A With Offset
\(z = a{(cx + d)}^{3} - b{(cx + d)}{(fy + g)}^{2}+ \text{Offset}\)
[a, b, c, d, f, g, Offset]
Monkey Saddle Transform B (
MonkeySaddle_TransformB)Monkey Saddle Transform B
\(z = a{(cy + d)}^{3} - b{(cy + d)}{(fx + g)}^{2}\)
[a, b, c, d, f, g]
Monkey Saddle Transform B With Offset
\(z = a{(cy + d)}^{3} - b{(cy + d)}{(fx + g)}^{2}+ \text{Offset}\)
[a, b, c, d, f, g, Offset]
Paraboloid (
Paraboloid)Paraboloid
\(z = a * {(x^{2} + y^{2})}\)
[a]
Paraboloid With Offset
\(z = a * {(x^{2} + y^{2})} + \text{Offset}\)
[a, Offset]
Paraboloid Transform (
Paraboloid_Transform)Paraboloid Transform
\(z = a * {({(bx + c)}^{2} + {(dy + f)}^{2})}\)
[a, b, c, d, f]
Paraboloid Transform With Offset
\(z = a * {({(bx + c)}^{2} + {(dy + f)}^{2})} +\text{Offset}\)
[a, b, c, d, f, Offset]
Paschen’s Law for Breakdown Field Strength (
PaschensBreakdownFieldStrengthLaw)Paschen’s Law for Breakdown Field Strength
\(Ebreakdown = pressure * {(a / {(ln{(pressure * distance)} + b)})}\)
[a, b]
Paschen’s Law for Breakdown Field Strength With Offset
\(Ebreakdown = pressure * {(a / {(ln{(pressure * distance)} + b)})} + \text{Offset}\)
[a, b, Offset]
Paschen’s Law for Breakdown Voltage (
PaschensBreakdownVoltageLaw)Paschen’s Law for Breakdown Voltage
\(Vbreakdown = a{(pressure * distance)} / {(ln{(pressure * distance)} + b)}\)
[a, b]
Paschen’s Law for Breakdown Voltage With Offset
\(Vbreakdown = a{(pressure * distance)} / {(ln{(pressure * distance)} + b)} +\text{Offset}\)
[a, b, Offset]
Rex Kelfkens’ Custom Equation (
RexKelfkens)Rex Kelfkens’ Custom Equation
\(z = \exp{(A+B*ln{(x)}+C*ln{(y)})}\)
[A, B, C]
Rex Kelfkens’ Custom Equation With Offset
\(z = \exp{(A+B*ln{(x)}+C*ln{(y)})} + \text{Offset}\)
[A, B, C, Offset]
Rex Kelfkens’ Custom Equation Transform (
RexKelfkensTransform)Rex Kelfkens’ Custom Equation Transform
\(z = \exp{(A+B*ln{(x * xscale + xoffset)}+C*ln{(y * yscale + yoffset)})}\)
[A, B, C, xscale, xoffset, yscale, yoffset]
Rex Kelfkens’ Custom Equation Transform With Offset
\(z = \exp{(A+B*ln{(x * xscale + xoffset)}+C*ln{(y * yscale + yoffset)})} +\text{Offset}\)
[A, B, C, xscale, xoffset, yscale, yoffset, Offset]
NIST¶
NIST Nelson (
NIST_Nelson)NIST Nelson
\(log{(y)} = b1 - b2 * X1 * \exp{(-b3*X2)}\)
[b1, b2, b3]
NIST Nelson Autolog (
NIST_NelsonAutolog)NIST Nelson Autolog
\(z = \exp{(b1 - b2 * x * \exp{(-b3*y)})}\)
[b1, b2, b3]
NIST Nelson Autolog With Offset
\(z = \exp{(b1 - b2 * x * \exp{(-b3*y)})} + \text{Offset}\)
[b1, b2, b3, Offset]
Optical¶
Sag For Asphere 0 (
SagForAsphere0)Sag For Asphere 0
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})}\)
[k, r]
Sag For Asphere 0 With Offset
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} + \text{Offset}\)
[k, r, Offset]
Sag For Asphere 0 Borisovsky (
SagForAsphere0_Borisovsky)Sag For Asphere 0 Borisovsky
\(s^{2} = {(x - a)}^{2} + {(y -b)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} + offset\)
[a, b, k, r, offset]
Sag For Asphere 0 Borisovsky With Offset
\(s^{2} = {(x - a)}^{2} + {(y -b)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} + offset +\text{Offset}\)
[a, b, k, r, offset, Offset]
Transform Sag For Asphere 0 (
SagForAsphere0_Transform)Transform Sag For Asphere 0
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})}\)
[k, r, a, b, c, d]
Transform Sag For Asphere 0 With Offset
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} + \text{Offset}\)
[k, r, a, b, c, d, Offset]
Sag For Asphere 0 Scaled (
SagForAsphere0_scaled)Sag For Asphere 0 Scaled
\(s^{2} = x^{2} + y^{2}\\z = Scale * {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})}\)
[k, r, Scale]
Sag For Asphere 0 Scaled With Offset
\(s^{2} = x^{2} + y^{2}\\z = Scale * {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} + \text{Offset}\)
[k, r, Scale, Offset]
Sag For Asphere 1 (
SagForAsphere1)Sag For Asphere 1
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4}\)
[k, r, A4]
Sag For Asphere 1 With Offset
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + \text{Offset}\)
[k, r, A4, Offset]
Transform Sag For Asphere 1 (
SagForAsphere1_Transform)Transform Sag For Asphere 1
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4}\)
[k, r, A4, a, b, c, d]
Transform Sag For Asphere 1 With Offset
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + \text{Offset}\)
[k, r, A4, a, b, c, d, Offset]
Sag For Asphere 2 (
SagForAsphere2)Sag For Asphere 2
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6}\)
[k, r, A4, A6]
Sag For Asphere 2 With Offset
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6} + \text{Offset}\)
[k, r, A4, A6, Offset]
Transform Sag For Asphere 2 (
SagForAsphere2_Transform)Transform Sag For Asphere 2
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6}\)
[k, r, A4, A6, a, b, c, d]
Transform Sag For Asphere 2 With Offset
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6} + \text{Offset}\)
[k, r, A4, A6, a, b, c, d, Offset]
Sag For Asphere 3 (
SagForAsphere3)Sag For Asphere 3
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6} +A8*s^{8}\)
[k, r, A4, A6, A8]
Sag For Asphere 3 With Offset
\(s^{2} = x^{2} + y^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6} +A8*s^{8} + \text{Offset}\)
[k, r, A4, A6, A8, Offset]
Transform Sag For Asphere 3 (
SagForAsphere3_Transform)Transform Sag For Asphere 3
