ZunZunNG - Online Curve Fitting and Surface Fitting

Welcome to ZunZunNG

Here you can curve fit and surface fit your 2D and 3D data online with a rich set of error histograms, error plots, curve plots, surface plots, contour plots, auto-generated source code, and PDF file output.

If you're looking for high quality curve fitting and surface fitting, this is the site for you! Source code is available at the GitHub Code Repository.

To begin, select an equation family from the drop-down menus above or try the "Function Finders" to help determine the best curve fit for your data.

Characterize Data

Characterize 1D (X) Data

Characterize 2D (XY) Data

Characterize 3D (XYZ) Data

Fit Data To Statistical Distributions

About ZunZunNG

ZunZunNG (Next Generation) is a permanent fork of ZunZunSite3, maintained by Kilo Scheffer since 2026.

The fork modernizes the codebase for cross-platform deployment (Linux, macOS, Windows) on Python 3.14 and Django 6.0, replaces the original os.fork() architecture with multiprocessing.Process(spawn), and drops the scipy.odr dependency in favor of the independent odrpack package — work done first in the companion pyeq3-ng fork and since merged into upstream pyeq3.

Discussion: FindCurves Google Group.
Source: github.com/kiloscheffer/zunzun-ng.

About the original ZunZunSite3 (James R. Phillips, 2016)

This site is dedicated to Jesus of Nazareth, and was written by James R. Phillips.

The site is a natural outgrowth of my previous Research and Development days in Washington, D.C., my previous software engineering work in Tokyo, Japan and now in Birmingham, AL, USA.

The name of the project, ZunZunSite3, is taken from my wife's Burmese nickname.

Historical Note

Prior to the invention of electronic calculation, only manual methods were available, of course — meaning that creating mathematical models from experimental data was done by hand. Even Napier's invention of logarithms did not help much in reducing the tediousness of this task. Linear regression techniques worked, but how to then compare models? — and so the F-statistic was created for the purpose of model selection, since graphing models and their confidence intervals was practically out of the question. Forward and backward regression techniques used linear methods, requiring less calculation than non-linear methods, but limited the possible mathematical models to linear combinations of functions.

With the advent of computerized calculations, non-linear methods which were impractical in the past could be automated and made practical. However, the non-linear fitting methods all required starting points for their solvers — meaning in practice you had to have a good idea of the final equation parameters to begin with!

If however a genetic or monte carlo algorithm searched error space for initial parameters prior to running the non-linear solvers, this problem could be strongly mitigated. This meant that instead of hit-or-miss forward and backward regression, large numbers of known linear and non-linear equations could be fitted to an experimental data set and then ranked by a fit statistic such as AIC or SSQ errors.

This technique is captured in the pyeq3 open source fitting code. Note that for an initial guesstimate of parameter values, not all data need be used. A reduced size data set with min, max, and (hopefully) evenly spaced additional data points in between are used. The total number of data points required is the number of equation parameters plus a few extra points.

Reducing the data set size used by the code's genetic algorithm greatly reduces total processing time. No secrets here, it's in the open source code. I tested many different methods before choosing the one in the code, a genetic algorithm named "Differential Evolution".

Server Load

1 minute: …
5 minutes: …
15 minutes: …

Load is the average number of threads competing for a CPU core. Below 2 leaves cores idle; near 2 uses them fully; above 2 means work is queuing for a core.

Dedication

This site is dedicated to James R. Phillips, creator of ZunZunSite3 and pyeq3, and original maintainer of zunzun.com.

2D Astrophysics

King 142D: f(x) = k * [1/sqrt(1 + (x/r_c) ** 2) - 1/sqrt(1 + (r_t/r_c) ** 2)] ** 2^{[web citation]}
King 14 With Offset2D: f(x) = k * [1/sqrt(1 + (x/r_c) ** 2) - 1/sqrt(1 + (r_t/r_c) ** 2)] ** 2 + Offset^{[web citation]}

2D BioScience

Aphid Population Growth2D: N(t) = a * exp(bt) * (1 + c * exp(bt))^-2^{[web citation]}
Beverton-Holt A2D: y = r / (1 + ((r-1)/K) * x)
Beverton-Holt B2D: y = rx / (1 + ((r-1)/K) * x)
BioScience A2D: y = a * (1.0 - (b * c^x))
BioScience B2D: y = a * (1.0 -(1.0 + (x/b)^c)^{-1.0 * d})
Cellular Conductance2D: g = p3/(1+exp((v-p1)/p2)) + p4*exp((v-45)/p5)^{[web citation]}
Derek Duncan Custom Equation2D: y = a / (1 + exp(-1/b*(x-c)))^d
Dose-Response A2D: y = b + (a-b) / (1 + 10^x-c)
Dose-Response B2D: y = b + (a-b) / (1 + 10^c-x)
Dose-Response C2D: y = b + (a-b) / (1 + 10^d*(x-c))
Dose-Response D2D: y = b + (a-b) / (1 + 10^d*(c-x))
Dose-Response E2D: y = b + (a-b) / (1 + (x/c)^d)
Generalized Negative Exponential2D: y = a * (1.0 - exp(-bx))^c
Generalized Product Accumulation2D: y = a(b-x) / (c + (b-x)) + d(b-x) + f
Generalized Substrate Depletion2D: y = ax / (b + x) - cx - d
High-Low Affinity2D: y = abx / (1+bx)
High-Low Affinity Double2D: y = abx / (1+bx) + cdx / (1+dx)
High-Low Affinity Double Isotope Displacement ([Hot] subsumed)2D: y = ab / (1+bx) + cd / (1+dx)
High-Low Affinity Isotope Displacement ([Hot] subsumed)2D: y = ab / (1+bx)
Hyperbolic A2D: y = (a + x) / (b + x)
Hyperbolic B2D: y = (a + bx) / (c + x)
Hyperbolic C2D: y = (a + x) / (b + cx)
Hyperbolic D2D: y = (a + bx) / (c + dx)
Hyperbolic E2D: y = ax / (b + x)
Hyperbolic F2D: y = ax / (b + x) + cx
Hyperbolic G2D: y = ax / (b + x) + cx / (d + x)
Hyperbolic H2D: y = ax / (b + x) + cx / (d + x) + fx
Hyperbolic I2D: y = ab / (b + x)
Hyperbolic J2D: y = x / (a + bx)
Hyperbolic Logistic2D: y = ax^b / (c + x^b)
Jorge Rabinovich Population Growth2D: Y = (P1*CC) / (P1 + (CC-P1)*exp(-R*X))
Membrane Transport2D: y = a(x-b) / (x² + cx + d)
Michaelis-Menten2D: y = ax / (b + x)
Michaelis-Menten Double2D: y = ax / (b + x) + cx / (d + x)
Michaelis-Menten Isotope Displacement ([Hot] subsumed)2D: y = a / (b + x)
Michaelis-Menten Isotope Displacement Double ([Hot] subsumed)2D: y = a / (b + x) + c / (d + x)
Michaelis-Menten Product Accumulation2D: y = a(b-x) / (c + (b-x))
Negative Exponential2D: y = a * (1.0 - exp(-bx))
New Zealand Ecology Logistic 12D: n = B0 + ((B1 - B0) / (1.0 + exp((B2 + D) * B3)))
New Zealand Ecology Logistic 22D: n = B0 + ((B1 - B0) / (1.0 + exp((B2 + D + (B4*D²)) * B3)))
Plant Disease Exponential Model2D: Incidence = y0 * exp(r * time)^{[web citation]}
Plant Disease Gompertz Model2D: Incidence = exp(ln(y0) * exp(-r * time))^{[web citation]}
Plant Disease Logistic Model2D: Incidence = 1 / (1 + (1 - y0) / (y0 * exp(-r * time)))^{[web citation]}
Plant Disease Monomolecular Model2D: Incidence = 1 - ((1 - y0) * exp(-r * time))^{[web citation]}
Plant Disease Weibull Model2D: Incidence = 1 - exp(-1.0 * ((time - a) / b)^c)^{[web citation]}
Plant Disease Weibull Model Scaled2D: y = Scale * (1 - exp(-1.0 * ((time - a) / b)^c))^{[web citation]}
Preece And Baines Growth2D: y = a - 2(a-b) / (exp(c(x-d)) + exp(f(x-d)))
Scaled Log2D: y = a * log(x)
Scaled Log Transform2D: y = a * log(bx + c)
Scaled Power2D: y = a * x^b
Scaled Power Transform2D: y = a * (cx + d)^b
Standard 3-Parameter Logistic Equation2D: y = d + (a - d) / (1 + (x / c))
Standard 4-Parameter Logistic Equation2D: y = d + (a - d) / (1 + (x / c)^b)
Standard 5-Parameter Logistic Equation2D: y = d + (a - d) / (1 + (x / c)^b )^f
Weibull2D: y = a * (1.0 - exp(-b * (x - c)^d))
Xiaogang Peng Immunoassay2D: y = K / (1.0 + exp(-1.0 * (a + blog(x) + cx)))
von Bertalanffy Growth2D: L(t) = L_inf * (1.0 - exp(-K * (t-t_zero)))

Aphid Population Growth With Offset2D: N(t) = a * exp(bt) * (1 + c * exp(bt))^-2 + Offset^{[web citation]}
Beverton-Holt A With Offset2D: y = r / (1 + ((r-1)/K) * x) + Offset
Beverton-Holt B With Offset2D: y = rx / (1 + ((r-1)/K) * x) + Offset
BioScience A With Offset2D: y = a * (1.0 - (b * c^x)) + Offset
BioScience B With Offset2D: y = a * (1.0 -(1.0 + (x/b)^c)^{-1.0 * d}) + Offset
Cellular Conductance With Offset2D: g = p3/(1+exp((v-p1)/p2)) + p4*exp((v-45)/p5) + Offset^{[web citation]}
Derek Duncan Custom Equation With Offset2D: y = a / (1 + exp(-1/b*(x-c)))^d + Offset
Generalized Negative Exponential With Offset2D: y = a * (1.0 - exp(-bx))^c + Offset
High-Low Affinity Double Isotope Displacement ([Hot] subsumed) With Offset2D: y = ab / (1+bx) + cd / (1+dx) + Offset
High-Low Affinity Double With Offset2D: y = abx / (1+bx) + cdx / (1+dx) + Offset
High-Low Affinity Isotope Displacement ([Hot] subsumed) With Offset2D: y = ab / (1+bx) + Offset
High-Low Affinity With Offset2D: y = abx / (1+bx) + Offset
Hyperbolic A With Offset2D: y = (a + x) / (b + x) + Offset
Hyperbolic B With Offset2D: y = (a + bx) / (c + x) + Offset
Hyperbolic C With Offset2D: y = (a + x) / (b + cx) + Offset
Hyperbolic D With Offset2D: y = (a + bx) / (c + dx) + Offset
Hyperbolic E With Offset2D: y = ax / (b + x) + Offset
Hyperbolic F With Offset2D: y = ax / (b + x) + cx + Offset
Hyperbolic G With Offset2D: y = ax / (b + x) + cx / (d + x) + Offset
Hyperbolic H With Offset2D: y = ax / (b + x) + cx / (d + x) + fx + Offset
Hyperbolic I With Offset2D: y = ab / (b + x) + Offset
Hyperbolic J With Offset2D: y = x / (a + bx) + Offset
Hyperbolic Logistic With Offset2D: y = ax^b / (c + x^b) + Offset
Jorge Rabinovich Population Growth With Offset2D: Y = (P1*CC) / (P1 + (CC-P1)*exp(-R*X)) + Offset
Membrane Transport With Offset2D: y = a(x-b) / (x² + cx + d) + Offset
Michaelis-Menten Double With Offset2D: y = ax / (b + x) + cx / (d + x) + Offset
Michaelis-Menten Isotope Displacement ([Hot] subsumed) With Offset2D: y = a / (b + x) + Offset
Michaelis-Menten Isotope Displacement Double ([Hot] subsumed) With Offset2D: y = a / (b + x) + c / (d + x) + Offset
Michaelis-Menten Product Accumulation With Offset2D: y = a(b-x) / (c + (b-x)) + Offset
Michaelis-Menten With Offset2D: y = ax / (b + x) + Offset
Negative Exponential With Offset2D: y = a * (1.0 - exp(-bx)) + Offset
Plant Disease Exponential Model With Offset2D: Incidence = y0 * exp(r * time) + Offset^{[web citation]}
Plant Disease Gompertz Model With Offset2D: Incidence = exp(ln(y0) * exp(-r * time)) + Offset^{[web citation]}
Plant Disease Logistic Model With Offset2D: Incidence = 1 / (1 + (1 - y0) / (y0 * exp(-r * time))) + Offset^{[web citation]}
Plant Disease Monomolecular Model With Offset2D: Incidence = 1 - ((1 - y0) * exp(-r * time)) + Offset^{[web citation]}
Plant Disease Weibull Model Scaled With Offset2D: y = Scale * (1 - exp(-1.0 * ((time - a) / b)^c)) + Offset^{[web citation]}
Plant Disease Weibull Model With Offset2D: Incidence = 1 - exp(-1.0 * ((time - a) / b)^c) + Offset^{[web citation]}
Scaled Log Transform With Offset2D: y = a * log(bx + c) + Offset
Scaled Log With Offset2D: y = a * log(x) + Offset
Scaled Power Transform With Offset2D: y = a * (cx + d)^b + Offset
Scaled Power With Offset2D: y = a * x^b + Offset
Weibull With Offset2D: y = a * (1.0 - exp(-b * (x - c)^d)) + Offset
Xiaogang Peng Immunoassay With Offset2D: y = K / (1.0 + exp(-1.0 * (a + blog(x) + cx))) + Offset
von Bertalanffy Growth With Offset2D: L(t) = L_inf * (1.0 - exp(-K * (t-t_zero))) + Offset

Beverton-Holt A Plus Line2D: y = r / (1 + ((r-1)/K) * x)
y = y + (c * x) + d
Beverton-Holt B Plus Line2D: y = rx / (1 + ((r-1)/K) * x)
y = y + (c * x) + d
High-Low Affinity Isotope Displacement ([Hot] subsumed) Plus Line2D: y = ab / (1+bx)
y = y + (c * x) + d
High-Low Affinity Plus Line2D: y = abx / (1+bx)
y = y + (c * x) + d
Hyperbolic A Plus Line2D: y = (a + x) / (b + x)
y = y + (c * x) + d
Hyperbolic E Plus Line2D: y = ax / (b + x)
y = y + (c * x) + d
Hyperbolic I Plus Line2D: y = ab / (b + x)
y = y + (c * x) + d
Hyperbolic J Plus Line2D: y = x / (a + bx)
y = y + (c * x) + d
Michaelis-Menten Isotope Displacement ([Hot] subsumed) Plus Line2D: y = a / (b + x)
y = y + (c * x) + d
Michaelis-Menten Plus Line2D: y = ax / (b + x)
y = y + (c * x) + d
Negative Exponential Plus Line2D: y = a * (1.0 - exp(-bx))
y = y + (c * x) + d
Plant Disease Exponential Model Plus Line2D: Incidence = y0 * exp(r * time)
Incidence = Incidence + (c * x) + d^{[web citation]}
Plant Disease Gompertz Model Plus Line2D: Incidence = exp(ln(y0) * exp(-r * time))
Incidence = Incidence + (c * x) + d^{[web citation]}
Plant Disease Logistic Model Plus Line2D: Incidence = 1 / (1 + (1 - y0) / (y0 * exp(-r * time)))
Incidence = Incidence + (c * x) + d^{[web citation]}
Plant Disease Monomolecular Model Plus Line2D: Incidence = 1 - ((1 - y0) * exp(-r * time))
Incidence = Incidence + (c * x) + d^{[web citation]}
Scaled Log Plus Line2D: y = a * log(x)
y = y + (b * x) + c
Scaled Power Plus Line2D: y = a * x^b
y = y + (c * x) + d

2D BurkardtCollectionBased

Arcsin CDF Based2D: y = a * asin( (bx+c) / d)^{[web citation]}
Arcsin PDF Based2D: y = a / sqrt( b² - x²)^{[web citation]}
Bradford CDF Based A2D: y = ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0)^{[web citation]}
Bradford CDF Based B2D: y = d * ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0)^{[web citation]}
Bradford PDF Based2D: y = c / (( c * (x-a) + b-a) * ln(c + 1.0))^{[web citation]}
Burr CDF Based A2D: y = 1.0 / ( 1.0 + ( b / ( x-a ))^c)^d^{[web citation]}
Burr CDF Based B2D: y = f / ( 1.0 + ( b / ( x-a ))^c)^d^{[web citation]}
Burr PDF Based2D: y = (c*d/b) * ((x-a)/b)^(-c-1.0) * (1.0+((x-a)/b)^(-c))^(-d-1.0)^{[web citation]}
Dipole CDF Based2D: y = a * arctan(x) + b/x^{[web citation]}
Exponential PDF Based2D: y = (1.0/b) * exp((a-x)/b)^{[web citation]}
Exponential PDF Based Scaled2D: y = Scale * (1.0/b) * exp((a-x)/b)^{[web citation]}
Extreme Values CDF Based A2D: y = exp(-exp(-((x-a)/b)))^{[web citation]}
Extreme Values CDF Based B2D: y = c * exp(-exp(-((x-a)/b)))^{[web citation]}
Extreme Values PDF Based2D: y = (1.0/b) * exp(((a-x)/b)-exp((a-x)/b))^{[web citation]}
Fisk CDF Based A2D: y = 1.0 / (1.0+(b/(x-a))^c)^{[web citation]}
Fisk CDF Based B2D: y = d / (1.0+(b/(x-a))^c)^{[web citation]}
Fisk PDF Based2D: y = (c/b) * ((x-a)/b)^(c-1.0) / (1.0 + ((x-a)/b)^c)²^{[web citation]}
Folded Normal PDF Based2D: y = c * (1/b) * cosh(a*x/b²) * exp(-0.5 * (x² + a²)/b²)^{[web citation]}
Frechet CDF Based A2D: y = exp(-1.0 / x^a)^{[web citation]}
Frechet CDF Based B2D: y = b * exp(-1.0 / x^a)^{[web citation]}
Frechet PDF Based A2D: y = exp(- 1.0 / x^a) / x^{( a + 1.0)}^{[web citation]}
Frechet PDF Based B2D: y = b * exp(- 1.0 / x^a) / x^{( a + 1.0)}^{[web citation]}
Genlogistic CDF Based A2D: y = (1.0/(1.0+exp(-(x-a)/b)))^c^{[web citation]}
Genlogistic CDF Based B2D: y = (d/(1.0+exp(-(x-a)/b)))^c^{[web citation]}
Genlogistic PDF Based2D: y = (c/b) * exp(-((x-a)/b)) / (1.0+exp(-((x-a)/b)))^(c+1.0)^{[web citation]}
Gompertz CDF Based2D: y = 1.0 - exp(-b * (a^x-1.0) / ln(a))^{[web citation]}
Gompertz CDF Based Scaled2D: y = Scale * (1.0 - exp(-b * (a^x-1.0) / ln(a)))^{[web citation]}
Gumbel CDF Based2D: y = a * exp(-exp(-x))^{[web citation]}
Gumbel PDF Based2D: y = a * exp(-x-exp(-x))^{[web citation]}
Half Normal PDF Based2D: y = c * ( 1.0/b) * exp(-0.5*((x-a)/b)*((x-a)/b))^{[web citation]}
Inverse_gaussian PDF Based A2D: y = sqrt(b/(c*x³))*exp(-b*(x-a)² / (2.0*a²*x))^{[web citation]}
Inverse_gaussian PDF Based B2D: y = sqrt(b/(c*x³))*exp(-b*(x-a)² / (2.0*a²*x))^{[web citation]}
Levy PDF Based2D: y = b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³)^{[web citation]}
Levy PDF Based Scaled2D: y = Scale * b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³)^{[web citation]}
Log Normal PDF Based2D: y = exp(-0.5*((ln(x)-a)/b)²) / (b*x)^{[web citation]}
Logistic PDF Based2D: y = exp((a-x)/b) / (b*(1.0+exp((a-x)/b))²)^{[web citation]}
Pareto PDF Based2D: y = b * a^b / x^(b+1.0)^{[web citation]}
Power PDF Based2D: y = (a/b) * (x/b)^(a-1.0)^{[web citation]}
Rayleigh CDF Based A2D: y = 1.0 - exp(-x²/(2.0*a²))^{[web citation]}
Rayleigh CDF Based B2D: y = b * exp(-x²/(2.0*a²))^{[web citation]}
Rayleigh PDF Based2D: y = (x/a²) * exp(-x²/(2.0*a²))^{[web citation]}
Rayleigh PDF Based Scaled2D: y = Scale * (x/a²) * exp(-x²/(2.0*a²))^{[web citation]}
Reciprocal CDF Based2D: y = ln(a/x) / ln(a/b)^{[web citation]}
Sech CDF Based2D: y = c * atan(exp((x-a)/b))^{[web citation]}
Weibull CDF Based A2D: y = 1.0 / exp(((x-a)/b)^c)^{[web citation]}
Weibull CDF Based B2D: y = d / exp(((x-a)/b)^c)^{[web citation]}
Weibull PDF Based2D: y = (c/b) * ((x-a)/b)^(c-1.0) / exp(((x-a)/b)^c)^{[web citation]}