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6} +A8*s^{8}\)
[k, r, A4, A6, A8, a, b, c, d]
Transform Sag For Asphere 3 With Offset
\(s^{2} = {(ax+b)}^{2} +{(cy+d)}^{2}\\z = {(s^{2}/r)} /{(1+{(1-{(k+1)}{(s/r)}^{2})}^{1/2})} +A4*s^{4} + A6*s^{6} +A8*s^{8} + \text{Offset}\)
[k, r, A4, A6, A8, a, b, c, d, Offset]
Peak¶
Extreme Value A (
ExtremeValueA)Extreme Value A
\(z = a * \exp{(-\exp{(-{(x-b)}/c)}-{(x-b)}/c+1)} + d *\exp{(-\exp{(-{(y-f)}/g)}-{(y-f)}/g+1)}\)
[a, b, c, d, f, g]
Extreme Value A With Offset
\(z = a * \exp{(-\exp{(-{(x-b)}/c)}-{(x-b)}/c+1)} + d *\exp{(-\exp{(-{(y-f)}/g)}-{(y-f)}/g+1)} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Extreme Value B (
ExtremeValueB)Extreme Value B
\(z = a * \exp{(-\exp{(-{(x-b)}/c)}-{(x-b)}/c+1)} * \exp{(-\exp{(-{(y-d)}/f)}-{(y-d)}/f+1)}\)
[a, b, c, d, f]
Extreme Value B With Offset
\(z = a * \exp{(-\exp{(-{(x-b)}/c)}-{(x-b)}/c+1)} * \exp{(-\exp{(-{(y-d)}/f)}-{(y-d)}/f+1)} +\text{Offset}\)
[a, b, c, d, f, Offset]
Gaussian A (
GaussianA)Gaussian A
\(z = a * \exp{(-0.5 * {({({(x-b)}/c)}^{2} +{({(y-d)}/f)}^{2})})}\)
[a, b, c, d, f]
Gaussian A With Offset
\(z = a * \exp{(-0.5 * {({({(x-b)}/c)}^{2} +{({(y-d)}/f)}^{2})})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Gaussian B (
GaussianB)Gaussian B
\(z = a * \exp{(-0.5 * {({({(x-b)}/c)}^{2})})} + d * \exp{(-0.5 *{({({(y-f)}/g)}^{2})})}\)
[a, b, c, d, f, g]
Gaussian B With Offset
\(z = a * \exp{(-0.5 * {({({(x-b)}/c)}^{2})})} + d * \exp{(-0.5 *{({({(y-f)}/g)}^{2})})} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Log-Normal A (
LogNormalA)Log-Normal A
\(z = a * \exp{(-0.5 * {({({(ln{(x)}-b)}/c)}^{2} +{({(ln{(y)}-d)}/f)}^{2})})}\)
[a, b, c, d, f]
Log-Normal A With Offset
\(z = a * \exp{(-0.5 * {({({(ln{(x)}-b)}/c)}^{2} +{({(ln{(y)}-d)}/f)}^{2})})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Log-Normal B (
LogNormalB)Log-Normal B
\(z = a * \exp{(-0.5 * {({({(ln{(x)}-b)}/c)}^{2})})} + d * \exp{(-0.5 *{({({(ln{(y)}-f)}/g)}^{2})})}\)
[a, b, c, d, f, g]
Log-Normal B With Offset
\(z = a * \exp{(-0.5 * {({({(ln{(x)}-b)}/c)}^{2})})} + d * \exp{(-0.5 *{({({(ln{(y)}-f)}/g)}^{2})})} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Logistic A (
LogisticA)Logistic A
\(z = 4a * \exp{(-{({(x-b)}/c)})}/{({(1+\exp{(-{({(x-b)}/c)})})}^{2})} + 4d *\exp{(-{({(y-f)}/g)})}/{({(1+\exp{(-{({(y-f)}/g)})})}^{2})}\)
[a, b, c, d, f, g]
Logistic A With Offset
\(z = 4a * \exp{(-{({(x-b)}/c)})}/{({(1+\exp{(-{({(x-b)}/c)})})}^{2})} + 4d *\exp{(-{({(y-f)}/g)})}/{({(1+\exp{(-{({(y-f)}/g)})})}^{2})} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Logistic B (
LogisticB)Logistic B
\(z = 16a * \exp{(-{({(x-b)}/c)}-{({(y-d)}/f)})} /{({(1+\exp{(-{({(x-b)}/c)})})}^{2} *{(1+\exp{(-{({(y-d)}/f)})})}^{2})}\)
[a, b, c, d, f]
Logistic B With Offset
\(z = 16a * \exp{(-{({(x-b)}/c)}-{({(y-d)}/f)})} /{({(1+\exp{(-{({(x-b)}/c)})})}^{2} *{(1+\exp{(-{({(y-d)}/f)})})}^{2})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Lorentzian A (
LorentzianA)Lorentzian A
\(z = a /{({(1+{({(x-b)}/c)}^{2})}*{(1+{({(y-d)}/f)}^{2})})}\)
[a, b, c, d, f]
Lorentzian A With Offset
\(z = a /{({(1+{({(x-b)}/c)}^{2})}*{(1+{({(y-d)}/f)}^{2})})} +\text{Offset}\)
[a, b, c, d, f, Offset]
Lorentzian B (
LorentzianB)Lorentzian B
\(z = a / {(1+{({(x-b)}/c)}^{2})} + d *{(1+{({(y-f)}/g)}^{2})}\)
[a, b, c, d, f, g]
Lorentzian B With Offset
\(z = a / {(1+{({(x-b)}/c)}^{2})} + d *{(1+{({(y-f)}/g)}^{2})} + \text{Offset}\)
[a, b, c, d, f, g, Offset]
Polyfunctional¶
User-Selectable Polyfunctional (
UserSelectablePolyfunctional)User-Selectable Polyfunctional
\(z = user-selectable function\)
[]
Polynomial¶
Full Cubic (
FullCubic)Full Cubic
\(z = a + bx + cy + dx^{2} + fy^{2} +gx^{3} + hy^{3} + ixy +jx^{2}y + kxy^{2}\)
[a, b, c, d, f, g, h, i, j, k]
Full Quadratic (
FullQuadratic)Full Quadratic
\(z = a + bx + cy + dx^{2} + fy^{2} + gxy\)
[a, b, c, d, f, g]
Linear (
Linear)Linear
\(z = a + bx + cy\)
[a, b, c]
Simplified Cubic (
SimplifiedCubic)Simplified Cubic
\(z = a + bx + cy + dx^{2} + fy^{2} +gx^{3} + hy^{3}\)
[a, b, c, d, f, g, h]
Simplified Quadratic (
SimplifiedQuadratic)Simplified Quadratic
\(z = a + bx + cy + dx^{2} + fy^{2}\)
[a, b, c, d, f]
User-Selectable Polynomial (
UserSelectablePolynomial)User-Selectable Polynomial
\(z = user-selectable polynomial\)
Power¶
Power A (
PowerA)Power A
\(z = a * {(x^{b} + y^{c})}\)
[a, b, c]
Power A With Offset
\(z = a * {(x^{b} + y^{c})} + \text{Offset}\)
[a, b, c, Offset]
Transform Power A (
PowerA_Transform)Transform Power A
\(z = a * {({(dx + f)}^{b} + {(gy + h)}^{c})}\)
[a, b, c, d, f, g, h]
Transform Power A With Offset
\(z = a * {({(dx + f)}^{b} + {(gy + h)}^{c})} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Power B (
PowerB)Power B
\(z = a + x^{b} + y^{c}\)
[a, b, c]
Transform Power B (
PowerB_Transform)Transform Power B
\(z = a + {(dx + f)}^{b} + {(gy + h)}^{c}\)
[a, b, c, d, f, g, h]
Power C (
PowerC)Power C
\(z = a + x^{b} * y^{c}\)
[a, b, c]
Transform Power C (
PowerC_Transform)Transform Power C
\(z = a + {(dx + f)}^{b} * {(gy + h)}^{c}\)
[a, b, c, d, f, g, h]
Power D (
PowerD)Power D
\(z = ax^{b} + cy^{d}\)
[a, b, c, d]
Power D With Offset
\(z = ax^{b} + cy^{d} + \text{Offset}\)
[a, b, c, d, Offset]
Transform Power D (
PowerD_Transform)Transform Power D
\(z = a{(fx + g)}^{b} + c{(hy + i)}^{d}\)
[a, b, c, d, f, g, h, i]
Transform Power D With Offset
\(z = a{(fx + g)}^{b} + c{(hy + i)}^{d} + \text{Offset}\)
[a, b, c, d, f, g, h, i, Offset]
Power E (
PowerE)Power E
\(z = a * x^{b} * y^{c}\)
[a, b, c]
Power E With Offset
\(z = a * x^{b} * y^{c} + \text{Offset}\)
[a, b, c, Offset]
Transform Power E (
PowerE_Transform)Transform Power E
\(z = a * {(dx + f)}^{b} * {(gy + h)}^{c}\)
[a, b, c, d, f, g, h]
Transform Power E With Offset
\(z = a * {(dx + f)}^{b} * {(gy + h)}^{c} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational¶
Rational A (
RationalA)Rational A
\(z = {(a + bx + cy)}/{(1 + dx + fy)}\)
[a, b, c, d, f]
Rational A With Offset
\(z = {(a + bx + cy)}/{(1 + dx + fy)} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational B (
RationalB)Rational B
\(z = {(a + b*ln{(x)} + c*ln{(y)})}/{(1 + dx + fy)}\)
[a, b, c, d, f]
Rational B With Offset
\(z = {(a + b*ln{(x)} + c*ln{(y)})}/{(1 + dx + fy)} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational C (
RationalC)Rational C
\(z = {(a + b*\exp{(x)} + c*ln{(y)})}/{(1 + dx + fy)}\)
[a, b, c, d, f]
Rational C With Offset
\(z = {(a + b*\exp{(x)} + c*ln{(y)})}/{(1 + dx + fy)} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational D (
RationalD)Rational D
\(z = {(a + b*ln{(x)} + c*\exp{(y)})}/{(1 + dx + fy)}\)
[a, b, c, d, f]
Rational D With Offset
\(z = {(a + b*ln{(x)} + c*\exp{(y)})}/{(1 + dx + fy)} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational E (
RationalE)Rational E
\(z = {(a + b*\exp{(x)} + c*\exp{(y)})}/{(1 + dx + fy)}\)
[a, b, c, d, f]
Rational E With Offset
\(z = {(a + b*\exp{(x)} + c*\exp{(y)})}/{(1 + dx + fy)} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational F (
RationalF)Rational F
\(z = {(a + bx + cy)}/{(1 + d*ln{(x)} + f*ln{(y)})}\)
[a, b, c, d, f]
Rational F With Offset
\(z = {(a + bx + cy)}/{(1 + d*ln{(x)} + f*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational G (
RationalG)Rational G
\(z = {(a + bx + cy)}/{(1 + d*\exp{(x)} + f*ln{(y)})}\)
[a, b, c, d, f]
Rational G With Offset
\(z = {(a + bx + cy)}/{(1 + d*\exp{(x)} + f*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational H (
RationalH)Rational H
\(z = {(a + bx + cy)}/{(1 + d*ln{(x)} + f*\exp{(y)})}\)
[a, b, c, d, f]
Rational H With Offset
\(z = {(a + bx + cy)}/{(1 + d*ln{(x)} + f*\exp{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational I (
RationalI)Rational I
\(z = {(a + bx + cy)}/{(1 + d*\exp{(x)} + f*\exp{(y)})}\)
[a, b, c, d, f]
Rational I With Offset
\(z = {(a + bx + cy)}/{(1 + d*\exp{(x)} + f*\exp{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational J (
RationalJ)Rational J
\(z = {(a + b*ln{(x)} + c*ln{(y)})}/{(1 + d*ln{(x)} + f*ln{(y)})}\)
[a, b, c, d, f]
Rational J With Offset
\(z = {(a + b*ln{(x)} + c*ln{(y)})}/{(1 + d*ln{(x)} + f*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational K (
RationalK)Rational K
\(z = {(a + b*\exp{(x)} + c*ln{(y)})}/{(1 + d*\exp{(x)} + f*ln{(y)})}\)
[a, b, c, d, f]
Rational K With Offset
\(z = {(a + b*\exp{(x)} + c*ln{(y)})}/{(1 + d*\exp{(x)} + f*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational L (
RationalL)Rational L
\(z = {(a + b*ln{(x)} + c*\exp{(y)})}/{(1 + d*ln{(x)} + f*\exp{(y)})}\)
[a, b, c, d, f]
Rational L With Offset
\(z = {(a + b*ln{(x)} + c*\exp{(y)})}/{(1 + d*ln{(x)} + f*\exp{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational M (
RationalM)Rational M
\(z = {(a + b*\exp{(x)} + c*\exp{(y)})}/{(1 + d*\exp{(x)} + f*\exp{(y)})}\)
[a, b, c, d, f]
Rational M With Offset
\(z = {(a + b*\exp{(x)} + c*\exp{(y)})}/{(1 + d*\exp{(x)} + f*\exp{(y)})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Rational N (
RationalN)Rational N
\(z = {(a + bx + cy + dxy)}/{(1 + fx + gy + hxy)}\)
[a, b, c, d, f, g, h]
Rational N With Offset
\(z = {(a + bx + cy + dxy)}/{(1 + fx + gy + hxy)} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational O (
RationalO)Rational O
\(z = {(a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}ln{(y)})}/{(1 + fx + gy + hxy)}\)
[a, b, c, d, f, g, h]
Rational O With Offset
\(z = {(a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}ln{(y)})}/{(1 + fx + gy + hxy)} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational P (
RationalP)Rational P
\(z = {(a + b*\exp{(x)} + c*ln{(y)} + d*\exp{(x)}ln{(y)})}/{(1 + fx + gy + hxy)}\)
[a, b, c, d, f, g, h]
Rational P With Offset
\(z = {(a + b*\exp{(x)} + c*ln{(y)} + d*\exp{(x)}ln{(y)})}/{(1 + fx + gy + hxy)} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational Q (
RationalQ)Rational Q
\(z = {(a + b*ln{(x)} + c*\exp{(y)} + d*ln{(x)}\exp{(y)})}/{(1 + fx + gy + hxy)}\)
[a, b, c, d, f, g, h]
Rational Q With Offset
\(z = {(a + b*ln{(x)} + c*\exp{(y)} + d*ln{(x)}\exp{(y)})}/{(1 + fx + gy + hxy)} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational R (
RationalR)Rational R
\(z = {(a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}\exp{(y)})}/{(1 + fx + gy + hxy)}\)
[a, b, c, d, f, g, h]
Rational R With Offset
\(z = {(a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}\exp{(y)})}/{(1 + fx + gy + hxy)} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational S (
RationalS)Rational S
\(z = {(a + bx + cy + dxy)}/{(1 + f*ln{(x)} + g*ln{(y)} + h*ln{(x)}*ln{(y)})}\)