Arcsin CDF Based With Offset2D: y = a * asin( (bx+c) / d) + Offset^{[web citation]}
Arcsin PDF Based With Offset2D: y = a / sqrt( b² - x²) + Offset^{[web citation]}
Bradford CDF Based A With Offset2D: y = ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0) + Offset^{[web citation]}
Bradford CDF Based B With Offset2D: y = d * ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0) + Offset^{[web citation]}
Bradford PDF Based With Offset2D: y = c / (( c * (x-a) + b-a) * ln(c + 1.0)) + Offset^{[web citation]}
Burr CDF Based A With Offset2D: y = 1.0 / ( 1.0 + ( b / ( x-a ))^c)^d + Offset^{[web citation]}
Burr CDF Based B With Offset2D: y = f / ( 1.0 + ( b / ( x-a ))^c)^d + Offset^{[web citation]}
Burr PDF Based With Offset2D: y = (c*d/b) * ((x-a)/b)^(-c-1.0) * (1.0+((x-a)/b)^(-c))^(-d-1.0) + Offset^{[web citation]}
Dipole CDF Based With Offset2D: y = a * arctan(x) + b/x + Offset^{[web citation]}
Exponential PDF Based Scaled With Offset2D: y = Scale * (1.0/b) * exp((a-x)/b) + Offset^{[web citation]}
Exponential PDF Based With Offset2D: y = (1.0/b) * exp((a-x)/b) + Offset^{[web citation]}
Extreme Values CDF Based A With Offset2D: y = exp(-exp(-((x-a)/b))) + Offset^{[web citation]}
Extreme Values CDF Based B With Offset2D: y = c * exp(-exp(-((x-a)/b))) + Offset^{[web citation]}
Extreme Values PDF Based With Offset2D: y = (1.0/b) * exp(((a-x)/b)-exp((a-x)/b)) + Offset^{[web citation]}
Fisk CDF Based A With Offset2D: y = 1.0 / (1.0+(b/(x-a))^c) + Offset^{[web citation]}
Fisk CDF Based B With Offset2D: y = d / (1.0+(b/(x-a))^c) + Offset^{[web citation]}
Fisk PDF Based With Offset2D: y = (c/b) * ((x-a)/b)^(c-1.0) / (1.0 + ((x-a)/b)^c)² + Offset^{[web citation]}
Folded Normal PDF Based With Offset2D: y = c * (1/b) * cosh(a*x/b²) * exp(-0.5 * (x² + a²)/b²) + Offset^{[web citation]}
Frechet CDF Based A With Offset2D: y = exp(-1.0 / x^a) + Offset^{[web citation]}
Frechet CDF Based B With Offset2D: y = b * exp(-1.0 / x^a) + Offset^{[web citation]}
Frechet PDF Based A With Offset2D: y = exp(- 1.0 / x^a) / x^{( a + 1.0)} + Offset^{[web citation]}
Frechet PDF Based B With Offset2D: y = b * exp(- 1.0 / x^a) / x^{( a + 1.0)} + Offset^{[web citation]}
Genlogistic CDF Based A With Offset2D: y = (1.0/(1.0+exp(-(x-a)/b)))^c + Offset^{[web citation]}
Genlogistic CDF Based B With Offset2D: y = (d/(1.0+exp(-(x-a)/b)))^c + Offset^{[web citation]}
Genlogistic PDF Based With Offset2D: y = (c/b) * exp(-((x-a)/b)) / (1.0+exp(-((x-a)/b)))^(c+1.0) + Offset^{[web citation]}
Gompertz CDF Based Scaled With Offset2D: y = Scale * (1.0 - exp(-b * (a^x-1.0) / ln(a))) + Offset^{[web citation]}
Gompertz CDF Based With Offset2D: y = 1.0 - exp(-b * (a^x-1.0) / ln(a)) + Offset^{[web citation]}
Gumbel CDF Based With Offset2D: y = a * exp(-exp(-x)) + Offset^{[web citation]}
Gumbel PDF Based With Offset2D: y = a * exp(-x-exp(-x)) + Offset^{[web citation]}
Half Normal PDF Based With Offset2D: y = c * ( 1.0/b) * exp(-0.5*((x-a)/b)*((x-a)/b)) + Offset^{[web citation]}
Inverse_gaussian PDF Based A With Offset2D: y = sqrt(b/(c*x³))*exp(-b*(x-a)² / (2.0*a²*x)) + Offset^{[web citation]}
Inverse_gaussian PDF Based B With Offset2D: y = sqrt(b/(c*x³))*exp(-b*(x-a)² / (2.0*a²*x)) + Offset^{[web citation]}
Levy PDF Based Scaled With Offset2D: y = Scale * b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³) + Offset^{[web citation]}
Levy PDF Based With Offset2D: y = b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³) + Offset^{[web citation]}
Log Normal PDF Based With Offset2D: y = exp(-0.5*((ln(x)-a)/b)²) / (b*x) + Offset^{[web citation]}
Logistic PDF Based With Offset2D: y = exp((a-x)/b) / (b*(1.0+exp((a-x)/b))²) + Offset^{[web citation]}
Pareto PDF Based With Offset2D: y = b * a^b / x^(b+1.0) + Offset^{[web citation]}
Power PDF Based With Offset2D: y = (a/b) * (x/b)^(a-1.0) + Offset^{[web citation]}
Rayleigh CDF Based A With Offset2D: y = 1.0 - exp(-x²/(2.0*a²)) + Offset^{[web citation]}
Rayleigh CDF Based B With Offset2D: y = b * exp(-x²/(2.0*a²)) + Offset^{[web citation]}
Rayleigh PDF Based Scaled With Offset2D: y = Scale * (x/a²) * exp(-x²/(2.0*a²)) + Offset^{[web citation]}
Rayleigh PDF Based With Offset2D: y = (x/a²) * exp(-x²/(2.0*a²)) + Offset^{[web citation]}
Reciprocal CDF Based With Offset2D: y = ln(a/x) / ln(a/b) + Offset^{[web citation]}
Sech CDF Based With Offset2D: y = c * atan(exp((x-a)/b)) + Offset^{[web citation]}
Weibull CDF Based A With Offset2D: y = 1.0 / exp(((x-a)/b)^c) + Offset^{[web citation]}
Weibull CDF Based B With Offset2D: y = d / exp(((x-a)/b)^c) + Offset^{[web citation]}
Weibull PDF Based With Offset2D: y = (c/b) * ((x-a)/b)^(c-1.0) / exp(((x-a)/b)^c) + Offset^{[web citation]}

Arcsin PDF Based Plus Line2D: y = a / sqrt( b² - x²)
y = y + (c * x) + d^{[web citation]}
Dipole CDF Based Plus Line2D: y = a * arctan(x) + b/x
y = y + (c * x) + d^{[web citation]}
Exponential PDF Based Plus Line2D: y = (1.0/b) * exp((a-x)/b)
y = y + (c * x) + d^{[web citation]}
Extreme Values CDF Based A Plus Line2D: y = exp(-exp(-((x-a)/b)))
y = y + (c * x) + d^{[web citation]}
Extreme Values PDF Based Plus Line2D: y = (1.0/b) * exp(((a-x)/b)-exp((a-x)/b))
y = y + (c * x) + d^{[web citation]}
Frechet CDF Based A Plus Line2D: y = exp(-1.0 / x^a)
y = y + (b * x) + c^{[web citation]}
Frechet CDF Based B Plus Line2D: y = b * exp(-1.0 / x^a)
y = y + (c * x) + d^{[web citation]}
Frechet PDF Based A Plus Line2D: y = exp(- 1.0 / x^a) / x^{( a + 1.0)}
y = y + (b * x) + c^{[web citation]}
Frechet PDF Based B Plus Line2D: y = b * exp(- 1.0 / x^a) / x^{( a + 1.0)}
y = y + (c * x) + d^{[web citation]}
Gompertz CDF Based Plus Line2D: y = 1.0 - exp(-b * (a^x-1.0) / ln(a))
y = y + (c * x) + d^{[web citation]}
Gumbel CDF Based Plus Line2D: y = a * exp(-exp(-x))
y = y + (b * x) + c^{[web citation]}
Gumbel PDF Based Plus Line2D: y = a * exp(-x-exp(-x))
y = y + (b * x) + c^{[web citation]}
Levy PDF Based Plus Line2D: y = b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³)
y = y + (c * x) + d^{[web citation]}
Log Normal PDF Based Plus Line2D: y = exp(-0.5*((ln(x)-a)/b)²) / (b*x)
y = y + (c * x) + d^{[web citation]}
Logistic PDF Based Plus Line2D: y = exp((a-x)/b) / (b*(1.0+exp((a-x)/b))²)
y = y + (c * x) + d^{[web citation]}
Pareto PDF Based Plus Line2D: y = b * a^b / x^(b+1.0)
y = y + (c * x) + d^{[web citation]}
Power PDF Based Plus Line2D: y = (a/b) * (x/b)^(a-1.0)
y = y + (c * x) + d^{[web citation]}
Rayleigh CDF Based A Plus Line2D: y = 1.0 - exp(-x²/(2.0*a²))
y = y + (b * x) + c^{[web citation]}
Rayleigh CDF Based B Plus Line2D: y = b * exp(-x²/(2.0*a²))
y = y + (c * x) + d^{[web citation]}
Rayleigh PDF Based Plus Line2D: y = (x/a²) * exp(-x²/(2.0*a²))
y = y + (b * x) + c^{[web citation]}
Rayleigh PDF Based Scaled Plus Line2D: y = Scale * (x/a²) * exp(-x²/(2.0*a²))
y = y + (c * x) + d^{[web citation]}
Reciprocal CDF Based Plus Line2D: y = ln(a/x) / ln(a/b)
y = y + (c * x) + d^{[web citation]}

2D Engineering

Dispersion Optical2D: n²(x) = A1 + A2*x² + A3/x² + A4/x⁴
Dispersion Optical Square Root2D: + A4/x⁴)^0.5
Electron Beam Lithography Point Spread2D: y = a*exp(-b*x) + c*exp(-(x-d)² / f²) + g*exp(-(x-h)² / i²) + j*exp(-(x-k)² / l²)
Extended Steinhart-Hart2D: 1/T = A + Bln(R) + C(ln(R))² + D(ln(R))³
Graeme Paterson Electric Motor2D: y = A*exp(-b*t)*cos(omega*t + phi) + A2*exp(-b2*t)
Klimpel Kinetics Flotation A2D: y = a * (1 - (1 - exp(-b*x)) / (b*x))
Maxwell - Wiechert 12D: y = a1*exp(-X/Tau1)^{[web citation]}
Maxwell - Wiechert 22D: y = a1*exp(-X/Tau1) + a2*exp(-X/Tau2)^{[web citation]}
Maxwell - Wiechert 32D: y = a1*exp(-X/Tau1) + a2*exp(-X/Tau2) + a3*exp(-X/Tau3)^{[web citation]}
Maxwell - Wiechert 42D: y = a1*exp(-X/Tau1) + a2*exp(-X/Tau2) + a3*exp(-X/Tau3) + a4*exp(-X/Tau4)^{[web citation]}
Modified Arps Well Production2D: y = (qi_x/((1.0-b_x)*Di_x)) * (1.0-((1.0+b_x*Di_x*x)**(1.0-1.0/b_x)))
Ramberg-Osgood2D: y = (Stress / Youngs_Modulus) + (Stress/K)^(1.0/n)
Reciprocal Extended Steinhart-Hart2D: T = 1.0 / (A + Bln(R) + C(ln(R))² + D(ln(R))³)
Reciprocal Steinhart-Hart2D: T = 1.0 / (A + Bln(R) + C(ln(R))³)
Sellmeier Optical2D: n²(x) = 1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3)
Sellmeier Optical Square Root2D: n = (1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3))^0.5
Steinhart-Hart2D: 1/T = A + Bln(R) + C(ln(R))³
VanDeemter Chromatography2D: y = a + b/x + cx

Electron Beam Lithography Point Spread With Offset2D: y = a*exp(-b*x) + c*exp(-(x-d)² / f²) + g*exp(-(x-h)² / i²) + j*exp(-(x-k)² / l²) + Offset
Graeme Paterson Electric Motor With Offset2D: y = A*exp(-b*t)*cos(omega*t + phi) + A2*exp(-b2*t) + Offset
Klimpel Kinetics Flotation A With Offset2D: y = a * (1 - (1 - exp(-b*x)) / (b*x)) + Offset
Maxwell - Wiechert 1 With Offset2D: y = a1*exp(-X/Tau1) + Offset^{[web citation]}
Maxwell - Wiechert 2 With Offset2D: y = a1*exp(-X/Tau1) + a2*exp(-X/Tau2) + Offset^{[web citation]}
Maxwell - Wiechert 3 With Offset2D: y = a1*exp(-X/Tau1) + a2*exp(-X/Tau2) + a3*exp(-X/Tau3) + Offset^{[web citation]}
Maxwell - Wiechert 4 With Offset2D: y = a1*exp(-X/Tau1) + a2*exp(-X/Tau2) + a3*exp(-X/Tau3) + a4*exp(-X/Tau4) + Offset^{[web citation]}
Modified Arps Well Production With Offset2D: y = (qi_x/((1.0-b_x)*Di_x)) * (1.0-((1.0+b_x*Di_x*x)**(1.0-1.0/b_x))) + Offset
Ramberg-Osgood With Offset2D: y = (Stress / Youngs_Modulus) + (Stress/K)^(1.0/n) + Offset
Reciprocal Extended Steinhart-Hart With Offset2D: T = 1.0 / (A + Bln(R) + C(ln(R))² + D(ln(R))³) + Offset
Reciprocal Steinhart-Hart With Offset2D: T = 1.0 / (A + Bln(R) + C(ln(R))³) + Offset
Sellmeier Optical Square Root With Offset2D: n = (1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3))^0.5 + Offset
Sellmeier Optical With Offset2D: n²(x) = 1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3) + Offset

Klimpel Kinetics Flotation A Plus Line2D: y = a * (1 - (1 - exp(-b*x)) / (b*x))
y = y + (c * x) + d
Maxwell - Wiechert 1 Plus Line2D: y = a1*exp(-X/Tau1)
y = y + (c * x) + d^{[web citation]}

2D Exponential

Asymptotic Exponential A2D: y = 1.0 - a^x
Asymptotic Exponential A Transform2D: y = 1.0 - a^{bx + c}
Asymptotic Exponential B2D: y = a * (1.0 - exp(bx))
Bruno Torremans Quadruple Exponential2D: y = Offset - R1 * exp(-x/T1) + R2 * exp(-x/T2) + R3 * exp(-x/T3) + R4 * exp(-x/T4)
Double Asymptotic Exponential B2D: y = a * (1.0 - exp(bx)) + c * (1.0 - exp(dx))
Double Exponential2D: y = a * exp(bx) + c * exp(dx)
Exponential2D: y = a * exp(bx)
Hocket-Sherby2D: y = b - (b-a) * exp(-c * (x^d))
Hoerl2D: y = x^a * exp(x)
Hoerl Transform2D: y = (bx + c)^a * exp(bx + c)
Inverted Exponential2D: y = a * exp(b/x)
Inverted Offset Exponential2D: y = a * exp(b/(x+c))
Jonathan Litz Custom Exponential2D: y = a + b * x + c * exp(-d * x) - c * x * exp(-d * x)^{[web citation]}
Lake Nganoke Samples Exponential2D: y = C/(1.0 + exp((x-A)/B)) + D * exp((x-B)/E)^{[web citation]}
Offset Exponential2D: y = a * exp(bx + c)
Scaled Exponential2D: y = a * exp(x)
Shifted Exponential2D: y = a * exp(x + b)
Simple Exponential2D: y = a^x
Standard Vapor Pressure2D: y = exp(a + (b/x) + c*ln(x))
Steve Battison Exponential A2D: y = exp((a + bx) / (c + dx))
Steve Battison Exponential B2D: y = a * exp((b + cx) / (d + fx))
Stirling2D: y = a * (exp(bx) - 1.0) / b
Triple Exponential2D: y = a * exp(bx) + c * exp(dx) + f * exp(gx)

Asymptotic Exponential A Transform With Offset2D: y = 1.0 - a^{bx + c} + Offset
Asymptotic Exponential A With Offset2D: y = 1.0 - a^x + Offset
Asymptotic Exponential B With Offset2D: y = a * (1.0 - exp(bx)) + Offset
Double Asymptotic Exponential B With Offset2D: y = a * (1.0 - exp(bx)) + c * (1.0 - exp(dx)) + Offset
Double Exponential With Offset2D: y = a * exp(bx) + c * exp(dx) + Offset
Exponential With Offset2D: y = a * exp(bx) + Offset
Hoerl Transform With Offset2D: y = (bx + c)^a * exp(bx + c) + Offset
Hoerl With Offset2D: y = x^a * exp(x) + Offset
Inverted Exponential With Offset2D: y = a * exp(b/x) + Offset
Inverted Offset Exponential With Offset2D: y = a * exp(b/(x+c)) + Offset
Lake Nganoke Samples Exponential With Offset2D: y = C/(1.0 + exp((x-A)/B)) + D * exp((x-B)/E) + Offset^{[web citation]}
Offset Exponential With Offset2D: y = a * exp(bx + c) + Offset
Scaled Exponential With Offset2D: y = a * exp(x) + Offset
Shifted Exponential With Offset2D: y = a * exp(x + b) + Offset
Simple Exponential With Offset2D: y = a^x + Offset
Standard Vapor Pressure With Offset2D: y = exp(a + (b/x) + c*ln(x)) + Offset
Steve Battison Exponential A With Offset2D: y = exp((a + bx) / (c + dx)) + Offset
Steve Battison Exponential B With Offset2D: y = a * exp((b + cx) / (d + fx)) + Offset
Stirling With Offset2D: y = a * (exp(bx) - 1.0) / b + Offset
Triple Exponential With Offset2D: y = a * exp(bx) + c * exp(dx) + f * exp(gx) + Offset