[a, b, c, d, f, g, h]
Rational S With Offset
\(z = {(a + bx + cy + dxy)}/{(1 + f*ln{(x)} + g*ln{(y)} + h*ln{(x)}*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational T (
RationalT)Rational T
\(z = {(a + bx + cy + dxy)}/{(1 + f*\exp{(x)} + g*ln{(y)} + h*\exp{(x)}*ln{(y)})}\)
[a, b, c, d, f, g, h]
Rational T With Offset
\(z = {(a + bx + cy + dxy)}/{(1 + f*\exp{(x)} + g*ln{(y)} + h*\exp{(x)}*ln{(y)})} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational U (
RationalU)Rational U
\(z = {(a + bx + cy + dxy)}/{(1 + f*ln{(x)} + g*\exp{(y)} + h*ln{(x)}*\exp{(y)})}\)
[a, b, c, d, f, g, h]
Rational U With Offset
\(z = {(a + bx + cy + dxy)}/{(1 + f*ln{(x)} + g*\exp{(y)} + h*ln{(x)}*\exp{(y)})} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational V (
RationalV)Rational V
\(z = {(a + bx + cy + dxy)}/{(1 + f*\exp{(x)} + g*\exp{(y)} + h*\exp{(x)}*\exp{(y)})}\)
[a, b, c, d, f, g, h]
Rational V With Offset
\(z = {(a + bx + cy + dxy)}/{(1 + f*\exp{(x)} + g*\exp{(y)} + h*\exp{(x)}*\exp{(y)})} +\text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational W (
RationalW)Rational W
\(z = {(a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}*ln{(y)})}/{(1 + f*ln{(x)} + g*ln{(y)} +h*ln{(x)}*ln{(y)})}\)
[a, b, c, d, f, g, h]
Rational W With Offset
\(z = {(a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}*ln{(y)})}/{(1 + f*ln{(x)} + g*ln{(y)} +h*ln{(x)}*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational X (
RationalX)Rational X
\(z = {(a + b*\exp{(x)} + c*ln{(y)} + d*\exp{(x)}*ln{(y)})}/{(1 + f*\exp{(x)} + g*ln{(y)} +h*\exp{(x)}*ln{(y)})}\)
[a, b, c, d, f, g, h]
Rational X With Offset
\(z = {(a + b*\exp{(x)} + c*ln{(y)} + d*\exp{(x)}*ln{(y)})}/{(1 + f*\exp{(x)} + g*ln{(y)} +h*\exp{(x)}*ln{(y)})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational Y (
RationalY)Rational Y
\(z = {(a + b*ln{(x)} + c*\exp{(y)} + d*ln{(x)}*\exp{(y)})}/{(1 + f*ln{(x)} + g*\exp{(y)} +h*ln{(x)}*\exp{(y)})}\)
[a, b, c, d, f, g, h]
Rational Y With Offset
\(z = {(a + b*ln{(x)} + c*\exp{(y)} + d*ln{(x)}*\exp{(y)})}/{(1 + f*ln{(x)} + g*\exp{(y)} +h*ln{(x)}*\exp{(y)})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
Rational Z (
RationalZ)Rational Z
\(z = {(a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}*\exp{(y)})}/{(1 + f*\exp{(x)} + g*\exp{(y)}+ h*\exp{(x)}*\exp{(y)})}\)
[a, b, c, d, f, g, h]
Rational Z With Offset
\(z = {(a + b*\exp{(x)} + c*\exp{(y)} + d*\exp{(x)}*\exp{(y)})}/{(1 + f*\exp{(x)} + g*\exp{(y)}+ h*\exp{(x)}*\exp{(y)})} + \text{Offset}\)
[a, b, c, d, f, g, h, Offset]
RomanSurfaces¶
Roman Surface (minus) (
RomanSurfaceMinus)Roman Surface (minus)
\(z = {(k{(y^{2}-x^{2})} -{(x^{2}-y^{2})}\sqrt{(k^{2}-x^{2}-y^{2})})}/ {(2{(x^{2}+y^{2})})}\)
[k]
Roman Surface (minus) With Offset
\(z = {(k{(y^{2}-x^{2})} -{(x^{2}-y^{2})}\sqrt{(k^{2}-x^{2}-y^{2})})}/ {(2{(x^{2}+y^{2})})} + \text{Offset}\)
[k, Offset]
Roman Surface (minus) Offset XY (
RomanSurfaceMinus_OffsetXY)Roman Surface (minus) Offset XY
\(z = {(k{({(y+b)}^{2}-{(x+a)}^{2})} -{({(x+a)}^{2}-{(y+b)}^{2})}\sqrt{(k^{2}-{(x+a)}^{2}-{(y+b)}^{2})})}/ {(2{({(x+a)}^{2}+{(y+b)}^{2})})}\)
[k, a, b]
Roman Surface (minus) Offset XY With Offset
\(z = {(k{({(y+b)}^{2}-{(x+a)}^{2})} -{({(x+a)}^{2}-{(y+b)}^{2})}\sqrt{(k^{2}-{(x+a)}^{2}-{(y+b)}^{2})})}/ {(2{({(x+a)}^{2}+{(y+b)}^{2})})} + \text{Offset}\)
[k, a, b, Offset]
Roman Surface (minus) Scaled And Offset XY (
RomanSurfaceMinus_ScaledAndOffsetXY)Roman Surface (minus) Scaled And Offset XY
\(z = {(k{({(cy+d)}^{2}-{(ax+b)}^{2})} -{({(ax+b)}^{2}-{(cy+d)}^{2})}\sqrt{(k^{2}-{(ax+b)}^{2}-{(cy+d)}^{2})})}/ {(2{({(ax+b)}^{2}+{(cy+d)}^{2})})}\)
[k, a, b, c, d]
Roman Surface (minus) Scaled And Offset XY With Offset
\(z = {(k{({(cy+d)}^{2}-{(ax+b)}^{2})} -{({(ax+b)}^{2}-{(cy+d)}^{2})}\sqrt{(k^{2}-{(ax+b)}^{2}-{(cy+d)}^{2})})}/ {(2{({(ax+b)}^{2}+{(cy+d)}^{2})})} + \text{Offset}\)
[k, a, b, c, d, Offset]
Roman Surface (plus) (
RomanSurfacePlus)Roman Surface (plus)
\(z = {(k{(y^{2}-x^{2})} +{(x^{2}-y^{2})}\sqrt{(k^{2}-x^{2}-y^{2})})}/ {(2{(x^{2}+y^{2})})}\)
[k]
Roman Surface (plus) With Offset
\(z = {(k{(y^{2}-x^{2})} +{(x^{2}-y^{2})}\sqrt{(k^{2}-x^{2}-y^{2})})}/ {(2{(x^{2}+y^{2})})} + \text{Offset}\)
[k, Offset]
Roman Surface (plus) Offset XY (
RomanSurfacePlus_OffsetXY)Roman Surface (plus) Offset XY
\(z = {(k{({(y+b)}^{2}-{(x+a)}^{2})} +{({(x+a)}^{2}-{(y+b)}^{2})}\sqrt{(k^{2}-{(x+a)}^{2}-{(y+b)}^{2})})}/ {(2{({(x+a)}^{2}+{(y+b)}^{2})})}\)
[k, a, b]
Roman Surface (plus) Offset XY With Offset
\(z = {(k{({(y+b)}^{2}-{(x+a)}^{2})} +{({(x+a)}^{2}-{(y+b)}^{2})}\sqrt{(k^{2}-{(x+a)}^{2}-{(y+b)}^{2})})}/ {(2{({(x+a)}^{2}+{(y+b)}^{2})})} + \text{Offset}\)
[k, a, b, Offset]
Roman Surface (plus) Scaled And Offset XY (
RomanSurfacePlus_ScaledAndOffsetXY)Roman Surface (plus) Scaled And Offset XY
\(z = {(k{({(cy+d)}^{2}-{(ax+b)}^{2})} +{({(ax+b)}^{2}-{(cy+d)}^{2})}\sqrt{(k^{2}-{(ax+b)}^{2}-{(cy+d)}^{2})})}/ {(2{({(ax+b)}^{2}+{(cy+d)}^{2})})}\)
[k, a, b, c, d]
Roman Surface (plus) Scaled And Offset XY With Offset
\(z = {(k{({(cy+d)}^{2}-{(ax+b)}^{2})} +{({(ax+b)}^{2}-{(cy+d)}^{2})}\sqrt{(k^{2}-{(ax+b)}^{2}-{(cy+d)}^{2})})}/ {(2{({(ax+b)}^{2}+{(cy+d)}^{2})})} + \text{Offset}\)
[k, a, b, c, d, Offset]
Roman Surface (plus) Scaled (
RomanSurfacePlus_scaled)Roman Surface (plus) Scaled
\(z = Scale * {(k{(y^{2}-x^{2})} +{(x^{2}-y^{2})}\sqrt{(k^{2}-x^{2}-y^{2})})}/ {(2{(x^{2}+y^{2})})}\)
[k, Scale]
Roman Surface (plus) Scaled With Offset
\(z = Scale * {(k{(y^{2}-x^{2})} +{(x^{2}-y^{2})}\sqrt{(k^{2}-x^{2}-y^{2})})}/ {(2{(x^{2}+y^{2})})} + \text{Offset}\)
[k, Scale, Offset]
Sigmoidal¶
Andrea Prunotto Sigmoid A (
AndreaPrunottoSigmoidA)Andrea Prunotto Sigmoid A
\(z = a0 + {(a1 / {(1.0 + \exp{(a2 * {(x + a3 + a4 * y + a5 * x * y)})})})}\)
[a0, a1, a2, a3, a4, a5]
Andrea Prunotto Sigmoid B (
AndreaPrunottoSigmoidB)Andrea Prunotto Sigmoid B
\(z = a0 + {(a1 / {(1.0 + \exp{(a2 * {(x * a3 + a4 * y + a5 * x * y)})})})}\)
[a0, a1, a2, a3, a4, a5]
Fraser Smith Sigmoid (
FraserSmithSigmoid)Fraser Smith Sigmoid
\(z = 1.0 / {({(1.0 + \exp{(a - bx)})} * {(1.0 + \exp{(c - dy)})})}\)
[a, b, c, d]
Fraser Smith Sigmoid With Offset
\(z = 1.0 / {({(1.0 + \exp{(a - bx)})} * {(1.0 + \exp{(c - dy)})})} + \text{Offset}\)
[a, b, c, d, Offset]
Fraser Smith Sigmoid Scaled (
FraserSmithSigmoid_scaled)Fraser Smith Sigmoid Scaled
\(z = Scale / {({(1.0 + \exp{(a - bx)})} * {(1.0 + \exp{(c - dy)})})}\)
[a, b, c, d, Scale]
Fraser Smith Sigmoid Scaled With Offset
\(z = Scale / {({(1.0 + \exp{(a - bx)})} * {(1.0 + \exp{(c - dy)})})} + \text{Offset}\)
[a, b, c, d, Scale, Offset]
Sigmoid (
Sigmoid)Sigmoid
\(z = a / {({(1.0 + \exp{(b - cx)})} * {(1.0 + \exp{(d - fy)})})}\)
[a, b, c, d, f]
Sigmoid With Offset
\(z = a / {({(1.0 + \exp{(b - cx)})} * {(1.0 + \exp{(d - fy)})})} + \text{Offset}\)
[a, b, c, d, f, Offset]
Simple¶
Simple Equation 01 (
SimpleEquation_01)Simple Equation 01
\(z = a*pow{(x,b)}*pow{(y,c)}\)
[a, b, c]
Simple Equation 01 With Offset
\(z = a*pow{(x,b)}*pow{(y,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 02 (
SimpleEquation_02)Simple Equation 02
\(z = x/{(a+b*y)}\)
[a, b]
Simple Equation 02 With Offset
\(z = x/{(a+b*y)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 03 (
SimpleEquation_03)Simple Equation 03
\(z = y/{(a+b*x)}\)
[a, b]
Simple Equation 03 With Offset
\(z = y/{(a+b*x)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 04 (
SimpleEquation_04)Simple Equation 04
\(z = a*pow{(x,b*y)}\)
[a, b]
Simple Equation 04 With Offset
\(z = a*pow{(x,b*y)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 05 (
SimpleEquation_05)Simple Equation 05
\(z = a*pow{(y,b*x)}\)
[a, b]
Simple Equation 05 With Offset
\(z = a*pow{(y,b*x)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 06 (
SimpleEquation_06)Simple Equation 06
\(z = a*pow{(x,b/y)}\)
[a, b]
Simple Equation 06 With Offset
\(z = a*pow{(x,b/y)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 07 (
SimpleEquation_07)Simple Equation 07
\(z = a*pow{(y,b/x)}\)
[a, b]
Simple Equation 07 With Offset
\(z = a*pow{(y,b/x)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 08 (
SimpleEquation_08)Simple Equation 08
\(z = a*x+b*pow{(y,2.0)}\)
[a, b]
Simple Equation 08 With Offset
\(z = a*x+b*pow{(y,2.0)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 09 (
SimpleEquation_09)Simple Equation 09
\(z = a*y+b*pow{(x,2.0)}\)
[a, b]
Simple Equation 09 With Offset
\(z = a*y+b*pow{(x,2.0)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 10 (
SimpleEquation_10)Simple Equation 10
\(z = x/{(a+b*pow{(y,2.0)})}\)
[a, b]
Simple Equation 10 With Offset
\(z = x/{(a+b*pow{(y,2.0)})} + \text{Offset}\)
[a, b, Offset]
Simple Equation 11 (
SimpleEquation_11)Simple Equation 11
\(z = y/{(a+b*pow{(x,2.0)})}\)
[a, b]
Simple Equation 11 With Offset
\(z = y/{(a+b*pow{(x,2.0)})} + \text{Offset}\)
[a, b, Offset]
Simple Equation 12 (
SimpleEquation_12)Simple Equation 12
\(z = a*pow{(b,x)}*pow{(y,c)}\)
[a, b, c]
Simple Equation 12 With Offset
\(z = a*pow{(b,x)}*pow{(y,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 13 (
SimpleEquation_13)Simple Equation 13
\(z = a*pow{(b,y)}*pow{(x,c)}\)
[a, b, c]
Simple Equation 13 With Offset
\(z = a*pow{(b,y)}*pow{(x,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 14 (
SimpleEquation_14)Simple Equation 14
\(z = a*pow{(x*y,b)}\)
[a, b]
Simple Equation 14 With Offset
\(z = a*pow{(x*y,b)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 15 (
SimpleEquation_15)Simple Equation 15
\(z = a*pow{(x/y,b)}\)
[a, b]
Simple Equation 15 With Offset
\(z = a*pow{(x/y,b)} + \text{Offset}\)
[a, b, Offset]
Simple Equation 16 (
SimpleEquation_16)Simple Equation 16
\(z = a*{(pow{(b,1.0/x)})}*pow{(y,c)}\)
[a, b, c]
Simple Equation 16 With Offset
\(z = a*{(pow{(b,1.0/x)})}*pow{(y,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 17 (
SimpleEquation_17)Simple Equation 17
\(z = a*pow{(b,1.0/y)}*pow{(x,c)}\)
[a, b, c]
Simple Equation 17 With Offset
\(z = a*pow{(b,1.0/y)}*pow{(x,c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 18 (
SimpleEquation_18)Simple Equation 18
\(z = a*pow{(x/b,c)}*\exp{(y/b)}\)
[a, b, c]
Simple Equation 18 With Offset
\(z = a*pow{(x/b,c)}*\exp{(y/b)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 19 (
SimpleEquation_19)Simple Equation 19
\(z = a*pow{(y/b,c)}*\exp{(x/b)}\)
[a, b, c]
Simple Equation 19 With Offset
\(z = a*pow{(y/b,c)}*\exp{(x/b)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 20 (
SimpleEquation_20)Simple Equation 20
\(z = a*pow{(x,b+c*y)}\)
[a, b, c]
Simple Equation 20 With Offset