Asymptotic Exponential A Plus Line2D: y = 1.0 - a^x
y = y + (b * x) + c
Asymptotic Exponential B Plus Line2D: y = a * (1.0 - exp(bx))
y = y + (c * x) + d
Exponential Plus Line2D: y = a * exp(bx)
y = y + (c * x) + d
Hoerl Plus Line2D: y = x^a * exp(x)
y = y + (b * x) + c
Inverted Exponential Plus Line2D: y = a * exp(b/x)
y = y + (c * x) + d
Scaled Exponential Plus Line2D: y = a * exp(x)
y = y + (b * x) + c
Shifted Exponential Plus Line2D: y = a * exp(x + b)
y = y + (c * x) + d
Simple Exponential Plus Line2D: y = a^x
y = y + (b * x) + c
Stirling Plus Line2D: y = a * (exp(bx) - 1.0) / b
y = y + (c * x) + d

2D FourierSeries

1 Term (Scaled X)2D: y = a0 + a1*sin(c1*x)+b1*cos(c1*x)^{[web citation]}
1 Term Standard2D: y = a0 + a1*sin(x)+b1*cos(x)^{[web citation]}
2 Term Standard2D: y = a0 + a1*sin(x)+b1*cos(x) + a2*sin(2x)+b2*cos(2x)^{[web citation]}
3 Term Standard2D: y = a0 + a1*sin(x)+b1*cos(x) + a2*sin(2x)+b2*cos(2x) + a3*sin(3x)+b3*cos(3x)^{[web citation]}
4 Term Standard2D: 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)^{[web citation]}

2D LegendrePolynomial

Gamma Ray Angular Distribution (degrees) A2D: y = A0 + A2 * P₂(cos(theta))
Gamma Ray Angular Distribution (degrees) B2D: y = A0 + A2 * P₂(cos(theta)) + A4 * P₄(cos(theta))
Gamma Ray Angular Distribution (radians) A2D: y = A0 + A2 * P₂(cos(theta))
Gamma Ray Angular Distribution (radians) B2D: y = A0 + A2 * P₂(cos(theta)) + A4 * P₄(cos(theta))
Legendre Polynomial A - Second Degree2D: y = a + bx + cP₂^{[web citation]}
Legendre Polynomial B - Third Degree2D: y = a + bx + cP₂ + dP₃^{[web citation]}
Legendre Polynomial C - Fourth Degree2D: y = a + bx + cP₂ + dP₃ + fP₄^{[web citation]}
Legendre Polynomial D - Fifth Degree2D: y = a + bx + cP₂ + dP₃ + fP₄ + gP₅^{[web citation]}
Legendre Polynomial E - Sixth Degree2D: y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆^{[web citation]}
Legendre Polynomial F - Seventh Degree2D: y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇^{[web citation]}
Legendre Polynomial G - Eighth Degree2D: y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ + jP₈^{[web citation]}
Legendre Polynomial H - Ninth Degree2D: y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ + jP₈ + kP₉^{[web citation]}
Legendre Polynomial I - Tenth Degree2D: y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ + jP₈ + kP₉ + mP₁₀^{[web citation]}

2D Logarithmic

Base 10 Logarithmic2D: y = a + b*log₁₀(x)
Bradley2D: y = a * ln(-b * ln(x))
Bradley Transform2D: y = a * ln(-b * ln(cx + d))
Crystal Resonator Ageing MIL-PRF-55310E2D: y = A(ln(Bt + 1)) + f0
Cubic Logarithmic2D: y = a + b*ln(x) + c*ln(x)² + d*ln(x)³
Cubic Logarithmic Scaled2D: y = a + b*ln(f*x) + c*ln(f*x)² + d*ln(f*x)³
Cubic Logarithmic Transform2D: y = a + b*ln(f*x+g) + c*ln(f*x+g)² + d*ln(f*x+g)³
Linear Logarithmic2D: y = a + b*ln(x)
Linear Logarithmic Scaled2D: y = a + b*ln(cx)
Linear Logarithmic Shifted2D: y = a + b*ln(c+x)
Linear Logarithmic Transform2D: y = a + b*ln(cx+d)
Quadratic Logarithmic2D: y = a + b*ln(x) + c*ln(x)²
Quadratic Logarithmic Scaled2D: y = a + b*ln(dx) + c*ln(dx)²
Quadratic Logarithmic Transform2D: y = a + b*ln(dx+f) + c*ln(dx+f)²
Quartic Logarithmic2D: y = a + b*ln(x) + c*ln(x)² + d*ln(x)³ + f*ln(x)⁴
Quartic Logarithmic Scaled2D: y = a + b*ln(h*x) + c*ln(h*x)² + d*ln(h*x)³ + f*ln(h*x)⁴
Quartic Logarithmic Transform2D: 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
Quintic Logarithmic2D: y = a + b*ln(x) + c*ln(x)² + d*ln(x)³ + f*ln(x)⁴ + g*ln(x)⁵
Quintic Logarithmic Scaled2D: 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
Quintic Logarithmic Transform2D: 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

Bradley Transform With Offset2D: y = a * ln(-b * ln(cx + d)) + Offset
Bradley With Offset2D: y = a * ln(-b * ln(x)) + Offset

Bradley Plus Line2D: y = a * ln(-b * ln(x))
y = y + (c * x) + d

2D Miscellaneous

Arrhenius Rate Constant Law2D: y = a * exp(-b/x)
Arrhenius Rate Constant Law Stretched2D: y = a * exp(-pow(b/x, c))
Bleasdale-Nelder2D: y = (a + bx)^-c
Catenary2D: y = a * cosh(x / a)^{[web citation]}
Catenary Transform2D: y = a * cosh((bx + c) / a)^{[web citation]}
Cissoid Of Diocles2D: y = a(x³ / (2b-x))^0.5^{[web citation]}
Cissoid Of Diocles Transform2D: y = a((x*c-d)³ / (2b-(x*c-d)))^0.5^{[web citation]}
Combined Power And Exponential2D: y = ax^b * exp(cx)
David Rodbard NIH2D: y = d + (a - d) / (1.0 + (x/c)^b)^{[web citation]}
Double Langmuir Probe Characteristic2D: y = a * tanh(bx+c)
Double Rectangular Hyperbola A2D: y = ax/(b+x) + cx/(d+x)
Double Rectangular Hyperbola B2D: y = ax/(b+x) + cx/(d+x) + fx
Figure Eight Curve2D: y = a(x² - (x⁴/b²))^0.5^{[web citation]}
Figure Eight Curve Transform2D: y = a((cx+d)² - ((cx+d)⁴/b²))^0.5^{[web citation]}
Gunary2D: y = x / (a + bx + cx^0.5)
Hyperbola A Modified2D: y = ax/(1+bx)
Hyperbola B Modified2D: y = x/(a+bx)
Hyperbolic Decay2D: y = ab/(b+x)
Karplus NMR Spectroscopy2D: J(da) = Acos²(da) + Bcos(da) + C^{[web citation]}
Karplus NMR Spectroscopy Scaled2D: J(da) = Acos²(s * da) + Bcos(s * da) + C^{[web citation]}
Lame's Cubic2D: y = (a³ - x³)^1/3^{[web citation]}
Lame's Cubic Transform2D: y = (a³ - (bx + c)³)^1/3^{[web citation]}
Miscellaneous 12D: y = 1.0 + a(1.0 - exp(bx))
Morse Potential2D: V = D*(exp(-2*m*(x-u)) - 2*exp(-m*(x-u))) + offset^{[web citation]}
Nelson-Siegel2D: y(m) = B0 + B1*((1-exp(-m/t))/(m/t)) + B2*(((1-exp(-m/t))/(m/t)) - exp(-m/t))^{[web citation]}
Nelson-Siegel-Svensson2D: 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))^{[web citation]}
Niele's Semi-cubical Parabola2D: y = (ax²)^1.0/3.0^{[web citation]}
Niele's Semi-cubical Parabola Transform2D: y = (a(b*x+c)²)^1.0/3.0^{[web citation]}
Pareto A2D: y = 1 - x^-a
Pareto B2D: y = a(1 - x^-b)
Pareto C2D: y = 1.0 - (1.0 / (1 + ax)^b)
Pareto D2D: y = 1.0 - (1.0 / x^a)
Pear-shaped Quartic2D: y = a(x³(b-x) / c²)^0.5^{[web citation]}
Pear-shaped Quartic Transform2D: y = a((dx+f)³(b-(dx+f)) / c²)^0.5^{[web citation]}
Physicist Peter's Custom Equation2D: y = A + B*(X-C) + 0.5*G*(X-C)**2
Physicist Peter's Pendulum Traversal2D: y = a*(x + b)^1/2
Polytrope2D: y = a / x^b^{[web citation]}
Polytrope Transform2D: y = a / (cx + d)^b^{[web citation]}
Pursuit Curve2D: y = ax² - log(x)
Pursuit Curve Transform2D: y = a(bx + c)² - log(bx + c)
Rectangular Hyperbola A2D: y = ax/(b+x)
Rectangular Hyperbola B2D: y = ax/(b+x) + cx
Serpentine2D: y = ax / (1.0 + bx²)
Shifted Reciprocal2D: y = 1.0 / (a - x)
Square Modified2D: y = x² - ax
Square Modified Transform2D: y = (bx + c)² - a(bx + c)
Timothy Strobel's Custom Equation2D: y = (A-B*X**C)*(1-(0.5+(arctan((X-D)/E))/pi))+(F-G*X**H)*(0.5+(arctan((X-D)/E))/pi)^{[web citation]}
Transition State Rate Constant Law2D: y = ax^b * exp(-c/x)
Trisectrix Of Maclaurin2D: y = a(x²(3b-x) / (b+x))^0.5^{[web citation]}
Trisectrix Of Maclaurin Transform2D: y = a((cx+d)²(3b-(cx+d)) / (b+(cx+d)))^0.5^{[web citation]}
Witch Of Maria Agnesi A2D: y = 8a³ / (x² + 4a²)
Witch Of Maria Agnesi B2D: y = a³ / (x² + a²)
Witch Of Maria Agnesi C2D: y = a³ / ((x * b + c)² + a²)

Arrhenius Rate Constant Law Stretched With Offset2D: y = a * exp(-pow(b/x, c)) + Offset
Arrhenius Rate Constant Law With Offset2D: y = a * exp(-b/x) + Offset
Bleasdale-Nelder With Offset2D: y = (a + bx)^-c + Offset
Catenary Transform With Offset2D: y = a * cosh((bx + c) / a) + Offset^{[web citation]}
Catenary With Offset2D: y = a * cosh(x / a) + Offset^{[web citation]}
Cissoid Of Diocles Transform With Offset2D: y = a((x*c-d)³ / (2b-(x*c-d)))^0.5 + Offset^{[web citation]}
Cissoid Of Diocles With Offset2D: y = a(x³ / (2b-x))^0.5 + Offset^{[web citation]}
Combined Power And Exponential With Offset2D: y = ax^b * exp(cx) + Offset
Double Langmuir Probe Characteristic With Offset2D: y = a * tanh(bx+c) + Offset
Double Rectangular Hyperbola A With Offset2D: y = ax/(b+x) + cx/(d+x) + Offset
Double Rectangular Hyperbola B With Offset2D: y = ax/(b+x) + cx/(d+x) + fx + Offset
Figure Eight Curve Transform With Offset2D: y = a((cx+d)² - ((cx+d)⁴/b²))^0.5 + Offset^{[web citation]}
Figure Eight Curve With Offset2D: y = a(x² - (x⁴/b²))^0.5 + Offset^{[web citation]}
Gunary With Offset2D: y = x / (a + bx + cx^0.5) + Offset
Hyperbola A Modified With Offset2D: y = ax/(1+bx) + Offset
Hyperbola B Modified With Offset2D: y = x/(a+bx) + Offset
Hyperbolic Decay With Offset2D: y = ab/(b+x) + Offset
Lame's Cubic Transform With Offset2D: y = (a³ - (bx + c)³)^1/3 + Offset^{[web citation]}
Lame's Cubic With Offset2D: y = (a³ - x³)^1/3 + Offset^{[web citation]}
Miscellaneous 1 With Offset2D: y = 1.0 + a(1.0 - exp(bx)) + Offset
Niele's Semi-cubical Parabola Transform With Offset2D: y = (a(b*x+c)²)^1.0/3.0 + Offset^{[web citation]}
Niele's Semi-cubical Parabola With Offset2D: y = (ax²)^1.0/3.0 + Offset^{[web citation]}
Pareto A With Offset2D: y = 1 - x^-a + Offset
Pareto B With Offset2D: y = a(1 - x^-b) + Offset
Pareto C With Offset2D: y = 1.0 - (1.0 / (1 + ax)^b) + Offset
Pareto D With Offset2D: y = 1.0 - (1.0 / x^a) + Offset
Pear-shaped Quartic Transform With Offset2D: y = a((dx+f)³(b-(dx+f)) / c²)^0.5 + Offset^{[web citation]}
Pear-shaped Quartic With Offset2D: y = a(x³(b-x) / c²)^0.5 + Offset^{[web citation]}
Physicist Peter's Pendulum Traversal With Offset2D: y = a*(x + b)^1/2 + Offset
Polytrope Transform With Offset2D: y = a / (cx + d)^b + Offset^{[web citation]}
Polytrope With Offset2D: y = a / x^b + Offset^{[web citation]}
Pursuit Curve Transform With Offset2D: y = a(bx + c)² - log(bx + c) + Offset
Pursuit Curve With Offset2D: y = ax² - log(x) + Offset
Rectangular Hyperbola A With Offset2D: y = ax/(b+x) + Offset
Rectangular Hyperbola B With Offset2D: y = ax/(b+x) + cx + Offset
Serpentine With Offset2D: y = ax / (1.0 + bx²) + Offset
Shifted Reciprocal With Offset2D: y = 1.0 / (a - x) + Offset
Square Modified Transform With Offset2D: y = (bx + c)² - a(bx + c) + Offset
Square Modified With Offset2D: y = x² - ax + Offset
Timothy Strobel's Custom Equation With Offset2D: y = (A-B*X**C)*(1-(0.5+(arctan((X-D)/E))/pi))+(F-G*X**H)*(0.5+(arctan((X-D)/E))/pi) + Offset^{[web citation]}
Transition State Rate Constant Law With Offset2D: y = ax^b * exp(-c/x) + Offset
Trisectrix Of Maclaurin Transform With Offset2D: y = a((cx+d)²(3b-(cx+d)) / (b+(cx+d)))^0.5 + Offset^{[web citation]}
Trisectrix Of Maclaurin With Offset2D: y = a(x²(3b-x) / (b+x))^0.5 + Offset^{[web citation]}
Witch Of Maria Agnesi A With Offset2D: y = 8a³ / (x² + 4a²) + Offset
Witch Of Maria Agnesi B With Offset2D: y = a³ / (x² + a²) + Offset
Witch Of Maria Agnesi C With Offset2D: y = a³ / ((x * b + c)² + a²) + Offset

Arrhenius Rate Constant Law Plus Line2D: y = a * exp(-b/x)
y = y + (c * x) + d
Catenary Plus Line2D: y = a * cosh(x / a)
y = y + (b * x) + c^{[web citation]}
Cissoid Of Diocles Plus Line2D: y = a(x³ / (2b-x))^0.5
y = y + (c * x) + d^{[web citation]}
Figure Eight Curve Plus Line2D: y = a(x² - (x⁴/b²))^0.5
y = y + (c * x) + d^{[web citation]}
Hyperbola A Modified Plus Line2D: y = ax/(1+bx)
y = y + (c * x) + d
Hyperbola B Modified Plus Line2D: y = x/(a+bx)
y = y + (c * x) + d
Hyperbolic Decay Plus Line2D: y = ab/(b+x)
y = y + (c * x) + d
Lame's Cubic Plus Line2D: y = (a³ - x³)^1/3
y = y + (b * x) + c^{[web citation]}
Miscellaneous 1 Plus Line2D: y = 1.0 + a(1.0 - exp(bx))
y = y + (c * x) + d
Niele's Semi-cubical Parabola Plus Line2D: y = (ax²)^1.0/3.0
y = y + (b * x) + c^{[web citation]}
Pareto A Plus Line2D: y = 1 - x^-a
y = y + (b * x) + c
Pareto B Plus Line2D: y = a(1 - x^-b)
y = y + (c * x) + d
Pareto C Plus Line2D: y = 1.0 - (1.0 / (1 + ax)^b)
y = y + (c * x) + d
Pareto D Plus Line2D: y = 1.0 - (1.0 / x^a)
y = y + (b * x) + c
Physicist Peter's Pendulum Traversal Plus Line2D: y = a*(x + b)^1/2
y = y + (c * x) + d
Polytrope Plus Line2D: y = a / x^b
y = y + (c * x) + d^{[web citation]}
Pursuit Curve Plus Line2D: y = ax² - log(x)
y = y + (b * x) + c
Rectangular Hyperbola A Plus Line2D: y = ax/(b+x)
y = y + (c * x) + d
Serpentine Plus Line2D: y = ax / (1.0 + bx²)
y = y + (c * x) + d
Shifted Reciprocal Plus Line2D: y = 1.0 / (a - x)
y = y + (b * x) + c
Square Modified Plus Line2D: y = x² - ax
y = y + (b * x) + c
Trisectrix Of Maclaurin Plus Line2D: y = a(x²(3b-x) / (b+x))^0.5
y = y + (c * x) + d^{[web citation]}
Witch Of Maria Agnesi A Plus Line2D: y = 8a³ / (x² + 4a²)
y = y + (b * x) + c
Witch Of Maria Agnesi B Plus Line2D: y = a³ / (x² + a²)
y = y + (b * x) + c

2D NIST

NIST Bennett52D: y = a * (b+x)^-1/c^{[web citation]}
NIST BoxBOD2D: y = a * (1.0-exp(-b*x))^{[web citation]}
NIST Chwirut2D: y = exp(-a*x) / (b + c*x)^{[web citation]}
NIST DanWood2D: y = a*x^b^{[web citation]}
NIST ENSO2D: 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)^{[web citation]}
NIST Eckerle42D: y = (a/b) * exp(-0.5*((x-c)/b)²)^{[web citation]}
NIST Gauss2D: y = a*exp(-b*x) + c*exp(-(x-d)² / f²) + g*exp(-(x-h)² / i²)^{[web citation]}
NIST Hahn2D: y = (a + b*x + c*x² + d*x³) / (1.0 + f*x + g*x² + h*x³)^{[web citation]}
NIST Kirby2D: y = (a + b*x + c*x²) / (1.0 + d*x + f*x²)^{[web citation]}
NIST Lanczos2D: y = a*exp(-b*x) + c*exp(-d*x) + f*exp(-g*x)^{[web citation]}
NIST MGH092D: y = a * (x² + b*x) / (x² + c*x + d)^{[web citation]}
NIST MGH102D: y = a * exp(b/(x+c))^{[web citation]}
NIST MGH172D: y = a + b*exp(-x*d) + c*exp(-x*f)^{[web citation]}
NIST Misra1a2D: y = a * (1.0 - exp(-b*x))^{[web citation]}
NIST Misra1b2D: y = a * (1.0 - (1.0+b*x/2.0)^-2.0)^{[web citation]}
NIST Misra1c2D: y = a * (1.0 - (1.0 + 2.0*b*x)^-0.5)^{[web citation]}
NIST Misra1d2D: y = a * b * x * (1.0 + b*x)^-1.0^{[web citation]}
NIST Rat422D: y = a / (1.0 + exp(b - c*x))^{[web citation]}
NIST Rat432D: y = a / ((1.0 + exp(b - c*x))^(1.0/d))^{[web citation]}
NIST Roszman2D: y = a - bx - (arctan(c/(x-d)) / pi)^{[web citation]}
NIST Thurber2D: y = (a + bx + cx² + dx³) / (1.0 + fx + gx² + hx³)^{[web citation]}