\(z = a*pow{(x,b+c*y)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 21 (
SimpleEquation_21)Simple Equation 21
\(z = a*pow{(y,b+c*x)}\)
[a, b, c]
Simple Equation 21 With Offset
\(z = a*pow{(y,b+c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 22 (
SimpleEquation_22)Simple Equation 22
\(z = a*pow{(x,b+c/y)}\)
[a, b, c]
Simple Equation 22 With Offset
\(z = a*pow{(x,b+c/y)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 23 (
SimpleEquation_23)Simple Equation 23
\(z = a*pow{(y,b+c/x)}\)
[a, b, c]
Simple Equation 23 With Offset
\(z = a*pow{(y,b+c/x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 24 (
SimpleEquation_24)Simple Equation 24
\(z = a*pow{(x,b+c*ln{(y)})}\)
[a, b, c]
Simple Equation 24 With Offset
\(z = a*pow{(x,b+c*ln{(y)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 25 (
SimpleEquation_25)Simple Equation 25
\(z = a*pow{(y,b+c*ln{(x)})}\)
[a, b, c]
Simple Equation 25 With Offset
\(z = a*pow{(y,b+c*ln{(x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 26 (
SimpleEquation_26)Simple Equation 26
\(z = a*pow{(y,b+c/ln{(x)})}\)
[a, b, c]
Simple Equation 26 With Offset
\(z = a*pow{(y,b+c/ln{(x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 27 (
SimpleEquation_27)Simple Equation 27
\(z = a*pow{(x,b+c/ln{(y)})}\)
[a, b, c]
Simple Equation 27 With Offset
\(z = a*pow{(x,b+c/ln{(y)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 28 (
SimpleEquation_28)Simple Equation 28
\(z = a*\exp{(b*x+c*pow{(y,2.0)})}\)
[a, b, c]
Simple Equation 28 With Offset
\(z = a*\exp{(b*x+c*pow{(y,2.0)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 29 (
SimpleEquation_29)Simple Equation 29
\(z = a*\exp{(b*y+c*pow{(x,2.0)})}\)
[a, b, c]
Simple Equation 29 With Offset
\(z = a*\exp{(b*y+c*pow{(x,2.0)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 30 (
SimpleEquation_30)Simple Equation 30
\(z = a*\exp{(b/x+c*y)}\)
[a, b, c]
Simple Equation 30 With Offset
\(z = a*\exp{(b/x+c*y)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 31 (
SimpleEquation_31)Simple Equation 31
\(z = a*\exp{(b/y+c*x)}\)
[a, b, c]
Simple Equation 31 With Offset
\(z = a*\exp{(b/y+c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 32 (
SimpleEquation_32)Simple Equation 32
\(z = {(a+x)}/{(b+c*y)}\)
[a, b, c]
Simple Equation 32 With Offset
\(z = {(a+x)}/{(b+c*y)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 33 (
SimpleEquation_33)Simple Equation 33
\(z = {(a+y)}/{(b+c*x)}\)
[a, b, c]
Simple Equation 33 With Offset
\(z = {(a+y)}/{(b+c*x)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 34 (
SimpleEquation_34)Simple Equation 34
\(z = {(a+x)}/{(b+c*pow{(y,2.0)})}\)
[a, b, c]
Simple Equation 34 With Offset
\(z = {(a+x)}/{(b+c*pow{(y,2.0)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 35 (
SimpleEquation_35)Simple Equation 35
\(z = {(a+y)}/{(b+c*pow{(x,2.0)})}\)
[a, b, c]
Simple Equation 35 With Offset
\(z = {(a+y)}/{(b+c*pow{(x,2.0)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 36 (
SimpleEquation_36)Simple Equation 36
\(z = a*{(\exp{(b*x)}-\exp{(c*y)})}\)
[a, b, c]
Simple Equation 36 With Offset
\(z = a*{(\exp{(b*x)}-\exp{(c*y)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 37 (
SimpleEquation_37)Simple Equation 37
\(z = a*pow{(x,b*pow{(y,c)})}\)
[a, b, c]
Simple Equation 37 With Offset
\(z = a*pow{(x,b*pow{(y,c)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 38 (
SimpleEquation_38)Simple Equation 38
\(z = a*pow{(y,b*pow{(x,c)})}\)
[a, b, c]
Simple Equation 38 With Offset
\(z = a*pow{(y,b*pow{(x,c)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 39 (
SimpleEquation_39)Simple Equation 39
\(z = x/{(a+b*y+c*pow{(y,0.5)})}\)
[a, b, c]
Simple Equation 39 With Offset
\(z = x/{(a+b*y+c*pow{(y,0.5)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 40 (
SimpleEquation_40)Simple Equation 40
\(z = y/{(a+b*x+c*pow{(x,0.5)})}\)
[a, b, c]
Simple Equation 40 With Offset
\(z = y/{(a+b*x+c*pow{(x,0.5)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 41 (
SimpleEquation_41)Simple Equation 41
\(z = \exp{(a+b/x+c*ln{(y)})}\)
[a, b, c]
Simple Equation 41 With Offset
\(z = \exp{(a+b/x+c*ln{(y)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 42 (
SimpleEquation_42)Simple Equation 42
\(z = \exp{(a+b/y+c*ln{(x)})}\)
[a, b, c]
Simple Equation 42 With Offset
\(z = \exp{(a+b/y+c*ln{(x)})} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 43 (
SimpleEquation_43)Simple Equation 43
\(z = a*pow{(x,b)}*ln{(y+c)}\)
[a, b, c]
Simple Equation 43 With Offset
\(z = a*pow{(x,b)}*ln{(y+c)} + \text{Offset}\)
[a, b, c, Offset]
Simple Equation 44 (
SimpleEquation_44)Simple Equation 44
\(z = a*pow{(y,b)}*ln{(x+c)}\)
[a, b, c]
Simple Equation 44 With Offset
\(z = a*pow{(y,b)}*ln{(x+c)} + \text{Offset}\)
[a, b, c, Offset]
Spline¶
Spline (
Spline)Spline
\(z = B-Spline Interpolation Surface\)
TaylorSeries¶
Taylor Series A (
TaylorA)Taylor Series A
\(z = a + bx + cy + dx^{2} + fy^{2} + gxy\)
[a, b, c, d, f, g]
Taylor Series B (
TaylorB)Taylor Series B
\(z = a + b*ln{(x)} + cy + d*ln{(x)}^{2} +fy^{2} + g*ln{(x)}*y\)
[a, b, c, d, f, g]
Taylor Series C (
TaylorC)Taylor Series C
\(z = a + bx + c*ln{(y)} + dx^{2} +f*ln{(y)}^{2} + g*x*ln{(y)}\)
[a, b, c, d, f, g]
Taylor Series D (
TaylorD)Taylor Series D
\(z = a + b*ln{(x)} + c*ln{(y)} + d*ln{(x)}^{2} +f*ln{(y)}^{2} + g*ln{(x)}*ln{(y)}\)