NIST Bennett5 With Offset2D: y = a * (b+x)^-1/c + Offset^{[web citation]}
NIST BoxBOD With Offset2D: y = a * (1.0-exp(-b*x)) + Offset^{[web citation]}
NIST Chwirut With Offset2D: y = exp(-a*x) / (b + c*x) + Offset^{[web citation]}
NIST DanWood With Offset2D: y = a*x^b + Offset^{[web citation]}
NIST Eckerle4 With Offset2D: y = (a/b) * exp(-0.5*((x-c)/b)²) + Offset^{[web citation]}
NIST Gauss With Offset2D: y = a*exp(-b*x) + c*exp(-(x-d)² / f²) + g*exp(-(x-h)² / i²) + Offset^{[web citation]}
NIST Hahn With Offset2D: y = (a + b*x + c*x² + d*x³) / (1.0 + f*x + g*x² + h*x³) + Offset^{[web citation]}
NIST Kirby With Offset2D: y = (a + b*x + c*x²) / (1.0 + d*x + f*x²) + Offset^{[web citation]}
NIST Lanczos With Offset2D: y = a*exp(-b*x) + c*exp(-d*x) + f*exp(-g*x) + Offset^{[web citation]}
NIST MGH09 With Offset2D: y = a * (x² + b*x) / (x² + c*x + d) + Offset^{[web citation]}
NIST MGH10 With Offset2D: y = a * exp(b/(x+c)) + Offset^{[web citation]}
NIST Misra1a With Offset2D: y = a * (1.0 - exp(-b*x)) + Offset^{[web citation]}
NIST Misra1b With Offset2D: y = a * (1.0 - (1.0+b*x/2.0)^-2.0) + Offset^{[web citation]}
NIST Misra1c With Offset2D: y = a * (1.0 - (1.0 + 2.0*b*x)^-0.5) + Offset^{[web citation]}
NIST Misra1d With Offset2D: y = a * b * x * (1.0 + b*x)^-1.0 + Offset^{[web citation]}
NIST Rat42 With Offset2D: y = a / (1.0 + exp(b - c*x)) + Offset^{[web citation]}
NIST Rat43 With Offset2D: y = a / ((1.0 + exp(b - c*x))^(1.0/d)) + Offset^{[web citation]}
NIST Thurber With Offset2D: y = (a + bx + cx² + dx³) / (1.0 + fx + gx² + hx³) + Offset^{[web citation]}

NIST BoxBOD Plus Line2D: y = a * (1.0-exp(-b*x))
y = y + (c * x) + d^{[web citation]}
NIST DanWood Plus Line2D: y = a*x^b
y = y + (c * x) + d^{[web citation]}
NIST Misra1a Plus Line2D: y = a * (1.0 - exp(-b*x))
y = y + (c * x) + d^{[web citation]}
NIST Misra1b Plus Line2D: y = a * (1.0 - (1.0+b*x/2.0)^-2.0)
y = y + (c * x) + d^{[web citation]}
NIST Misra1c Plus Line2D: y = a * (1.0 - (1.0 + 2.0*b*x)^-0.5)
y = y + (c * x) + d^{[web citation]}
NIST Misra1d Plus Line2D: y = a * b * x * (1.0 + b*x)^-1.0
y = y + (c * x) + d^{[web citation]}

2D Optical

CAUCHY2D: n = A + B/x² + C/x⁴^{[web citation]}
CONRADY12D: n = A + B/x + C/x^3.5^{[web citation]}
CONRADY22D: n = A + B/x² + C/x^3.5^{[web citation]}
HARTMANN12D: n = A + B/(C - x)^{[web citation]}
HARTMANN22D: n = A + B/(C - x)²^{[web citation]}
HARTMANN3a2D: n = A + B/(C - x)^1.2^{[web citation]}
HARTMANN3b2D: n = A/(x - B)^1.2^{[web citation]}
HARTMANN42D: n = A + B/(C - x) + D/(E - x)^{[web citation]}
HERZBRGR2X22D: n = A + Bx² + C / (x² - 0.028) + D / (x² - 0.028)²^{[web citation]}
HERZBRGR3X22D: n = A + Bx² + Cx⁴ + D / (x² - 0.028) + E / (x² - 0.028)²^{[web citation]}
HERZBRGR3X32D: n = A + Bx² + Cx⁴ + D / (x² - 0.028) + E / (x² - 0.028)² + F / (x² - 0.028)⁴^{[web citation]}
HERZBRGR4X22D: n = A + Bx² + Cx⁴ + Dx⁶ + E / (x² - 0.028) + F / (x² - 0.028)²^{[web citation]}
HERZBRGR5X22D: n = A + Bx² + Cx⁴ + Dx⁶ + Ex⁸ + F / (x² - 0.028) + G / (x² - 0.028)²^{[web citation]}
HERZBRGRJK2D: n = A + Bx² + Cx⁴ + Dx⁶ + E / (x² - J) + F / (x² - K)²^{[web citation]}
HoO12D: n² = A + Bx² + C / (x² - D²)^{[web citation]}
HoO22D: n² = A + Bx² + Cx² / (x² - D²)^{[web citation]}
KINGSLAKE12D: n² = A + B/(x²-C²) + D/(x²-E²)^{[web citation]}
KINGSLAKE22D: n² = A + B/(x²-C²) + D/(x²-E²) + F/(x²-G²)^{[web citation]}
MISC012D: n² = A + B/(x²-C²)^{[web citation]}
MISC022D: n² = A + Bx² + C/(x²-D²)^{[web citation]}
MISC032D: n² = A + B/x² + Cx²/(x²-D²)^{[web citation]}
MISC042D: n² = A + Bx² + Cx⁴ + D/x² + Ex²/(x²-F+(Gx²/(x²-F)))^{[web citation]}
SCHOTT2X32D: n² = A + Bx² + C/x² + D/x⁴ + E/x⁶^{[web citation]}
SCHOTT2X42D: n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ + F/x⁸^{[web citation]}
SCHOTT2X52D: n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ + F/x⁸ + G/x¹⁰^{[web citation]}
SCHOTT2X62D: n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ + F/x⁸ + G/x¹⁰ + H/x¹²^{[web citation]}
SCHOTT3X32D: n² = A + Bx² + Cx⁴ + D/x² + E/x⁴ + F/x⁶^{[web citation]}
SCHOTT3X42D: n² = A + Bx² + Cx⁴ + D/x² + E/x⁴ + F/x⁶ + G/x⁸^{[web citation]}
SCHOTT3X52D: n² = A + Bx² + Cx⁴ + D/x² + E/x⁴ + F/x⁶ + G/x⁸ + H/x¹⁰^{[web citation]}
SCHOTT4X42D: n² = A + Bx² + Cx⁴ + Dx⁶ + E/x² + F/x⁴ + G/x⁶ + H/x⁸^{[web citation]}
SCHOTT5X52D: n² = A + Bx² + Cx⁴ + Dx⁶ + Ex⁸ + F/x² + G/x⁴ + H/x⁶ + J/x⁸ + K/x¹⁰^{[web citation]}
SELL1T2D: n² = 1 + Ax² / (x² - B²)^{[web citation]}
SELL1TA2D: n² = A + Bx² / (x² - C²)^{[web citation]}
SELL2T2D: n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²)^{[web citation]}
SELL2TA2D: n² = A + Bx²/(x²-C²) + Dx²/(x²-E²)^{[web citation]}
SELL3T2D: n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) + Ex²/(x²-F²)^{[web citation]}
SELL3TA2D: n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²)^{[web citation]}
SELL4T2D: n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) + Ex²/(x²-F²) + Gx²/(x²-H²)^{[web citation]}
SELL4TA2D: n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²)^{[web citation]}
SELL5T2D: n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) + Ex²/(x²-F²) + Gx²/(x²-H²) + Jx²/(x²-K²)^{[web citation]}
SELL5TA2D: n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) + Kx²/(x²-M²)^{[web citation]}
SELL6TA2D: n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) + Kx²/(x²-M²) + Nx²/(x²-P²)^{[web citation]}
SELL7TA2D: n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) + Kx²/(x²-M²) + Nx²/(x²-P²) + Qx²/(x²-R²)^{[web citation]}
SELLMOD12D: n² = A + Bx + Cx² + Dx²/(x²-E²)^{[web citation]}
SELLMOD1A2D: n² = A + Bx + Cx² + D/(x²-E²)^{[web citation]}
SELLMOD22D: n² = A + Bx + Cx⁴ + Dx²/(x²-E²)^{[web citation]}
SELLMOD2A2D: n² = A + Bx + Cx⁴ + D/(x²-E²)^{[web citation]}
SELLMOD32D: n² = (Ax²+B)/(x²-C²) + Dx²/(x²-E²)^{[web citation]}
SELLMOD42D: n² = A + Bx² + C/x² + Dx²/(x²-E²) + Fx²/(x²-G²)^{[web citation]}
SELLMOD4A2D: n² = A + Bx² + C/x² + D/(x²-E²) + F/(x²-G²)^{[web citation]}
SELLMOD52D: n² = A + Bx² + Cx²/(x²-D²) + Ex²/(x²-F²)^{[web citation]}
SELLMOD62D: n² = A + Bx²/(x²-C²) + D/(x²-E²)^{[web citation]}
SELLMOD72D: n² = A + Bx² + Cx⁴ + D/x⁶ + Ex²/(x²-F²)^{[web citation]}
SELLMOD7A2D: n² = A + Bx² + Cx⁴ + D/x⁶ + E/(x²-F²)^{[web citation]}
SELLMOD82D: n² = A + Bx² + Cx⁴ + D/(x²-E²) + F/(x²-G²)^{[web citation]}
SELLMOD92D: n² = A + B/x² + C/x⁴ + D/x⁶ + Ex²/(x²-F²)^{[web citation]}

HARTMANN3b With Offset2D: n = A/(x - B)^1.2 + Offset^{[web citation]}
SELLMOD3 With Offset2D: n² = (Ax²+B)/(x²-C²) + Dx²/(x²-E²) + Offset^{[web citation]}

HARTMANN3b Plus Line2D: n = A/(x - B)^1.2
n = n + (c * x) + d^{[web citation]}

2D Peak

Arnold Cohen Log-Normal Peak Shifted2D: y = a * (exp(-0.5 * ((ln(x-f)-b)/c)²)) / (d * (x-g))
Arnold Cohen Two-Parameter Log-Normal Peak Shifted2D: y = exp(-0.5 * ((ln(x-d)-b)/c)²) / (sqrt(2*pi) * c * (x-f))
Box Lucas A2D: y = a * (1.0 - b^x)
Box Lucas A Shifted2D: y = a * (1.0 - b^x-c)
Box Lucas B2D: y = a * (1.0 - exp(-bx))
Box Lucas B Shifted2D: y = a * (1.0 - exp(-b(x-c)))
Box Lucas C2D: y = (a / (a-b)) * (exp(-bx) - exp(-ax))
Box Lucas C shifted2D: y = (a / (a-b)) * (exp(-b(x-c)) - exp(-a(x-c)))
Extreme Value 4 Parameter Peak2D: y = a * exp(-x + b + c - c*d*exp(-1.0 * ((x + c*ln(d) - b) / c)) / (c*d))
Extreme Value Area2D: y = (a/c) * exp(-exp(-((x-b)/c))-((x-b)/c))
Extreme Value Peak2D: y = a * exp(-exp(-((x-b)/c))-((x-b)/c)+1.0)
Gaussian Area2D: y = (a / (pow(2*pi, 0.5) * c)) * exp(-0.5 * ((x-b)/c)²)
Gaussian Peak2D: y = a * exp(-0.5 * ((x-b)/c)²)
Gaussian Peak Modified2D: y = a * exp(-0.5 * ((x-b)/c)^d)
Hamilton2D: Vb = Gb * (I/mu)^{ln(mu/I)/(B*B)} + (Vb_max * I)/(I + sigma_b)
Laplace Area2D: y = (a / (pow(2.0, 0.5) * c)) * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c)
Laplace Peak2D: y = a * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c)
Log-Normal 4 Parameter2D: y = a * exp(-1.0 * (ln(2) * ln((((x-b) * (d²-1)) / (c*d)) + 1.0)²) / ln(d)²)
Log-Normal Peak A2D: y = a * exp(-0.5 * ((ln(x)-b)/c)²)
Log-Normal Peak A Modified2D: y = a * exp(-0.5 * ((ln(x)-b)/c)^d)
Log-Normal Peak A Modified Shifted2D: y = a * exp(-0.5 * ((ln(x-f)-b)/c)^d)
Log-Normal Peak A Shifted2D: y = a * exp(-0.5 * ((ln(x-d)-b)/c)²)
Log-Normal Peak B2D: y = a * exp(-0.5 * (ln(x/b)/c)²)
Log-Normal Peak B Modified2D: y = a * exp(-0.5 * (ln(x/b)/c)^d)
Log-Normal Peak B Modified Shifted2D: y = a * exp(-0.5 * (ln((x-f)/b)/c)^d)
Log-Normal Peak B Shifted2D: y = a * exp(-0.5 * (ln((x-d/b))/c)²)
Logistic Area2D: y = a * exp(-1.0 * (x-b) / c) / (c * (1.0 + exp(-1.0 * (x-b) / c))²)
Logistic Peak2D: y = 4a * exp(-1.0 * (x-b) / c) / (1.0 + exp(-1.0 * (x-b) / c))²
Lorentzian Modified Peak A2D: y = 1.0 / (1.0 + (x-a)^b)
Lorentzian Modified Peak B2D: y = 1.0 / (a + (x-b)^c)
Lorentzian Modified Peak C2D: y = a / (b + (x-c)^d)
Lorentzian Modified Peak D2D: y = 1.0 / (1.0 + ((x-a)/b)^c)
Lorentzian Modified Peak E2D: y = 1.0 / (a + ((x-b)/c)^d)
Lorentzian Modified Peak F2D: y = a / (b + ((x-c)/d)^f)
Lorentzian Modified Peak G2D: y = a / (1.0 + ((x-b)/c)^d)
Lorentzian Peak A2D: y = 1.0 / (1.0 + (x-a)²)
Lorentzian Peak B2D: y = 1.0 / (a + (x-b)²)
Lorentzian Peak C2D: y = a / (b + (x-c)²)
Lorentzian Peak D2D: y = 1.0 / (1.0 + ((x-a)/b)²)
Lorentzian Peak E2D: y = 1.0 / (a + ((x-b)/c)²)
Lorentzian Peak F2D: y = a / (b + ((x-c)/d)²)
Lorentzian Peak G2D: y = a / (1.0 + ((x-b)/c)²)
Pseudo-Voight Peak2D: y = a * (d * (1/(1+((x-b)/c)²)) + (1-d) * exp(-0.5 * ((x-b)/c)²))
Pseudo-Voight Peak Modified2D: y = a * (d * (1/(1+((x-b)/c)^f)) + (1-d) * exp(-0.5 * ((x-b)/c)^g))
Pulse Peak2D: y = 4a * exp(-(x-b)/c) * (1.0 - exp(-(x-b)/c))
UVED Fruit Growth Rate2D: y = ((t/5)^(a-1)*(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)*((b-1)/(a+b-2))^(b-1))^{[web citation]}
UVED Fruit Growth Rate B2D: 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))^{[web citation]}
UVED Fruit Growth Rate Scaled2D: y = (c*t)^(a-1)*(1-(c*t)^(b-1))/(((a-1)/(a+b-2))^(a-1)*((b-1)/(a+b-2))^(b-1))^{[web citation]}
UVED Fruit Growth Rate Scaled B2D: 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))^{[web citation]}
UVED Fruit Growth Rate Transform2D: 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))^{[web citation]}
UVED Fruit Growth Rate Transform B2D: 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))^{[web citation]}
Weibull Peak2D: y = a * exp(-0.5 * (ln(x/b)/c)²)
Weibull Peak Modified2D: y = a * exp(-0.5 * (ln(x/b)/c)^d)
Weibull Peak Modified Shifted2D: y = a * exp(-0.5 * (ln((x-f)/b)/c)^d)
Weibull Peak Shifted2D: y = a * exp(-0.5 * (ln((x-d)/b)/c)²)

Arnold Cohen Log-Normal Peak Shifted With Offset2D: y = a * (exp(-0.5 * ((ln(x-f)-b)/c)²)) / (d * (x-g)) + Offset
Arnold Cohen Two-Parameter Log-Normal Peak Shifted With Offset2D: y = exp(-0.5 * ((ln(x-d)-b)/c)²) / (sqrt(2*pi) * c * (x-f)) + Offset
Box Lucas A Shifted With Offset2D: y = a * (1.0 - b^x-c) + Offset
Box Lucas A With Offset2D: y = a * (1.0 - b^x) + Offset
Box Lucas B Shifted With Offset2D: y = a * (1.0 - exp(-b(x-c))) + Offset
Box Lucas B With Offset2D: y = a * (1.0 - exp(-bx)) + Offset
Box Lucas C With Offset2D: y = (a / (a-b)) * (exp(-bx) - exp(-ax)) + Offset
Box Lucas C shifted With Offset2D: y = (a / (a-b)) * (exp(-b(x-c)) - exp(-a(x-c))) + Offset
Extreme Value 4 Parameter Peak With Offset2D: y = a * exp(-x + b + c - c*d*exp(-1.0 * ((x + c*ln(d) - b) / c)) / (c*d)) + Offset
Extreme Value Area With Offset2D: y = (a/c) * exp(-exp(-((x-b)/c))-((x-b)/c)) + Offset
Extreme Value Peak With Offset2D: y = a * exp(-exp(-((x-b)/c))-((x-b)/c)+1.0) + Offset
Gaussian Area With Offset2D: y = (a / (pow(2*pi, 0.5) * c)) * exp(-0.5 * ((x-b)/c)²) + Offset
Gaussian Peak Modified With Offset2D: y = a * exp(-0.5 * ((x-b)/c)^d) + Offset
Gaussian Peak With Offset2D: y = a * exp(-0.5 * ((x-b)/c)²) + Offset
Hamilton With Offset2D: Vb = Gb * (I/mu)^{ln(mu/I)/(B*B)} + (Vb_max * I)/(I + sigma_b) + Offset
Laplace Area With Offset2D: y = (a / (pow(2.0, 0.5) * c)) * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c) + Offset
Laplace Peak With Offset2D: y = a * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c) + Offset
Log-Normal 4 Parameter With Offset2D: y = a * exp(-1.0 * (ln(2) * ln((((x-b) * (d²-1)) / (c*d)) + 1.0)²) / ln(d)²) + Offset
Log-Normal Peak A Modified Shifted With Offset2D: y = a * exp(-0.5 * ((ln(x-f)-b)/c)^d) + Offset
Log-Normal Peak A Modified With Offset2D: y = a * exp(-0.5 * ((ln(x)-b)/c)^d) + Offset
Log-Normal Peak A Shifted With Offset2D: y = a * exp(-0.5 * ((ln(x-d)-b)/c)²) + Offset
Log-Normal Peak A With Offset2D: y = a * exp(-0.5 * ((ln(x)-b)/c)²) + Offset
Log-Normal Peak B Modified Shifted With Offset2D: y = a * exp(-0.5 * (ln((x-f)/b)/c)^d) + Offset
Log-Normal Peak B Modified With Offset2D: y = a * exp(-0.5 * (ln(x/b)/c)^d) + Offset
Log-Normal Peak B Shifted With Offset2D: y = a * exp(-0.5 * (ln((x-d/b))/c)²) + Offset
Log-Normal Peak B With Offset2D: y = a * exp(-0.5 * (ln(x/b)/c)²) + Offset
Logistic Area With Offset2D: y = a * exp(-1.0 * (x-b) / c) / (c * (1.0 + exp(-1.0 * (x-b) / c))²) + Offset
Logistic Peak With Offset2D: y = 4a * exp(-1.0 * (x-b) / c) / (1.0 + exp(-1.0 * (x-b) / c))² + Offset
Lorentzian Modified Peak A With Offset2D: y = 1.0 / (1.0 + (x-a)^b) + Offset
Lorentzian Modified Peak B With Offset2D: y = 1.0 / (a + (x-b)^c) + Offset
Lorentzian Modified Peak C With Offset2D: y = a / (b + (x-c)^d) + Offset
Lorentzian Modified Peak D With Offset2D: y = 1.0 / (1.0 + ((x-a)/b)^c) + Offset
Lorentzian Modified Peak E With Offset2D: y = 1.0 / (a + ((x-b)/c)^d) + Offset
Lorentzian Modified Peak F With Offset2D: y = a / (b + ((x-c)/d)^f) + Offset
Lorentzian Modified Peak G With Offset2D: y = a / (1.0 + ((x-b)/c)^d) + Offset
Lorentzian Peak A With Offset2D: y = 1.0 / (1.0 + (x-a)²) + Offset
Lorentzian Peak B With Offset2D: y = 1.0 / (a + (x-b)²) + Offset
Lorentzian Peak C With Offset2D: y = a / (b + (x-c)²) + Offset
Lorentzian Peak D With Offset2D: y = 1.0 / (1.0 + ((x-a)/b)²) + Offset
Lorentzian Peak E With Offset2D: y = 1.0 / (a + ((x-b)/c)²) + Offset
Lorentzian Peak F With Offset2D: y = a / (b + ((x-c)/d)²) + Offset
Lorentzian Peak G With Offset2D: y = a / (1.0 + ((x-b)/c)²) + Offset
Pseudo-Voight Peak Modified With Offset2D: y = a * (d * (1/(1+((x-b)/c)^f)) + (1-d) * exp(-0.5 * ((x-b)/c)^g)) + Offset
Pseudo-Voight Peak With Offset2D: y = a * (d * (1/(1+((x-b)/c)²)) + (1-d) * exp(-0.5 * ((x-b)/c)²)) + Offset
Pulse Peak With Offset2D: y = 4a * exp(-(x-b)/c) * (1.0 - exp(-(x-b)/c)) + Offset
UVED Fruit Growth Rate B With Offset2D: 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)) + Offset^{[web citation]}
UVED Fruit Growth Rate Scaled B With Offset2D: 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)) + Offset^{[web citation]}
UVED Fruit Growth Rate Scaled With Offset2D: y = (c*t)^(a-1)*(1-(c*t)^(b-1))/(((a-1)/(a+b-2))^(a-1)*((b-1)/(a+b-2))^(b-1)) + Offset^{[web citation]}
UVED Fruit Growth Rate Transform B With Offset2D: 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)) + Offset^{[web citation]}
UVED Fruit Growth Rate Transform With Offset2D: 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)) + Offset^{[web citation]}
UVED Fruit Growth Rate With Offset2D: y = ((t/5)^(a-1)*(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)*((b-1)/(a+b-2))^(b-1)) + Offset^{[web citation]}
Weibull Peak Modified Shifted With Offset2D: y = a * exp(-0.5 * (ln((x-f)/b)/c)^d) + Offset
Weibull Peak Modified With Offset2D: y = a * exp(-0.5 * (ln(x/b)/c)^d) + Offset
Weibull Peak Shifted With Offset2D: y = a * exp(-0.5 * (ln((x-d)/b)/c)²) + Offset
Weibull Peak With Offset2D: y = a * exp(-0.5 * (ln(x/b)/c)²) + Offset

Box Lucas A Plus Line2D: y = a * (1.0 - b^x)
y = y + (c * x) + d
Box Lucas B Plus Line2D: y = a * (1.0 - exp(-bx))
y = y + (c * x) + d
Box Lucas C Plus Line2D: y = (a / (a-b)) * (exp(-bx) - exp(-ax))
y = y + (c * x) + d
Lorentzian Modified Peak A Plus Line2D: y = 1.0 / (1.0 + (x-a)^b)
y = y + (c * x) + d
Lorentzian Peak A Plus Line2D: y = 1.0 / (1.0 + (x-a)²)
y = y + (b * x) + c
Lorentzian Peak B Plus Line2D: y = 1.0 / (a + (x-b)²)
y = y + (c * x) + d
Lorentzian Peak D Plus Line2D: y = 1.0 / (1.0 + ((x-a)/b)²)
y = y + (c * x) + d
UVED Fruit Growth Rate Plus Line2D: y = ((t/5)^(a-1)*(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)*((b-1)/(a+b-2))^(b-1))
y = y + (c * x) + d^{[web citation]}

2D Polynomial

1st Order (Linear)2D: y = a + bx
2nd Order (Quadratic)2D: y = a + bx + cx²
3rd Order (Cubic)2D: y = a + bx + cx² + dx³
4th Order (Quartic)2D: y = a + bx + cx² + dx³ + fx⁴
5th Order (Quintic)2D: y = a + bx + cx² + dx³ + fx⁴ + gx⁵
Marc Plante's Custom Quadratic2D: y = (-b + (b² - 4 a (c - x))^0.5) / 2 / a
User-Customizable Polynomial2D: y = user-customizable polynomial
User-Selectable Polynomial2D: y = user-selectable polynomial

Marc Plante's Custom Quadratic With Offset2D: y = (-b + (b² - 4 a (c - x))^0.5) / 2 / a + Offset

2D Power

Geometric Modified2D: y = a * x^(b/x)
Power A Modified2D: y = a * b^x
Power A Modified Transform2D: y = a * b^{cx + d}
Power B Modified2D: y = a^ln(x)
Power B Modified Transform2D: y = a^{ln(bx + c)}
Power C Modified2D: y = (a + x)^b
Power C Modified Transform2D: y = (a + bx)^c
Power Law With Exponential Cutoff2D: p(k) = C * k^(-T) * exp(-k/K)
Root2D: y = a^(1.0/x)
Simple Power2D: y = x^a
Standard Geometric2D: y = a * x^bx
Standard Power2D: y = a * x^b
X Shifted Power2D: y = a * (x-b)^c

Geometric Modified With Offset2D: y = a * x^(b/x) + Offset
Power A Modified Transform With Offset2D: y = a * b^{cx + d} + Offset
Power A Modified With Offset2D: y = a * b^x + Offset
Power B Modified Transform With Offset2D: y = a^{ln(bx + c)} + Offset
Power B Modified With Offset2D: y = a^ln(x) + Offset
Power C Modified Transform With Offset2D: y = (a + bx)^c + Offset
Power C Modified With Offset2D: y = (a + x)^b + Offset
Power Law With Exponential Cutoff With Offset2D: p(k) = C * k^(-T) * exp(-k/K) + Offset
Root With Offset2D: y = a^(1.0/x) + Offset
Simple Power With Offset2D: y = x^a + Offset
Standard Geometric With Offset2D: y = a * x^bx + Offset
Standard Power With Offset2D: y = a * x^b + Offset
X Shifted Power With Offset2D: y = a * (x-b)^c + Offset

Geometric Modified Plus Line2D: y = a * x^(b/x)
y = y + (c * x) + d
Power A Modified Plus Line2D: y = a * b^x
y = y + (c * x) + d
Power B Modified Plus Line2D: y = a^ln(x)
y = y + (b * x) + c
Power C Modified Plus Line2D: y = (a + x)^b
y = y + (c * x) + d
Root Plus Line2D: y = a^(1.0/x)
y = y + (b * x) + c
Simple Power Plus Line2D: y = x^a
y = y + (b * x) + c
Standard Geometric Plus Line2D: y = a * x^bx
y = y + (c * x) + d
Standard Power Plus Line2D: y = a * x^b
y = y + (c * x) + d

2D Sigmoidal

BET Sigmoidal A2D: y = x / (a + bx - (a+b)x²)
BET Sigmoidal B2D: y = abx / (1.0 + (b-2.0)x - (b-1.0)x²)
Boltzmann Sigmoid A2D: y = (a - b) / (1.0 + exp((x-c)/d)) + b
Boltzmann Sigmoid B2D: y = (a - b) / (1.0 + exp((x-c)/(dx))) + b
Chapman2D: y = a * (1.0 - exp(-bx))^c
Don Levin Sigmoid2D: y = a1 / (1.0 + exp(-(x-b1)/c1)) + a2 / (1.0 + exp(-(x-b2)/c2)) + a3 / (1.0 + exp(-(x-b3)/c3))
Five-Parameter Logistic2D: y = d + (a-d) / (1.0 + (x/c)^b)^f
Four-Parameter Logistic2D: y = d + (a-d) / (1.0 + (x/c)^b)
Generalised Logistic2D: y = A + C / (1 + T * exp(-B * (x - M)))^1/T^{[web citation]}
Gompertz A2D: y = a * exp(-exp(b - cx))
Gompertz B2D: y = a * exp(-exp((x-b)/c))
Gompertz C2D: y = a * exp(b * exp(c * x))
Hill2D: y = ax^b / (c^b + x^b)
JJacquelin Generalised Logistic2D: y = L / (1.0 + (b * exp(-k*t)) + (c * exp(h*t)))^{[web citation]}
Janoschek Growth2D: w = a - (1.0 - exp(-b * t^c))^{[web citation]}
Janoschek Growth Modified2D: w = a - (a - w0) * (1.0 - exp(-b * t^c))^{[web citation]}
Logistic A2D: y = a / (1.0 + b*exp(-cx))
Logistic B2D: y = a / (1.0 + (x/b)^c)
Lomolino2D: y = a / (1.0 + b^ln(c/x))
Magnetic Saturation2D: y = ax * (1.0 + b*exp(cx))
Morgan-Mercer-Flodin (MMF)2D: y = (a * b + c * x^d) / (b + x^d)
Peters-Baskin Step-Stool: y (1)2D: y = ln(c + exp(b*d*x)) / d^{[web citation]}
Peters-Baskin Step-Stool: yI (2)2D: yI = ln(exp(b2*c1*d1) + exp(b2*d1*x)) / d1^{[web citation]}
Peters-Baskin Step-Stool: yII (3)2D: K = ln( exp(b2*c1*d1) + exp(b2*d1*x) )
yII = b1*x + K/d1^{[web citation]}
Peters-Baskin Step-Stool: yIII (6)2D: 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^{[web citation]}
Peters-Baskin Step-Stool: yIV (9)2D: 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^{[web citation]}
Peters-Baskin Step-Stool: yV (10)2D: 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^{[web citation]}
Peters-Baskin Step-Stool: yV (10) Scaled2D: 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^{[web citation]}
Richards2D: y = 1.0 / (a + b * e^(c*x))^d
Sigmoid A2D: y = 1.0 / (1.0 + exp(-a(x-b)))
Sigmoid A Modified2D: y = 1.0 / (1.0 + exp(-a(x-b)))^c
Sigmoid B2D: y = a / (1.0 + exp(-(x-b)/c))
Sigmoid B Modified2D: y = a / (1.0 + exp(-(x-b)/c))^d
Weibull2D: y = a - b*exp(-cx^d)
Weibull CDF2D: y = 1.0 - exp(-(x/b)^a)
Weibull CDF Scaled2D: y = Scale * (1.0 - exp(-(x/b)^a))
Weibull PDF2D: y = (a/b) * (x/b)^(a-1.0) * exp(-(x/b)^a)

BET Sigmoidal A With Offset2D: y = x / (a + bx - (a+b)x²) + Offset
BET Sigmoidal B With Offset2D: y = abx / (1.0 + (b-2.0)x - (b-1.0)x²) + Offset
Chapman With Offset2D: y = a * (1.0 - exp(-bx))^c + Offset
Don Levin Sigmoid With Offset2D: y = a1 / (1.0 + exp(-(x-b1)/c1)) + a2 / (1.0 + exp(-(x-b2)/c2)) + a3 / (1.0 + exp(-(x-b3)/c3)) + Offset
Gompertz A With Offset2D: y = a * exp(-exp(b - cx)) + Offset
Gompertz B With Offset2D: y = a * exp(-exp((x-b)/c)) + Offset
Gompertz C With Offset2D: y = a * exp(b * exp(c * x)) + Offset
Hill With Offset2D: y = ax^b / (c^b + x^b) + Offset
JJacquelin Generalised Logistic With Offset2D: y = L / (1.0 + (b * exp(-k*t)) + (c * exp(h*t))) + Offset^{[web citation]}
Logistic A With Offset2D: y = a / (1.0 + b*exp(-cx)) + Offset
Logistic B With Offset2D: y = a / (1.0 + (x/b)^c) + Offset
Lomolino With Offset2D: y = a / (1.0 + b^ln(c/x)) + Offset
Magnetic Saturation With Offset2D: y = ax * (1.0 + b*exp(cx)) + Offset
Morgan-Mercer-Flodin (MMF) With Offset2D: y = (a * b + c * x^d) / (b + x^d) + Offset
Peters-Baskin Step-Stool: y (1) With Offset2D: y = ln(c + exp(b*d*x)) / d + Offset^{[web citation]}
Peters-Baskin Step-Stool: yI (2) With Offset2D: yI = ln(exp(b2*c1*d1) + exp(b2*d1*x)) / d1 + Offset^{[web citation]}
Peters-Baskin Step-Stool: yII (3) With Offset2D: K = ln( exp(b2*c1*d1) + exp(b2*d1*x) )
yII = b1*x + K/d1 + Offset^{[web citation]}
Peters-Baskin Step-Stool: yIII (6) With Offset2D: 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 + Offset^{[web citation]}
Peters-Baskin Step-Stool: yIV (9) With Offset2D: 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 + Offset^{[web citation]}
Richards With Offset2D: y = 1.0 / (a + b * e^(c*x))^d + Offset
Sigmoid A Modified With Offset2D: y = 1.0 / (1.0 + exp(-a(x-b)))^c + Offset
Sigmoid A With Offset2D: y = 1.0 / (1.0 + exp(-a(x-b))) + Offset
Sigmoid B Modified With Offset2D: y = a / (1.0 + exp(-(x-b)/c))^d + Offset
Sigmoid B With Offset2D: y = a / (1.0 + exp(-(x-b)/c)) + Offset
Weibull CDF Scaled With Offset2D: y = Scale * (1.0 - exp(-(x/b)^a)) + Offset
Weibull CDF With Offset2D: y = 1.0 - exp(-(x/b)^a) + Offset
Weibull PDF With Offset2D: y = (a/b) * (x/b)^(a-1.0) * exp(-(x/b)^a) + Offset

BET Sigmoidal A Plus Line2D: y = x / (a + bx - (a+b)x²)
y = y + (c * x) + d
BET Sigmoidal B Plus Line2D: y = abx / (1.0 + (b-2.0)x - (b-1.0)x²)
y = y + (c * x) + d
Sigmoid A Plus Line2D: y = 1.0 / (1.0 + exp(-a(x-b)))
y = y + (c * x) + d
Weibull CDF Plus Line2D: y = 1.0 - exp(-(x/b)^a)
y = y + (c * x) + d
Weibull PDF Plus Line2D: y = (a/b) * (x/b)^(a-1.0) * exp(-(x/b)^a)
y = y + (c * x) + d

2D Simple

Simple Equation 012D: y = a
Simple Equation 022D: y = a/pow(x,-2.0)
Simple Equation 032D: y = a*pow(ln(x),b)
Simple Equation 042D: y = a*pow(x,3.0)
Simple Equation 052D: y = a*pow(x,4.0)
Simple Equation 062D: y = x/(a+b*pow(x,2.0))
Simple Equation 072D: y = a * pow(b,x) * pow(x,c)
Simple Equation 082D: y = a*pow(b,1.0/x)*pow(x,c)
Simple Equation 092D: y = a*exp(pow(x-b,2.0)/c)
Simple Equation 102D: y = a*exp(pow(ln(x)-b,2.0)/c)
Simple Equation 132D: y = a*pow(x/b,c)*exp(x/b)
Simple Equation 142D: y = a*pow(x,b+c*x)
Simple Equation 152D: y = a*pow(x,b+c/x)
Simple Equation 162D: y = a*pow(x,b+c*ln(x))
Simple Equation 172D: y = a*pow(x,b*x+c*pow(x,2.0))
Simple Equation 182D: y = a*exp(b*x+c*pow(x,0.5))
Simple Equation 192D: y = a*exp(b/x+c*x)
Simple Equation 202D: y = (a+x)/(b+c*x)
Simple Equation 212D: y = (a+x)/(b+c*pow(x,2.0))
Simple Equation 222D: y = a*(exp(b*x)-exp(c*x))
Simple Equation 232D: y = a*exp(b*exp(c*x))
Simple Equation 242D: y = a/(1.0 + b * exp(c*x))
Simple Equation 252D: y = a/(b+pow(x,c))
Simple Equation 262D: y = a/pow(1.0 + b * pow(x,c),2.0)
Simple Equation 272D: y = pow(a+b*x,c)
Simple Equation 282D: y = exp(a+b/x+c*ln(x))
Simple Equation 292D: y = a*exp(b*pow(x,c))
Simple Equation 302D: y = a*pow(x,b*pow(x,c))
Simple Equation 312D: y = a*ln(x+b)
Simple Equation 322D: y = a/x+b*pow(x,c)
Simple Equation 332D: y = a/x+b*exp(c/x)
Simple Equation 342D: y = a/x+b*exp(c*x)
Simple Equation 352D: y = a*exp(b*x)/x
Simple Equation 362D: y = a*exp(b/x)/x
Simple Equation 372D: y = a*pow(x,b)*ln(x)
Simple Equation 382D: y = a*pow(x,b)/ln(x)
Simple Equation 392D: y = a*pow(x,b)*ln(x+c)
Simple Equation 402D: y = a*pow(ln(x+b),c)
Simple Equation 412D: y = a*pow(x,b/x)+c*x
Simple Equation 422D: y = a*pow(x,b/x)+c*ln(x)
Simple Reciprocal2D: y = a / x