[a, b, c, d, f, g]
Taylor Series E (
TaylorE)Taylor Series E
\(z = a + b/x + cy + d/x^{2} + fy^{2} + gy/x\)
[a, b, c, d, f, g]
Taylor Series F (
TaylorF)Taylor Series F
\(z = a + b/ln{(x)} + cy + d/ln{(x)}^{2} +fy^{2} + gy/ln{(x)}\)
[a, b, c, d, f, g]
Taylor Series G (
TaylorG)Taylor Series G
\(z = a + b/x + c*ln{(y)} + d/x^{2} +f*ln{(y)}^{2} + g*ln{(y)}/x\)
[a, b, c, d, f, g]
Taylor Series H (
TaylorH)Taylor Series H
\(z = a + b/ln{(x)} + c*ln{(y)} + d/ln{(x)}^{2} +f*ln{(y)}^{2} + g*ln{(y)}/ln{(x)}\)
[a, b, c, d, f, g]
Taylor Series I (
TaylorI)Taylor Series I
\(z = a + bx + c/y + dx^{2} + f/y^{2} + gx/y\)
[a, b, c, d, f, g]
Taylor Series J (
TaylorJ)Taylor Series J
\(z = a + b*ln{(x)} + c/y + d*ln{(x)}^{2} +f/y^{2} + g*ln{(x)}/y\)
[a, b, c, d, f, g]
Taylor Series K (
TaylorK)Taylor Series K
\(z = a + bx + c/ln{(y)} + dx^{2} +f/ln{(y)}^{2} + gx/ln{(y)}\)
[a, b, c, d, f, g]
Taylor Series L (
TaylorL)Taylor Series L
\(z = a + b*ln{(x)} + c/ln{(y)} + d*ln{(x)}^{2} +f/ln{(y)}^{2} + g*ln{(x)}/ln{(y)}\)
[a, b, c, d, f, g]
Taylor Series M (
TaylorM)Taylor Series M
\(z = a + b/x + c/y + d/x^{2} + f/y^{2} +g/{(xy)}\)
[a, b, c, d, f, g]
Taylor Series N (
TaylorN)Taylor Series N
\(z = a + b/ln{(x)} + c/y + d/ln{(x)}^{2} +f/y^{2} + g/{(ln{(x)}*y)}\)
[a, b, c, d, f, g]
Taylor Series O (
TaylorO)Taylor Series O
\(z = a + b/x + c/ln{(y)} + d/x^{2} +f/ln{(y)}^{2} + g/{(x*ln{(y)})}\)
[a, b, c, d, f, g]
Taylor Series P (
TaylorP)Taylor Series P
\(z = a + b/ln{(x)} + c/ln{(y)} + d/ln{(x)}^{2} +f/ln{(y)}^{2} + g/{(ln{(x)}*ln{(y)})}\)
[a, b, c, d, f, g]
Trigonometric¶
Cosh XY [radians] (
CoshXY)Cosh XY [radians]
\(z = amplitude * cosh{(pi * {(xy - center)} / width)}\)
[amplitude, center, width]
Cosh XY [radians] With Offset
\(z = amplitude * cosh{(pi * {(xy - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Cosh X Plus Cosh Y [radians] (
CoshX_Plus_CoshY)Cosh X Plus Cosh Y [radians]
\(z = amplitude\_x * cosh{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y* cosh{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Cosh X Plus Cosh Y [radians] With Offset
\(z = amplitude\_x * cosh{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y* cosh{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Cosh X Plus Sine Y [radians] (
CoshX_Plus_SineY)Cosh X Plus Sine Y [radians]
\(z = amplitude\_x * cosh{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y* sin{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Cosh X Plus Sine Y [radians] With Offset
\(z = amplitude\_x * cosh{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y* sin{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Cosh X Plus Tangent Y [radians] (
CoshX_Plus_TangentY)Cosh X Plus Tangent Y [radians]
\(z = amplitude\_x * cosh{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y* tan{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Cosh X Plus Tangent Y [radians] With Offset
\(z = amplitude\_x * cosh{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y* tan{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Cosh X Times Cosh Y[radians] (
CoshX_Times_CoshY)Cosh X Times Cosh Y[radians]
\(z = amplitude * cosh{(pi * {(x - center\_x)} / width\_x)} * cosh{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Cosh X Times Cosh Y[radians] With Offset
\(z = amplitude * cosh{(pi * {(x - center\_x)} / width\_x)} * cosh{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Cosh X Times Sine Y [radians] (
CoshX_Times_SineY)Cosh X Times Sine Y [radians]
\(z = amplitude * cosh{(pi * {(x - center\_x)} / width\_x)} * sin{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Cosh X Times Sine Y [radians] With Offset
\(z = amplitude * cosh{(pi * {(x - center\_x)} / width\_x)} * sin{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Cosh X Times Tangent Y [radians] (
CoshX_Times_TangentY)Cosh X Times Tangent Y [radians]
\(z = amplitude * cosh{(pi * {(x - center\_x)} / width\_x)} * tan{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Cosh X Times Tangent Y [radians] With Offset
\(z = amplitude * cosh{(pi * {(x - center\_x)} / width\_x)} * tan{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Reza’s Custom Equation One [radians] (
RezaCustomOne)Reza’s Custom Equation One [radians]
\(z = {(cos{(a*x - b*y)} + sin{(c*x - d*y)})}^{n} - {(cos{(f*x -g*y)} + sin{(h*x- i*y)})}^{n}\)
[a, b, c, d, f, g, h, i, n]
Reza’s Custom Equation One [radians] With Offset
\(z = {(cos{(a*x - b*y)} + sin{(c*x - d*y)})}^{n} - {(cos{(f*x -g*y)} + sin{(h*x- i*y)})}^{n} + \text{Offset}\)
[a, b, c, d, f, g, h, i, n, Offset]
Reza’s Custom Equation Two [radians] (
RezaCustomTwo)Reza’s Custom Equation Two [radians]
\(z = abs{(cos{({(A*{(x+B)})} + C*{(y+D)})})} + abs{(cos{({(A*{(x+B)})} - C*{(y+D)})})} -{(sin{(E*x+F)})}^{2} - {(sin{(E*y+G)})}^{2}\)
[A, B, C, D, E, F, G]
Reza’s Custom Equation Two [radians] With Offset
\(z = abs{(cos{({(A*{(x+B)})} + C*{(y+D)})})} + abs{(cos{({(A*{(x+B)})} - C*{(y+D)})})} -{(sin{(E*x+F)})}^{2} - {(sin{(E*y+G)})}^{2} +\text{Offset}\)
[A, B, C, D, E, F, G, Offset]
Sine XY [radians] (
SineXY)Sine XY [radians]
\(z = amplitude * sin{(pi * {(xy - center)} / width)}\)
[amplitude, center, width]
Sine XY [radians] With Offset
\(z = amplitude * sin{(pi * {(xy - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Sine X Plus Cosh Y [radians] (