Simple Equation 02 With Offset2D: y = a/pow(x,-2.0) + Offset
Simple Equation 03 With Offset2D: y = a*pow(ln(x),b) + Offset
Simple Equation 04 With Offset2D: y = a*pow(x,3.0) + Offset
Simple Equation 05 With Offset2D: y = a*pow(x,4.0) + Offset
Simple Equation 06 With Offset2D: y = x/(a+b*pow(x,2.0)) + Offset
Simple Equation 07 With Offset2D: y = a * pow(b,x) * pow(x,c) + Offset
Simple Equation 08 With Offset2D: y = a*pow(b,1.0/x)*pow(x,c) + Offset
Simple Equation 09 With Offset2D: y = a*exp(pow(x-b,2.0)/c) + Offset
Simple Equation 10 With Offset2D: y = a*exp(pow(ln(x)-b,2.0)/c) + Offset
Simple Equation 13 With Offset2D: y = a*pow(x/b,c)*exp(x/b) + Offset
Simple Equation 14 With Offset2D: y = a*pow(x,b+c*x) + Offset
Simple Equation 15 With Offset2D: y = a*pow(x,b+c/x) + Offset
Simple Equation 16 With Offset2D: y = a*pow(x,b+c*ln(x)) + Offset
Simple Equation 17 With Offset2D: y = a*pow(x,b*x+c*pow(x,2.0)) + Offset
Simple Equation 18 With Offset2D: y = a*exp(b*x+c*pow(x,0.5)) + Offset
Simple Equation 19 With Offset2D: y = a*exp(b/x+c*x) + Offset
Simple Equation 20 With Offset2D: y = (a+x)/(b+c*x) + Offset
Simple Equation 21 With Offset2D: y = (a+x)/(b+c*pow(x,2.0)) + Offset
Simple Equation 22 With Offset2D: y = a*(exp(b*x)-exp(c*x)) + Offset
Simple Equation 23 With Offset2D: y = a*exp(b*exp(c*x)) + Offset
Simple Equation 24 With Offset2D: y = a/(1.0 + b * exp(c*x)) + Offset
Simple Equation 25 With Offset2D: y = a/(b+pow(x,c)) + Offset
Simple Equation 26 With Offset2D: y = a/pow(1.0 + b * pow(x,c),2.0) + Offset
Simple Equation 27 With Offset2D: y = pow(a+b*x,c) + Offset
Simple Equation 28 With Offset2D: y = exp(a+b/x+c*ln(x)) + Offset
Simple Equation 29 With Offset2D: y = a*exp(b*pow(x,c)) + Offset
Simple Equation 30 With Offset2D: y = a*pow(x,b*pow(x,c)) + Offset
Simple Equation 31 With Offset2D: y = a*ln(x+b) + Offset
Simple Equation 32 With Offset2D: y = a/x+b*pow(x,c) + Offset
Simple Equation 33 With Offset2D: y = a/x+b*exp(c/x) + Offset
Simple Equation 34 With Offset2D: y = a/x+b*exp(c*x) + Offset
Simple Equation 35 With Offset2D: y = a*exp(b*x)/x + Offset
Simple Equation 36 With Offset2D: y = a*exp(b/x)/x + Offset
Simple Equation 37 With Offset2D: y = a*pow(x,b)*ln(x) + Offset
Simple Equation 38 With Offset2D: y = a*pow(x,b)/ln(x) + Offset
Simple Equation 39 With Offset2D: y = a*pow(x,b)*ln(x+c) + Offset
Simple Equation 40 With Offset2D: y = a*pow(ln(x+b),c) + Offset
Simple Equation 41 With Offset2D: y = a*pow(x,b/x)+c*x + Offset
Simple Equation 42 With Offset2D: y = a*pow(x,b/x)+c*ln(x) + Offset
Simple Reciprocal With Offset2D: y = a / x + Offset

Simple Equation 02 Plus Line2D: y = a/pow(x,-2.0)
y = y + (b * x) + c
Simple Equation 03 Plus Line2D: y = a*pow(ln(x),b)
y = y + (c * x) + d
Simple Equation 04 Plus Line2D: y = a*pow(x,3.0)
y = y + (b * x) + c
Simple Equation 05 Plus Line2D: y = a*pow(x,4.0)
y = y + (b * x) + c
Simple Equation 06 Plus Line2D: y = x/(a+b*pow(x,2.0))
y = y + (c * x) + d
Simple Equation 31 Plus Line2D: y = a*ln(x+b)
y = y + (c * x) + d
Simple Equation 35 Plus Line2D: y = a*exp(b*x)/x
y = y + (c * x) + d
Simple Equation 36 Plus Line2D: y = a*exp(b/x)/x
y = y + (c * x) + d
Simple Equation 37 Plus Line2D: y = a*pow(x,b)*ln(x)
y = y + (c * x) + d
Simple Equation 38 Plus Line2D: y = a*pow(x,b)/ln(x)
y = y + (c * x) + d
Simple Reciprocal Plus Line2D: y = a / x
y = y + (b * x) + c

2D Trigonometric

Cardinal Sine (sinc) Squared [radians]2D: y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width)
Cardinal Sine (sinc) Squared [radians] (Nyquist Limited)2D: y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width)
Cardinal Sine (sinc) [radians]2D: y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width)
Cardinal Sine (sinc) [radians] (Nyquist Limited)2D: y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width)
Great Circle [Degrees]2D: latitude = arctan(A*cos((B + longitude) / 57.2957795131)) * 57.2957795131
Great Circle [radians]2D: latitude = arctan(A*cos(B + longitude))
Hyperbolic Cosine [radians]2D: y = amplitude * cosh(pi * (x - center) / width)
Hyperbolic Cosine [radians] (Nyquist Limited)2D: y = amplitude * cosh(pi * (x - center) / width)
Sine Squared [radians]2D: y = amplitude * sin(pi * (x - center) / width)²
Sine Squared [radians] (Nyquist Limited)2D: y = amplitude * sin(pi * (x - center) / width)²
Sine [radians]2D: y = amplitude * sin(pi * (x - center) / width)
Sine [radians] (Nyquist Limited)2D: y = amplitude * sin(pi * (x - center) / width)
Tangent [radians]2D: y = amplitude * tan(pi * (x - center) / width)
Tangent [radians] (Nyquist Limited)2D: y = amplitude * tan(pi * (x - center) / width)

Cardinal Sine (sinc) Squared [radians] (Nyquist Limited) With Offset2D: y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width) + Offset
Cardinal Sine (sinc) Squared [radians] With Offset2D: y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width) + Offset
Cardinal Sine (sinc) [radians] (Nyquist Limited) With Offset2D: y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width) + Offset
Cardinal Sine (sinc) [radians] With Offset2D: y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width) + Offset
Hyperbolic Cosine [radians] (Nyquist Limited) With Offset2D: y = amplitude * cosh(pi * (x - center) / width) + Offset
Hyperbolic Cosine [radians] With Offset2D: y = amplitude * cosh(pi * (x - center) / width) + Offset
Sine Squared [radians] (Nyquist Limited) With Offset2D: y = amplitude * sin(pi * (x - center) / width)² + Offset
Sine Squared [radians] With Offset2D: y = amplitude * sin(pi * (x - center) / width)² + Offset
Sine [radians] (Nyquist Limited) With Offset2D: y = amplitude * sin(pi * (x - center) / width) + Offset
Sine [radians] With Offset2D: y = amplitude * sin(pi * (x - center) / width) + Offset
Tangent [radians] (Nyquist Limited) With Offset2D: y = amplitude * tan(pi * (x - center) / width) + Offset
Tangent [radians] With Offset2D: y = amplitude * tan(pi * (x - center) / width) + Offset

Cardinal Sine (sinc) Squared [radians] (Nyquist Limited) Plus Line2D: y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width)
y = y + (d * x) + f
Cardinal Sine (sinc) [radians] (Nyquist Limited) Plus Line2D: y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width)
y = y + (d * x) + f
Hyperbolic Cosine [radians] (Nyquist Limited) Plus Line2D: y = amplitude * cosh(pi * (x - center) / width)
y = y + (d * x) + f
Sine Squared [radians] (Nyquist Limited) Plus Line2D: y = amplitude * sin(pi * (x - center) / width)²
y = y + (d * x) + f
Sine [radians] (Nyquist Limited) Plus Line2D: y = amplitude * sin(pi * (x - center) / width)
y = y + (d * x) + f
Tangent [radians] (Nyquist Limited) Plus Line2D: y = amplitude * tan(pi * (x - center) / width)
y = y + (d * x) + f

2D YieldDensity

Bleasdale2D: y = 1.0 / (a + bx)^(-1.0/c)
Extended Holliday2D: y = a / (a + bx + cx²)
Harris2D: y = 1.0 / (a + bx^c)
Holliday2D: y = 1.0 / (a + bx + cx²)
Inverse Bleasdale2D: y = x / (a + bx)^(-1.0/c)
InverseHarris2D: y = x / (a + bx^c)
Nelder2D: y = (a + x) / (b + c(a + x) + d(a + x)²)

Bleasdale With Offset2D: y = 1.0 / (a + bx)^(-1.0/c) + Offset
Extended Holliday With Offset2D: y = a / (a + bx + cx²) + Offset
Harris With Offset2D: y = 1.0 / (a + bx^c) + Offset
Holliday With Offset2D: y = 1.0 / (a + bx + cx²) + Offset
Inverse Bleasdale With Offset2D: y = x / (a + bx)^(-1.0/c) + Offset
InverseHarris With Offset2D: y = x / (a + bx^c) + Offset
Nelder With Offset2D: y = (a + x) / (b + c(a + x) + d(a + x)²) + Offset

3D BioScience

Chen-Clayton3D: r.h.(T_k,M) = exp(-(C1/T^C2) * exp(-C3*T^C4*M))^{[web citation]}
Chen-Clayton Scaled3D: z = Scale * exp(-(C1/T^C2) * exp(-C3*T^C4*M))^{[web citation]}
High-Low Affinity Double Isotope Displacement (y = [Hot])3D: z = aby / (1+b(x+y)) + cdy / (1+d(x+y))
High-Low Affinity Isotope Displacement (y = [Hot])3D: z = aby / (1+b(x+y))
Logistic Growth3D: z = a / (1 + exp(-(b + cx + dy + fxy))) + g
Michaelis-Menten Double Isotope Displacement (y = [Hot])3D: z = ay / (b + x + y) + cy / (d + x + y)
Michaelis-Menten Isotope Displacement (y = [Hot])3D: z = ay / (b + x + y)
Modified Chung-Pfost3D: r.h.(T,M) = exp(-(C1/(T+C2)) * exp(-C3*M))^{[web citation]}
Modified Halsey3D: r.h.(T,M) = exp(-exp(C1 + C2*T) * M^-C3)^{[web citation]}
Modified Halsey Scaled3D: z = Scale * exp(-exp(C1 + C2*T) * M^-C3)^{[web citation]}
Modified Henderson3D: r.h.(T,M) = 1 - exp(-C1 * (T + C2) * M^C3)^{[web citation]}
Strohman-Yoerger3D: r.h.(P_s,M) = exp(C1*exp(-C2*M)*ln(P_s) - C3*exp(-C4*M))^{[web citation]}

Chen-Clayton Scaled With Offset3D: z = Scale * exp(-(C1/T^C2) * exp(-C3*T^C4*M)) + Offset^{[web citation]}
Chen-Clayton With Offset3D: r.h.(T_k,M) = exp(-(C1/T^C2) * exp(-C3*T^C4*M)) + Offset^{[web citation]}
High-Low Affinity Double Isotope Displacement (y = [Hot]) With Offset3D: z = aby / (1+b(x+y)) + cdy / (1+d(x+y)) + Offset
High-Low Affinity Isotope Displacement (y = [Hot]) With Offset3D: z = aby / (1+b(x+y)) + Offset
Michaelis-Menten Double Isotope Displacement (y = [Hot]) With Offset3D: z = ay / (b + x + y) + cy / (d + x + y) + Offset
Michaelis-Menten Isotope Displacement (y = [Hot]) With Offset3D: z = ay / (b + x + y) + Offset
Modified Chung-Pfost With Offset3D: r.h.(T,M) = exp(-(C1/(T+C2)) * exp(-C3*M)) + Offset^{[web citation]}
Modified Halsey Scaled With Offset3D: z = Scale * exp(-exp(C1 + C2*T) * M^-C3) + Offset^{[web citation]}
Modified Halsey With Offset3D: r.h.(T,M) = exp(-exp(C1 + C2*T) * M^-C3) + Offset^{[web citation]}
Modified Henderson With Offset3D: r.h.(T,M) = 1 - exp(-C1 * (T + C2) * M^C3) + Offset^{[web citation]}
Strohman-Yoerger With Offset3D: r.h.(P_s,M) = exp(C1*exp(-C2*M)*ln(P_s) - C3*exp(-C4*M)) + Offset^{[web citation]}

High-Low Affinity Isotope Displacement (y = [Hot]) Plus Plane3D: z = aby / (1+b(x+y))
z = z + (c * x) + (d * y) + f
Michaelis-Menten Isotope Displacement (y = [Hot]) Plus Plane3D: z = ay / (b + x + y)
z = z + (c * x) + (d * y) + f
Modified Chung-Pfost Plus Plane3D: r.h.(T,M) = exp(-(C1/(T+C2)) * exp(-C3*M))
r.h.(T,M) = r.h.(T,M) + (d * x) + (f * y) + g^{[web citation]}
Modified Halsey Plus Plane3D: r.h.(T,M) = exp(-exp(C1 + C2*T) * M^-C3)
r.h.(T,M) = r.h.(T,M) + (d * x) + (f * y) + g^{[web citation]}
Modified Henderson Plus Plane3D: r.h.(T,M) = 1 - exp(-C1 * (T + C2) * M^C3)
r.h.(T,M) = r.h.(T,M) + (d * x) + (f * y) + g^{[web citation]}

3D EnzymeKinetics

Competitive Inhibition A3D: z = ax / (b(1 + y/c) + x)
Competitive Inhibition B3D: z = ay / (b(1 + x/c) + y)
Competitive Inhibition C3D: z = axy / (b(1 + x/c) + y)
Inhibition By Competing Substrate A3D: z = (ax/b) / (1 + x/b + y/c)
Inhibition By Competing Substrate B3D: z = (ay/b) / (1 + y/b + x/c)
Inhibition By Competing Substrate C3D: z = (axy/b) / (1 + y/b + x/c)
Michaelis Menten Product Inhibition3D: z = (ax/b - cy/d) / (1 + x/b + y/d)
Mixed Inhibition A3D: z = ax / (b(1 + y/c) + x(1 + y/d))
Mixed Inhibition B3D: z = ay / (b(1 + x/c) + y(1 + x/d))
Noncompetitive Inhibition A3D: z = ax / ((b + x)(1 + y/c))
Noncompetitive Inhibition B3D: z = ay / ((b + y)(1 + x/c))
Ping Pong Bi Bi A3D: z = ax / (bx + cy + xy)
Ping Pong Bi Bi B3D: z = ay / (by + cx + xy)
Ping Pong Bi Bi C3D: z = axy / (by + cx + xy)
Uncompetitive Inhibition A3D: z = ax / (b + x(1 + y/c))
Uncompetitive Inhibition B3D: z = ay / (b + y(1 + x/c))

Competitive Inhibition A With Offset3D: z = ax / (b(1 + y/c) + x) + Offset
Competitive Inhibition B With Offset3D: z = ay / (b(1 + x/c) + y) + Offset
Competitive Inhibition C With Offset3D: z = axy / (b(1 + x/c) + y) + Offset
Inhibition By Competing Substrate A With Offset3D: z = (ax/b) / (1 + x/b + y/c) + Offset
Inhibition By Competing Substrate B With Offset3D: z = (ay/b) / (1 + y/b + x/c) + Offset
Inhibition By Competing Substrate C With Offset3D: z = (axy/b) / (1 + y/b + x/c) + Offset
Michaelis Menten Product Inhibition With Offset3D: z = (ax/b - cy/d) / (1 + x/b + y/d) + Offset
Mixed Inhibition A With Offset3D: z = ax / (b(1 + y/c) + x(1 + y/d)) + Offset
Mixed Inhibition B With Offset3D: z = ay / (b(1 + x/c) + y(1 + x/d)) + Offset
Noncompetitive Inhibition A With Offset3D: z = ax / ((b + x)(1 + y/c)) + Offset
Noncompetitive Inhibition B With Offset3D: z = ay / ((b + y)(1 + x/c)) + Offset
Ping Pong Bi Bi A With Offset3D: z = ax / (bx + cy + xy) + Offset
Ping Pong Bi Bi B With Offset3D: z = ay / (by + cx + xy) + Offset
Ping Pong Bi Bi C With Offset3D: z = axy / (by + cx + xy) + Offset
Uncompetitive Inhibition A With Offset3D: z = ax / (b + x(1 + y/c)) + Offset
Uncompetitive Inhibition B With Offset3D: z = ay / (b + y(1 + x/c)) + Offset

Competitive Inhibition A Plus Plane3D: z = ax / (b(1 + y/c) + x)
z = z + (d * x) + (f * y) + g
Competitive Inhibition B Plus Plane3D: z = ay / (b(1 + x/c) + y)
z = z + (d * x) + (f * y) + g
Competitive Inhibition C Plus Plane3D: z = axy / (b(1 + x/c) + y)
z = z + (d * x) + (f * y) + g
Inhibition By Competing Substrate A Plus Plane3D: z = (ax/b) / (1 + x/b + y/c)
z = z + (d * x) + (f * y) + g
Inhibition By Competing Substrate B Plus Plane3D: z = (ay/b) / (1 + y/b + x/c)
z = z + (d * x) + (f * y) + g
Inhibition By Competing Substrate C Plus Plane3D: z = (axy/b) / (1 + y/b + x/c)
z = z + (d * x) + (f * y) + g
Noncompetitive Inhibition A Plus Plane3D: z = ax / ((b + x)(1 + y/c))
z = z + (d * x) + (f * y) + g
Noncompetitive Inhibition B Plus Plane3D: z = ay / ((b + y)(1 + x/c))
z = z + (d * x) + (f * y) + g
Ping Pong Bi Bi A Plus Plane3D: z = ax / (bx + cy + xy)
z = z + (d * x) + (f * y) + g
Ping Pong Bi Bi B Plus Plane3D: z = ay / (by + cx + xy)
z = z + (d * x) + (f * y) + g
Ping Pong Bi Bi C Plus Plane3D: z = axy / (by + cx + xy)
z = z + (d * x) + (f * y) + g
Uncompetitive Inhibition A Plus Plane3D: z = ax / (b + x(1 + y/c))
z = z + (d * x) + (f * y) + g
Uncompetitive Inhibition B Plus Plane3D: z = ay / (b + y(1 + x/c))
z = z + (d * x) + (f * y) + g

3D Exponential

Full Cubic Exponential3D: 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
Full Quadratic Exponential3D: z = a + b*exp(x) + c*exp(y) + d*exp(x)² + f*exp(y)² + g*exp(x)*exp(y)
Linear Exponential3D: z = a + b*exp(x) + c*exp(y)
Simplified Cubic Exponential3D: z = a + b*exp(x) + c*exp(y) + d*exp(x)² + e*exp(y)² + f*exp(x)³ + g*exp(y)³
Simplified Quadratic Exponential3D: z = a + b*exp(x) + c*exp(y) + d*exp(x)² + f*exp(y)²
Transform Full Cubic Exponential3D: 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
Transform Full Quadratic Exponential3D: 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)
Transform Linear Exponential3D: z = a + b*exp(d*x+f) + c*exp(g*y+h)
Transform Simplified Cubic Exponential3D: 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
Transform Simplified Quadratic Exponential3D: z = a + b*exp(g*x+h) + c*exp(i*y+j) + d*exp(g*x+h)² + f*exp(i*y+j)²

3D Logarithmic

Full Cubic Logarithmic3D: 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
Full Quadratic Logarithmic3D: z = a + b*ln(x) + c*ln(y) + d*ln(x)² + f*ln(y)² + g*ln(x)*ln(y)
Linear Logarithmic3D: z = a + b*ln(x) + c*ln(y)
Simplified Cubic Logarithmic3D: z = a + b*ln(x) + c*ln(y) + d*ln(x)² + f*ln(y)² + g*ln(x)³ + h*ln(y)³
Simplified Quadratic Logarithmic3D: z = a + b*ln(x) + c*ln(y) + d*ln(x)² + f*ln(y)²
Transform Full Cubic Logarithmic3D: 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
Transform Full Quadratic Logarithmic3D: 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)
Transform Linear Logarithmic3D: z = a + b*ln(d*x+f) + c*ln(g*y+h)
Transform Simplified Cubic Logarithmic3D: 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
Transform Simplified Quadratic Logarithmic3D: z = a + b*ln(g*x+h) + c*ln(i*y+j) + d*ln(g*x+h)² + f*ln(i*y+j)²

3D Miscellaneous

Gary Cler's Custom Equation Transform3D: z = a * (dx + f)^b * (gy + h)^c
Gaussian Curvature Of Paraboloid3D: z = 4a² / (1 + 4a² * (x² + y²))²
Gaussian Curvature Of Paraboloid Scaled3D: z = Scale * 4a² / (1 + 4a² * (x² + y²))²
Gaussian Curvature Of Richmond's Minimal Surface3D: z = -1.0 * a * (x² + y²)³ / (b + (x² + y²)²)⁴
Gaussian Curvature Of Whitney's Umbrella A3D: z = -1.0 * a * y² / (x² + a * (y² + y⁴))²
Gaussian Curvature Of Whitney's Umbrella B3D: z = -1.0 * a * x² / (y² + a * (x² + x⁴))²
Liping Zheng's core loss coefficients3D: z = ax²y + bx²y² + cx^1.5y^1.5
Mean Curvature Of Paraboloid3D: z = 2 * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5
Mean Curvature Of Paraboloid Scaled3D: z = Scale * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5
Mean Curvature Of Whitney's Umbrella A3D: z = -1.0 * x * (a + b * y²) / (x² + a * (y² + y⁴))^1.5
Mean Curvature Of Whitney's Umbrella B3D: z = -1.0 * y * (a + b * x²) / (y² + a * (x² + x⁴))^1.5
Menn's Surface A3D: z = ax⁴ + bx²y - cy²
Menn's Surface B3D: z = ay⁴ + by²x - cx²
Monkey Saddle A3D: z = ax³ - bxy²
Monkey Saddle B3D: z = ay³ - byx²
Monkey Saddle Transform A3D: z = a(cx + d)³ - b(cx + d)(fy + g)²
Monkey Saddle Transform B3D: z = a(cy + d)³ - b(cy + d)(fx + g)²
Paraboloid3D: z = a * (x² + y²)
Paraboloid Transform3D: z = a * ((bx + c)² + (dy + f)²)
Paschen's Law for Breakdown Field Strength3D: Ebreakdown = pressure * (a / (ln(pressure * distance) + b))
Paschen's Law for Breakdown Voltage3D: Vbreakdown = a(pressure * distance) / (ln(pressure * distance) + b)
Rex Kelfkens' Custom Equation3D: z = exp(A+B*ln(x)+C*ln(y))
Rex Kelfkens' Custom Equation Transform3D: z = exp(A+B*ln(x * xscale + xoffset)+C*ln(y * yscale + yoffset))

Gary Cler's Custom Equation Transform With Offset3D: z = a * (dx + f)^b * (gy + h)^c + Offset
Gaussian Curvature Of Paraboloid Scaled With Offset3D: z = Scale * 4a² / (1 + 4a² * (x² + y²))² + Offset
Gaussian Curvature Of Paraboloid With Offset3D: z = 4a² / (1 + 4a² * (x² + y²))² + Offset
Gaussian Curvature Of Richmond's Minimal Surface With Offset3D: z = -1.0 * a * (x² + y²)³ / (b + (x² + y²)²)⁴ + Offset
Gaussian Curvature Of Whitney's Umbrella A With Offset3D: z = -1.0 * a * y² / (x² + a * (y² + y⁴))² + Offset
Gaussian Curvature Of Whitney's Umbrella B With Offset3D: z = -1.0 * a * x² / (y² + a * (x² + x⁴))² + Offset
Liping Zheng's core loss coefficients With Offset3D: z = ax²y + bx²y² + cx^1.5y^1.5 + Offset
Mean Curvature Of Paraboloid Scaled With Offset3D: z = Scale * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5 + Offset
Mean Curvature Of Paraboloid With Offset3D: z = 2 * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5 + Offset
Mean Curvature Of Whitney's Umbrella A With Offset3D: z = -1.0 * x * (a + b * y²) / (x² + a * (y² + y⁴))^1.5 + Offset
Mean Curvature Of Whitney's Umbrella B With Offset3D: z = -1.0 * y * (a + b * x²) / (y² + a * (x² + x⁴))^1.5 + Offset
Menn's Surface A With Offset3D: z = ax⁴ + bx²y - cy² + Offset
Menn's Surface B With Offset3D: z = ay⁴ + by²x - cx² + Offset
Monkey Saddle A With Offset3D: z = ax³ - bxy² + Offset
Monkey Saddle B With Offset3D: z = ay³ - byx² + Offset
Monkey Saddle Transform A With Offset3D: z = a(cx + d)³ - b(cx + d)(fy + g)² + Offset
Monkey Saddle Transform B With Offset3D: z = a(cy + d)³ - b(cy + d)(fx + g)² + Offset
Paraboloid Transform With Offset3D: z = a * ((bx + c)² + (dy + f)²) + Offset
Paraboloid With Offset3D: z = a * (x² + y²) + Offset
Paschen's Law for Breakdown Field Strength With Offset3D: Ebreakdown = pressure * (a / (ln(pressure * distance) + b)) + Offset
Paschen's Law for Breakdown Voltage With Offset3D: Vbreakdown = a(pressure * distance) / (ln(pressure * distance) + b) + Offset
Rex Kelfkens' Custom Equation Transform With Offset3D: z = exp(A+B*ln(x * xscale + xoffset)+C*ln(y * yscale + yoffset)) + Offset
Rex Kelfkens' Custom Equation With Offset3D: z = exp(A+B*ln(x)+C*ln(y)) + Offset

Gaussian Curvature Of Paraboloid Plus Plane3D: z = 4a² / (1 + 4a² * (x² + y²))²
z = z + (b * x) + (c * y) + d
Gaussian Curvature Of Paraboloid Scaled Plus Plane3D: z = Scale * 4a² / (1 + 4a² * (x² + y²))²
z = z + (c * x) + (d * y) + f
Gaussian Curvature Of Richmond's Minimal Surface Plus Plane3D: z = -1.0 * a * (x² + y²)³ / (b + (x² + y²)²)⁴
z = z + (c * x) + (d * y) + f
Gaussian Curvature Of Whitney's Umbrella A Plus Plane3D: z = -1.0 * a * y² / (x² + a * (y² + y⁴))²
z = z + (b * x) + (c * y) + d
Gaussian Curvature Of Whitney's Umbrella B Plus Plane3D: z = -1.0 * a * x² / (y² + a * (x² + x⁴))²
z = z + (b * x) + (c * y) + d
Liping Zheng's core loss coefficients Plus Plane3D: z = ax²y + bx²y² + cx^1.5y^1.5
z = z + (d * x) + (f * y) + g
Mean Curvature Of Paraboloid Plus Plane3D: z = 2 * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5
z = z + (b * x) + (c * y) + d
Mean Curvature Of Paraboloid Scaled Plus Plane3D: z = Scale * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5
z = z + (c * x) + (d * y) + f
Mean Curvature Of Whitney's Umbrella A Plus Plane3D: z = -1.0 * x * (a + b * y²) / (x² + a * (y² + y⁴))^1.5
z = z + (c * x) + (d * y) + f
Mean Curvature Of Whitney's Umbrella B Plus Plane3D: z = -1.0 * y * (a + b * x²) / (y² + a * (x² + x⁴))^1.5
z = z + (c * x) + (d * y) + f
Menn's Surface A Plus Plane3D: z = ax⁴ + bx²y - cy²
z = z + (d * x) + (f * y) + g
Menn's Surface B Plus Plane3D: z = ay⁴ + by²x - cx²
z = z + (d * x) + (f * y) + g
Monkey Saddle A Plus Plane3D: z = ax³ - bxy²
z = z + (c * x) + (d * y) + f
Monkey Saddle B Plus Plane3D: z = ay³ - byx²
z = z + (c * x) + (d * y) + f
Paraboloid Plus Plane3D: z = a * (x² + y²)
z = z + (b * x) + (c * y) + d
Paschen's Law for Breakdown Field Strength Plus Plane3D: Ebreakdown = pressure * (a / (ln(pressure * distance) + b))
Ebreakdown = Ebreakdown + (c * x) + (d * y) + f
Paschen's Law for Breakdown Voltage Plus Plane3D: Vbreakdown = a(pressure * distance) / (ln(pressure * distance) + b)
Vbreakdown = Vbreakdown + (c * x) + (d * y) + f
Rex Kelfkens' Custom Equation Plus Plane3D: z = exp(A+B*ln(x)+C*ln(y))
z = z + (d * x) + (f * y) + g

3D NIST

NIST Nelson3D: log(y) = b1 - b2 * X1 * exp(-b3*X2)^{[web citation]}
NIST Nelson Autolog3D: z = exp(b1 - b2 * x * exp(-b3*y))^{[web citation]}

NIST Nelson Autolog With Offset3D: z = exp(b1 - b2 * x * exp(-b3*y)) + Offset^{[web citation]}

NIST Nelson Autolog Plus Plane3D: z = exp(b1 - b2 * x * exp(-b3*y))
z = z + (d * x) + (f * y) + g^{[web citation]}

3D Optical

Sag For Asphere 03D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2)^{[web citation]}
Sag For Asphere 0 Borisovsky3D: s² = (x - a)² + (y - b)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + offset
Sag For Asphere 0 Scaled3D: s² = x² + y²
z = Scale * (s²/r) / (1+(1-(k+1)(s/r)²)^1/2)^{[web citation]}
Sag For Asphere 13D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴^{[web citation]}
Sag For Asphere 23D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶^{[web citation]}
Sag For Asphere 33D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶ + A8*s⁸^{[web citation]}
Transform Sag For Asphere 03D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2)^{[web citation]}
Transform Sag For Asphere 13D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴^{[web citation]}
Transform Sag For Asphere 23D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶^{[web citation]}
Transform Sag For Asphere 33D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶ + A8*s⁸^{[web citation]}

Sag For Asphere 0 Borisovsky With Offset3D: s² = (x - a)² + (y - b)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + offset + Offset
Sag For Asphere 0 Scaled With Offset3D: s² = x² + y²
z = Scale * (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + Offset^{[web citation]}
Sag For Asphere 0 With Offset3D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + Offset^{[web citation]}
Sag For Asphere 1 With Offset3D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + Offset^{[web citation]}
Sag For Asphere 2 With Offset3D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶ + Offset^{[web citation]}
Sag For Asphere 3 With Offset3D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶ + A8*s⁸ + Offset^{[web citation]}
Transform Sag For Asphere 0 With Offset3D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + Offset^{[web citation]}
Transform Sag For Asphere 1 With Offset3D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + Offset^{[web citation]}
Transform Sag For Asphere 2 With Offset3D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶ + Offset^{[web citation]}
Transform Sag For Asphere 3 With Offset3D: s² = (ax+b)² + (cy+d)²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + A6*s⁶ + A8*s⁸ + Offset^{[web citation]}

Sag For Asphere 0 Plus Plane3D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2)
z = z + (c * x) + (d * y) + f^{[web citation]}
Sag For Asphere 0 Scaled Plus Plane3D: s² = x² + y²
z = Scale * (s²/r) / (1+(1-(k+1)(s/r)²)^1/2)
z = z + (d * x) + (f * y) + g^{[web citation]}
Sag For Asphere 1 Plus Plane3D: s² = x² + y²
z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴
z = z + (d * x) + (f * y) + g^{[web citation]}

3D Peak

Extreme Value A3D: z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) + d * exp(-exp(-(y-f)/g)-(y-f)/g+1)
Extreme Value B3D: z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) * exp(-exp(-(y-d)/f)-(y-d)/f+1)
Gaussian A3D: z = a * exp(-0.5 * (((x-b)/c)² + ((y-d)/f)²))
Gaussian B3D: z = a * exp(-0.5 * (((x-b)/c)²)) + d * exp(-0.5 * (((y-f)/g)²))
Log-Normal A3D: z = a * exp(-0.5 * (((ln(x)-b)/c)² + ((ln(y)-d)/f)²))
Log-Normal B3D: z = a * exp(-0.5 * (((ln(x)-b)/c)²)) + d * exp(-0.5 * (((ln(y)-f)/g)²))
Logistic A3D: z = 4a * exp(-((x-b)/c))/((1+exp(-((x-b)/c)))²) + 4d * exp(-((y-f)/g))/((1+exp(-((y-f)/g)))²)
Logistic B3D: z = 16a * exp(-((x-b)/c)-((y-d)/f)) / ((1+exp(-((x-b)/c)))² * (1+exp(-((y-d)/f)))²)
Lorentzian A3D: z = a / ((1+((x-b)/c)²)*(1+((y-d)/f)²))
Lorentzian B3D: z = a / (1+((x-b)/c)²) + d * (1+((y-f)/g)²)

Extreme Value A With Offset3D: z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) + d * exp(-exp(-(y-f)/g)-(y-f)/g+1) + Offset
Extreme Value B With Offset3D: z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) * exp(-exp(-(y-d)/f)-(y-d)/f+1) + Offset
Gaussian A With Offset3D: z = a * exp(-0.5 * (((x-b)/c)² + ((y-d)/f)²)) + Offset
Gaussian B With Offset3D: z = a * exp(-0.5 * (((x-b)/c)²)) + d * exp(-0.5 * (((y-f)/g)²)) + Offset
Log-Normal A With Offset3D: z = a * exp(-0.5 * (((ln(x)-b)/c)² + ((ln(y)-d)/f)²)) + Offset
Log-Normal B With Offset3D: z = a * exp(-0.5 * (((ln(x)-b)/c)²)) + d * exp(-0.5 * (((ln(y)-f)/g)²)) + Offset
Logistic A With Offset3D: z = 4a * exp(-((x-b)/c))/((1+exp(-((x-b)/c)))²) + 4d * exp(-((y-f)/g))/((1+exp(-((y-f)/g)))²) + Offset
Logistic B With Offset3D: z = 16a * exp(-((x-b)/c)-((y-d)/f)) / ((1+exp(-((x-b)/c)))² * (1+exp(-((y-d)/f)))²) + Offset
Lorentzian A With Offset3D: z = a / ((1+((x-b)/c)²)*(1+((y-d)/f)²)) + Offset
Lorentzian B With Offset3D: z = a / (1+((x-b)/c)²) + d * (1+((y-f)/g)²) + Offset

3D Polynomial

Full Cubic3D: z = a + bx + cy + dx² + fy² + gx³ + hy³ + ixy + jx²y + kxy²
Full Quadratic3D: z = a + bx + cy + dx² + fy² + gxy
Linear3D: z = a + bx + cy
Simplified Cubic3D: z = a + bx + cy + dx² + fy² + gx³ + hy³
Simplified Quadratic3D: z = a + bx + cy + dx² + fy²
User-Selectable Polynomial3D: z = user-selectable polynomial

3D Power

Power A3D: z = a * (x^b + y^c)
Power B3D: z = a + x^b + y^c
Power C3D: z = a + x^b * y^c
Power D3D: z = ax^b + cy^d
Power E3D: z = a * x^b * y^c
Transform Power A3D: z = a * ((dx + f)^b + (gy + h)^c)
Transform Power B3D: z = a + (dx + f)^b + (gy + h)^c
Transform Power C3D: z = a + (dx + f)^b * (gy + h)^c
Transform Power D3D: z = a(fx + g)^b + c(hy + i)^d
Transform Power E3D: z = a * (dx + f)^b * (gy + h)^c

Power A With Offset3D: z = a * (x^b + y^c) + Offset
Power D With Offset3D: z = ax^b + cy^d + Offset
Power E With Offset3D: z = a * x^b * y^c + Offset
Transform Power A With Offset3D: z = a * ((dx + f)^b + (gy + h)^c) + Offset
Transform Power D With Offset3D: z = a(fx + g)^b + c(hy + i)^d + Offset
Transform Power E With Offset3D: z = a * (dx + f)^b * (gy + h)^c + Offset

Power A Plus Plane3D: z = a * (x^b + y^c)
z = z + (d * x) + (f * y) + g
Power E Plus Plane3D: z = a * x^b * y^c
z = z + (d * x) + (f * y) + g

3D Rational

Rational A3D: z = (a + bx + cy)/(1 + dx + fy)
Rational B3D: z = (a + b*ln(x) + c*ln(y))/(1 + dx + fy)
Rational C3D: z = (a + b*exp(x) + c*ln(y))/(1 + dx + fy)
Rational D3D: z = (a + b*ln(x) + c*exp(y))/(1 + dx + fy)
Rational E3D: z = (a + b*exp(x) + c*exp(y))/(1 + dx + fy)
Rational F3D: z = (a + bx + cy)/(1 + d*ln(x) + f*ln(y))
Rational G3D: z = (a + bx + cy)/(1 + d*exp(x) + f*ln(y))
Rational H3D: z = (a + bx + cy)/(1 + d*ln(x) + f*exp(y))
Rational I3D: z = (a + bx + cy)/(1 + d*exp(x) + f*exp(y))
Rational J3D: z = (a + b*ln(x) + c*ln(y))/(1 + d*ln(x) + f*ln(y))
Rational K3D: z = (a + b*exp(x) + c*ln(y))/(1 + d*exp(x) + f*ln(y))
Rational L3D: z = (a + b*ln(x) + c*exp(y))/(1 + d*ln(x) + f*exp(y))
Rational M3D: z = (a + b*exp(x) + c*exp(y))/(1 + d*exp(x) + f*exp(y))
Rational N3D: z = (a + bx + cy + dxy)/(1 + fx + gy + hxy)
Rational O3D: z = (a + b*ln(x) + c*ln(y) + d*ln(x)ln(y))/(1 + fx + gy + hxy)
Rational P3D: z = (a + b*exp(x) + c*ln(y) + d*exp(x)ln(y))/(1 + fx + gy + hxy)
Rational Q3D: z = (a + b*ln(x) + c*exp(y) + d*ln(x)exp(y))/(1 + fx + gy + hxy)
Rational R3D: z = (a + b*exp(x) + c*exp(y) + d*exp(x)exp(y))/(1 + fx + gy + hxy)
Rational S3D: z = (a + bx + cy + dxy)/(1 + f*ln(x) + g*ln(y) + h*ln(x)*ln(y))
Rational T3D: z = (a + bx + cy + dxy)/(1 + f*exp(x) + g*ln(y) + h*exp(x)*ln(y))
Rational U3D: z = (a + bx + cy + dxy)/(1 + f*ln(x) + g*exp(y) + h*ln(x)*exp(y))
Rational V3D: z = (a + bx + cy + dxy)/(1 + f*exp(x) + g*exp(y) + h*exp(x)*exp(y))
Rational W3D: 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))
Rational X3D: 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))
Rational Y3D: 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))
Rational Z3D: 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))