SineX_Plus_CoshY)Sine X Plus Cosh Y [radians]
\(z = amplitude\_x * sin{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *cosh{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Sine X Plus Cosh Y [radians] With Offset
\(z = amplitude\_x * sin{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *cosh{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Sine X Plus Sine Y [radians] (
SineX_Plus_SineY)Sine X Plus Sine Y [radians]
\(z = amplitude\_x * sin{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *sin{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Sine X Plus Sine Y [radians] With Offset
\(z = amplitude\_x * sin{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *sin{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Sine X Plus Tangent Y [radians] (
SineX_Plus_TangentY)Sine X Plus Tangent Y [radians]
\(z = amplitude\_x * sin{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *tan{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Sine X Plus Tangent Y [radians] With Offset
\(z = amplitude\_x * sin{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *tan{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Sine X Times Cosh Y [radians] (
SineX_Times_CoshY)Sine X Times Cosh Y [radians]
\(z = amplitude * sine{(pi * {(x - center\_x)} / width\_x)} * cosh{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Sine X Times Cosh Y [radians] With Offset
\(z = amplitude * sine{(pi * {(x - center\_x)} / width\_x)} * cosh{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Sine X Times Sine Y [radians] (
SineX_Times_SineY)Sine X Times Sine Y [radians]
\(z = amplitude * sin{(pi * {(x - center\_x)} / width\_x)} * sin{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Sine X Times Sine Y [radians] With Offset
\(z = amplitude * sin{(pi * {(x - center\_x)} / width\_x)} * sin{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Sine X Times Tangent Y [radians] (
SineX_Times_TangentY)Sine X Times Tangent Y [radians]
\(z = amplitude * sin{(pi * {(x - center\_x)} / width\_x)} * tan{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Sine X Times Tangent Y [radians] With Offset
\(z = amplitude * sin{(pi * {(x - center\_x)} / width\_x)} * tan{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Tangent XY [radians] (
TangentXY)Tangent XY [radians]
\(z = amplitude * tan{(pi * {(xy - center)} / width)}\)
[amplitude, center, width]
Tangent XY [radians] With Offset
\(z = amplitude * tan{(pi * {(xy - center)} / width)} + \text{Offset}\)
[amplitude, center, width, Offset]
Tangent X Plus Cosh Y [radians] (
TangentX_Plus_CoshY)Tangent X Plus Cosh Y [radians]
\(z = amplitude\_x * tan{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *cosh{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Tangent X Plus Cosh Y [radians] With Offset
\(z = amplitude\_x * tan{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *cosh{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Tangent X Plus Sine Y [radians] (
TangentX_Plus_SineY)Tangent X Plus Sine Y [radians]
\(z = amplitude\_x * tan{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *sin{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Tangent X Plus Sine Y [radians] With Offset
\(z = amplitude\_x * tan{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *sin{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Tangent X Plus Tangent Y [radians] (
TangentX_Plus_TangentY)Tangent X Plus Tangent Y [radians]
\(z = amplitude\_x * tan{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *tan{(pi * {(y - center\_y)} / width\_y)}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y]
Tangent X Plus Tangent Y [radians] With Offset
\(z = amplitude\_x * tan{(pi * {(x - center\_x)} / width\_x)} + amplitude\_y *tan{(pi * {(y - center\_y)} / width\_y)} + \text{Offset}\)
[amplitude_x, center_x, width_x, amplitude_y, center_y, width_y, Offset]
Tangent X Times Cosh Y [radians] (
TangentX_Times_CoshY)Tangent X Times Cosh Y [radians]
\(z = amplitude * tan{(pi * {(x - center\_x)} / width\_x)} * cosh{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Tangent X Times Cosh Y [radians] With Offset
\(z = amplitude * tan{(pi * {(x - center\_x)} / width\_x)} * cosh{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Tangent X Times Sine Y [radians] (
TangentX_Times_SineY)Tangent X Times Sine Y [radians]
\(z = amplitude * tan{(pi * {(x - center\_x)} / width\_x)} * sin{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Tangent X Times Sine Y [radians] With Offset
\(z = amplitude * tan{(pi * {(x - center\_x)} / width\_x)} * sin{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
Tangent X Times Tangent Y [radians] (
TangentX_Times_TangentY)Tangent X Times Tangent Y [radians]
\(z = amplitude * tan{(pi * {(x - center\_x)} / width\_x)} * tan{(pi * {(y -center\_y)} / width\_y)}\)
[amplitude, center_x, width_x, center_y, width_y]
Tangent X Times Tangent Y [radians] With Offset
\(z = amplitude * tan{(pi * {(x - center\_x)} / width\_x)} * tan{(pi * {(y -center\_y)} / width\_y)} + \text{Offset}\)
[amplitude, center_x, width_x, center_y, width_y, Offset]
UserDefinedFunction¶
User Defined Function (
UserDefinedFunction)User Defined Function
\(z = User Defined Function\)