Rational A With Offset3D: z = (a + bx + cy)/(1 + dx + fy) + Offset
Rational B With Offset3D: z = (a + b*ln(x) + c*ln(y))/(1 + dx + fy) + Offset
Rational C With Offset3D: z = (a + b*exp(x) + c*ln(y))/(1 + dx + fy) + Offset
Rational D With Offset3D: z = (a + b*ln(x) + c*exp(y))/(1 + dx + fy) + Offset
Rational E With Offset3D: z = (a + b*exp(x) + c*exp(y))/(1 + dx + fy) + Offset
Rational F With Offset3D: z = (a + bx + cy)/(1 + d*ln(x) + f*ln(y)) + Offset
Rational G With Offset3D: z = (a + bx + cy)/(1 + d*exp(x) + f*ln(y)) + Offset
Rational H With Offset3D: z = (a + bx + cy)/(1 + d*ln(x) + f*exp(y)) + Offset
Rational I With Offset3D: z = (a + bx + cy)/(1 + d*exp(x) + f*exp(y)) + Offset
Rational J With Offset3D: z = (a + b*ln(x) + c*ln(y))/(1 + d*ln(x) + f*ln(y)) + Offset
Rational K With Offset3D: z = (a + b*exp(x) + c*ln(y))/(1 + d*exp(x) + f*ln(y)) + Offset
Rational L With Offset3D: z = (a + b*ln(x) + c*exp(y))/(1 + d*ln(x) + f*exp(y)) + Offset
Rational M With Offset3D: z = (a + b*exp(x) + c*exp(y))/(1 + d*exp(x) + f*exp(y)) + Offset
Rational N With Offset3D: z = (a + bx + cy + dxy)/(1 + fx + gy + hxy) + Offset
Rational O With Offset3D: z = (a + b*ln(x) + c*ln(y) + d*ln(x)ln(y))/(1 + fx + gy + hxy) + Offset
Rational P With Offset3D: z = (a + b*exp(x) + c*ln(y) + d*exp(x)ln(y))/(1 + fx + gy + hxy) + Offset
Rational Q With Offset3D: z = (a + b*ln(x) + c*exp(y) + d*ln(x)exp(y))/(1 + fx + gy + hxy) + Offset
Rational R With Offset3D: z = (a + b*exp(x) + c*exp(y) + d*exp(x)exp(y))/(1 + fx + gy + hxy) + Offset
Rational S With Offset3D: z = (a + bx + cy + dxy)/(1 + f*ln(x) + g*ln(y) + h*ln(x)*ln(y)) + Offset
Rational T With Offset3D: z = (a + bx + cy + dxy)/(1 + f*exp(x) + g*ln(y) + h*exp(x)*ln(y)) + Offset
Rational U With Offset3D: z = (a + bx + cy + dxy)/(1 + f*ln(x) + g*exp(y) + h*ln(x)*exp(y)) + Offset
Rational V With Offset3D: z = (a + bx + cy + dxy)/(1 + f*exp(x) + g*exp(y) + h*exp(x)*exp(y)) + Offset
Rational W With Offset3D: 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)) + Offset
Rational X With Offset3D: 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)) + Offset
Rational Y With Offset3D: 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)) + Offset
Rational Z With Offset3D: 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)) + Offset

3D RomanSurfaces

Roman Surface (minus)3D: z = (k(y²-x²) - (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
Roman Surface (minus) Offset XY3D: z = (k((y+b)²-(x+a)²) - ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²))
Roman Surface (minus) Scaled And Offset XY3D: z = (k((cy+d)²-(ax+b)²) - ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²))
Roman Surface (plus)3D: z = (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
Roman Surface (plus) Offset XY3D: z = (k((y+b)²-(x+a)²) + ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²))
Roman Surface (plus) Scaled3D: z = Scale * (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
Roman Surface (plus) Scaled And Offset XY3D: z = (k((cy+d)²-(ax+b)²) + ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²))

Roman Surface (minus) Offset XY With Offset3D: z = (k((y+b)²-(x+a)²) - ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²)) + Offset
Roman Surface (minus) Scaled And Offset XY With Offset3D: z = (k((cy+d)²-(ax+b)²) - ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²)) + Offset
Roman Surface (minus) With Offset3D: z = (k(y²-x²) - (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²)) + Offset
Roman Surface (plus) Offset XY With Offset3D: z = (k((y+b)²-(x+a)²) + ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²)) + Offset
Roman Surface (plus) Scaled And Offset XY With Offset3D: z = (k((cy+d)²-(ax+b)²) + ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²)) + Offset
Roman Surface (plus) Scaled With Offset3D: z = Scale * (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²)) + Offset
Roman Surface (plus) With Offset3D: z = (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²)) + Offset

Roman Surface (minus) Offset XY Plus Plane3D: z = (k((y+b)²-(x+a)²) - ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²))
z = z + (d * x) + (f * y) + g
Roman Surface (minus) Plus Plane3D: z = (k(y²-x²) - (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
z = z + (b * x) + (c * y) + d
Roman Surface (plus) Offset XY Plus Plane3D: z = (k((y+b)²-(x+a)²) + ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²))
z = z + (d * x) + (f * y) + g
Roman Surface (plus) Plus Plane3D: z = (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
z = z + (b * x) + (c * y) + d
Roman Surface (plus) Scaled Plus Plane3D: z = Scale * (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
z = z + (c * x) + (d * y) + f

3D Sigmoidal

Andrea Prunotto Sigmoid A3D: z = a0 + (a1 / (1.0 + exp(a2 * (x + a3 + a4 * y + a5 * x * y))))
Andrea Prunotto Sigmoid B3D: z = a0 + (a1 / (1.0 + exp(a2 * (x * a3 + a4 * y + a5 * x * y))))
Fraser Smith Sigmoid3D: z = 1.0 / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy)))
Fraser Smith Sigmoid Scaled3D: z = Scale / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy)))
Sigmoid3D: z = a / ((1.0 + exp(b - cx)) * (1.0 + exp(d - fy)))

Fraser Smith Sigmoid Scaled With Offset3D: z = Scale / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy))) + Offset
Fraser Smith Sigmoid With Offset3D: z = 1.0 / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy))) + Offset
Sigmoid With Offset3D: z = a / ((1.0 + exp(b - cx)) * (1.0 + exp(d - fy))) + Offset

3D Simple

Simple Equation 013D: z = a*pow(x,b)*pow(y,c)
Simple Equation 023D: z = x/(a+b*y)
Simple Equation 033D: z = y/(a+b*x)
Simple Equation 043D: z = a*pow(x,b*y)
Simple Equation 053D: z = a*pow(y,b*x)
Simple Equation 063D: z = a*pow(x,b/y)
Simple Equation 073D: z = a*pow(y,b/x)
Simple Equation 083D: z = a*x+b*pow(y,2.0)
Simple Equation 093D: z = a*y+b*pow(x,2.0)
Simple Equation 103D: z = x/(a+b*pow(y,2.0))
Simple Equation 113D: z = y/(a+b*pow(x,2.0))
Simple Equation 123D: z = a*pow(b,x)*pow(y,c)
Simple Equation 133D: z = a*pow(b,y)*pow(x,c)
Simple Equation 143D: z = a*pow(x*y,b)
Simple Equation 153D: z = a*pow(x/y,b)
Simple Equation 163D: z = a*(pow(b,1.0/x))*pow(y,c)
Simple Equation 173D: z = a*pow(b,1.0/y)*pow(x,c)
Simple Equation 183D: z = a*pow(x/b,c)*exp(y/b)
Simple Equation 193D: z = a*pow(y/b,c)*exp(x/b)
Simple Equation 203D: z = a*pow(x,b+c*y)
Simple Equation 213D: z = a*pow(y,b+c*x)
Simple Equation 223D: z = a*pow(x,b+c/y)
Simple Equation 233D: z = a*pow(y,b+c/x)
Simple Equation 243D: z = a*pow(x,b+c*ln(y))
Simple Equation 253D: z = a*pow(y,b+c*ln(x))
Simple Equation 263D: z = a*pow(y,b+c/ln(x))
Simple Equation 273D: z = a*pow(x,b+c/ln(y))
Simple Equation 283D: z = a*exp(b*x+c*pow(y,2.0))
Simple Equation 293D: z = a*exp(b*y+c*pow(x,2.0))
Simple Equation 303D: z = a*exp(b/x+c*y)
Simple Equation 313D: z = a*exp(b/y+c*x)
Simple Equation 323D: z = (a+x)/(b+c*y)
Simple Equation 333D: z = (a+y)/(b+c*x)
Simple Equation 343D: z = (a+x)/(b+c*pow(y,2.0))
Simple Equation 353D: z = (a+y)/(b+c*pow(x,2.0))
Simple Equation 363D: z = a*(exp(b*x)-exp(c*y))
Simple Equation 373D: z = a*pow(x,b*pow(y,c))
Simple Equation 383D: z = a*pow(y,b*pow(x,c))
Simple Equation 393D: z = x/(a+b*y+c*pow(y,0.5))
Simple Equation 403D: z = y/(a+b*x+c*pow(x,0.5))
Simple Equation 413D: z = exp(a+b/x+c*ln(y))
Simple Equation 423D: z = exp(a+b/y+c*ln(x))
Simple Equation 433D: z = a*pow(x,b)*ln(y+c)
Simple Equation 443D: z = a*pow(y,b)*ln(x+c)

Simple Equation 01 With Offset3D: z = a*pow(x,b)*pow(y,c) + Offset
Simple Equation 02 With Offset3D: z = x/(a+b*y) + Offset
Simple Equation 03 With Offset3D: z = y/(a+b*x) + Offset
Simple Equation 04 With Offset3D: z = a*pow(x,b*y) + Offset
Simple Equation 05 With Offset3D: z = a*pow(y,b*x) + Offset
Simple Equation 06 With Offset3D: z = a*pow(x,b/y) + Offset
Simple Equation 07 With Offset3D: z = a*pow(y,b/x) + Offset
Simple Equation 08 With Offset3D: z = a*x+b*pow(y,2.0) + Offset
Simple Equation 09 With Offset3D: z = a*y+b*pow(x,2.0) + Offset
Simple Equation 10 With Offset3D: z = x/(a+b*pow(y,2.0)) + Offset
Simple Equation 11 With Offset3D: z = y/(a+b*pow(x,2.0)) + Offset
Simple Equation 12 With Offset3D: z = a*pow(b,x)*pow(y,c) + Offset
Simple Equation 13 With Offset3D: z = a*pow(b,y)*pow(x,c) + Offset
Simple Equation 14 With Offset3D: z = a*pow(x*y,b) + Offset
Simple Equation 15 With Offset3D: z = a*pow(x/y,b) + Offset
Simple Equation 16 With Offset3D: z = a*(pow(b,1.0/x))*pow(y,c) + Offset
Simple Equation 17 With Offset3D: z = a*pow(b,1.0/y)*pow(x,c) + Offset
Simple Equation 18 With Offset3D: z = a*pow(x/b,c)*exp(y/b) + Offset
Simple Equation 19 With Offset3D: z = a*pow(y/b,c)*exp(x/b) + Offset
Simple Equation 20 With Offset3D: z = a*pow(x,b+c*y) + Offset
Simple Equation 21 With Offset3D: z = a*pow(y,b+c*x) + Offset
Simple Equation 22 With Offset3D: z = a*pow(x,b+c/y) + Offset
Simple Equation 23 With Offset3D: z = a*pow(y,b+c/x) + Offset
Simple Equation 24 With Offset3D: z = a*pow(x,b+c*ln(y)) + Offset
Simple Equation 25 With Offset3D: z = a*pow(y,b+c*ln(x)) + Offset
Simple Equation 26 With Offset3D: z = a*pow(y,b+c/ln(x)) + Offset
Simple Equation 27 With Offset3D: z = a*pow(x,b+c/ln(y)) + Offset
Simple Equation 28 With Offset3D: z = a*exp(b*x+c*pow(y,2.0)) + Offset
Simple Equation 29 With Offset3D: z = a*exp(b*y+c*pow(x,2.0)) + Offset
Simple Equation 30 With Offset3D: z = a*exp(b/x+c*y) + Offset
Simple Equation 31 With Offset3D: z = a*exp(b/y+c*x) + Offset
Simple Equation 32 With Offset3D: z = (a+x)/(b+c*y) + Offset
Simple Equation 33 With Offset3D: z = (a+y)/(b+c*x) + Offset
Simple Equation 34 With Offset3D: z = (a+x)/(b+c*pow(y,2.0)) + Offset
Simple Equation 35 With Offset3D: z = (a+y)/(b+c*pow(x,2.0)) + Offset
Simple Equation 36 With Offset3D: z = a*(exp(b*x)-exp(c*y)) + Offset
Simple Equation 37 With Offset3D: z = a*pow(x,b*pow(y,c)) + Offset
Simple Equation 38 With Offset3D: z = a*pow(y,b*pow(x,c)) + Offset
Simple Equation 39 With Offset3D: z = x/(a+b*y+c*pow(y,0.5)) + Offset
Simple Equation 40 With Offset3D: z = y/(a+b*x+c*pow(x,0.5)) + Offset
Simple Equation 41 With Offset3D: z = exp(a+b/x+c*ln(y)) + Offset
Simple Equation 42 With Offset3D: z = exp(a+b/y+c*ln(x)) + Offset
Simple Equation 43 With Offset3D: z = a*pow(x,b)*ln(y+c) + Offset
Simple Equation 44 With Offset3D: z = a*pow(y,b)*ln(x+c) + Offset

Simple Equation 01 Plus Plane3D: z = a*pow(x,b)*pow(y,c)
z = z + (d * x) + (f * y) + g
Simple Equation 02 Plus Plane3D: z = x/(a+b*y)
z = z + (c * x) + (d * y) + f
Simple Equation 03 Plus Plane3D: z = y/(a+b*x)
z = z + (c * x) + (d * y) + f
Simple Equation 04 Plus Plane3D: z = a*pow(x,b*y)
z = z + (c * x) + (d * y) + f
Simple Equation 05 Plus Plane3D: z = a*pow(y,b*x)
z = z + (c * x) + (d * y) + f
Simple Equation 06 Plus Plane3D: z = a*pow(x,b/y)
z = z + (c * x) + (d * y) + f
Simple Equation 07 Plus Plane3D: z = a*pow(y,b/x)
z = z + (c * x) + (d * y) + f
Simple Equation 08 Plus Plane3D: z = a*x+b*pow(y,2.0)
z = z + (c * x) + (d * y) + f
Simple Equation 09 Plus Plane3D: z = a*y+b*pow(x,2.0)
z = z + (c * x) + (d * y) + f
Simple Equation 10 Plus Plane3D: z = x/(a+b*pow(y,2.0))
z = z + (c * x) + (d * y) + f
Simple Equation 11 Plus Plane3D: z = y/(a+b*pow(x,2.0))
z = z + (c * x) + (d * y) + f
Simple Equation 12 Plus Plane3D: z = a*pow(b,x)*pow(y,c)
z = z + (d * x) + (f * y) + g
Simple Equation 13 Plus Plane3D: z = a*pow(b,y)*pow(x,c)
z = z + (d * x) + (f * y) + g
Simple Equation 14 Plus Plane3D: z = a*pow(x*y,b)
z = z + (c * x) + (d * y) + f
Simple Equation 15 Plus Plane3D: z = a*pow(x/y,b)
z = z + (c * x) + (d * y) + f
Simple Equation 16 Plus Plane3D: z = a*(pow(b,1.0/x))*pow(y,c)
z = z + (d * x) + (f * y) + g
Simple Equation 17 Plus Plane3D: z = a*pow(b,1.0/y)*pow(x,c)
z = z + (d * x) + (f * y) + g
Simple Equation 18 Plus Plane3D: z = a*pow(x/b,c)*exp(y/b)
z = z + (d * x) + (f * y) + g
Simple Equation 19 Plus Plane3D: z = a*pow(y/b,c)*exp(x/b)
z = z + (d * x) + (f * y) + g
Simple Equation 20 Plus Plane3D: z = a*pow(x,b+c*y)
z = z + (d * x) + (f * y) + g
Simple Equation 21 Plus Plane3D: z = a*pow(y,b+c*x)
z = z + (d * x) + (f * y) + g
Simple Equation 22 Plus Plane3D: z = a*pow(x,b+c/y)
z = z + (d * x) + (f * y) + g
Simple Equation 23 Plus Plane3D: z = a*pow(y,b+c/x)
z = z + (d * x) + (f * y) + g
Simple Equation 24 Plus Plane3D: z = a*pow(x,b+c*ln(y))
z = z + (d * x) + (f * y) + g
Simple Equation 25 Plus Plane3D: z = a*pow(y,b+c*ln(x))
z = z + (d * x) + (f * y) + g
Simple Equation 26 Plus Plane3D: z = a*pow(y,b+c/ln(x))
z = z + (d * x) + (f * y) + g
Simple Equation 27 Plus Plane3D: z = a*pow(x,b+c/ln(y))
z = z + (d * x) + (f * y) + g
Simple Equation 28 Plus Plane3D: z = a*exp(b*x+c*pow(y,2.0))
z = z + (d * x) + (f * y) + g
Simple Equation 29 Plus Plane3D: z = a*exp(b*y+c*pow(x,2.0))
z = z + (d * x) + (f * y) + g
Simple Equation 30 Plus Plane3D: z = a*exp(b/x+c*y)
z = z + (d * x) + (f * y) + g
Simple Equation 31 Plus Plane3D: z = a*exp(b/y+c*x)
z = z + (d * x) + (f * y) + g
Simple Equation 32 Plus Plane3D: z = (a+x)/(b+c*y)
z = z + (d * x) + (f * y) + g
Simple Equation 33 Plus Plane3D: z = (a+y)/(b+c*x)
z = z + (d * x) + (f * y) + g
Simple Equation 34 Plus Plane3D: z = (a+x)/(b+c*pow(y,2.0))
z = z + (d * x) + (f * y) + g
Simple Equation 35 Plus Plane3D: z = (a+y)/(b+c*pow(x,2.0))
z = z + (d * x) + (f * y) + g
Simple Equation 36 Plus Plane3D: z = a*(exp(b*x)-exp(c*y))
z = z + (d * x) + (f * y) + g
Simple Equation 37 Plus Plane3D: z = a*pow(x,b*pow(y,c))
z = z + (d * x) + (f * y) + g
Simple Equation 38 Plus Plane3D: z = a*pow(y,b*pow(x,c))
z = z + (d * x) + (f * y) + g
Simple Equation 39 Plus Plane3D: z = x/(a+b*y+c*pow(y,0.5))
z = z + (d * x) + (f * y) + g
Simple Equation 40 Plus Plane3D: z = y/(a+b*x+c*pow(x,0.5))
z = z + (d * x) + (f * y) + g
Simple Equation 41 Plus Plane3D: z = exp(a+b/x+c*ln(y))
z = z + (d * x) + (f * y) + g
Simple Equation 42 Plus Plane3D: z = exp(a+b/y+c*ln(x))
z = z + (d * x) + (f * y) + g
Simple Equation 43 Plus Plane3D: z = a*pow(x,b)*ln(y+c)
z = z + (d * x) + (f * y) + g
Simple Equation 44 Plus Plane3D: z = a*pow(y,b)*ln(x+c)
z = z + (d * x) + (f * y) + g

3D TaylorSeries

Taylor Series A3D: z = a + bx + cy + dx² + fy² + gxy
Taylor Series B3D: z = a + b*ln(x) + cy + d*ln(x)² + fy² + g*ln(x)*y
Taylor Series C3D: z = a + bx + c*ln(y) + dx² + f*ln(y)² + g*x*ln(y)
Taylor Series D3D: z = a + b*ln(x) + c*ln(y) + d*ln(x)² + f*ln(y)² + g*ln(x)*ln(y)
Taylor Series E3D: z = a + b/x + cy + d/x² + fy² + gy/x
Taylor Series F3D: z = a + b/ln(x) + cy + d/ln(x)² + fy² + gy/ln(x)
Taylor Series G3D: z = a + b/x + c*ln(y) + d/x² + f*ln(y)² + g*ln(y)/x
Taylor Series H3D: z = a + b/ln(x) + c*ln(y) + d/ln(x)² + f*ln(y)² + g*ln(y)/ln(x)
Taylor Series I3D: z = a + bx + c/y + dx² + f/y² + gx/y
Taylor Series J3D: z = a + b*ln(x) + c/y + d*ln(x)² + f/y² + g*ln(x)/y
Taylor Series K3D: z = a + bx + c/ln(y) + dx² + f/ln(y)² + gx/ln(y)
Taylor Series L3D: z = a + b*ln(x) + c/ln(y) + d*ln(x)² + f/ln(y)² + g*ln(x)/ln(y)
Taylor Series M3D: z = a + b/x + c/y + d/x² + f/y² + g/(xy)
Taylor Series N3D: z = a + b/ln(x) + c/y + d/ln(x)² + f/y² + g/(ln(x)*y)
Taylor Series O3D: z = a + b/x + c/ln(y) + d/x² + f/ln(y)² + g/(x*ln(y))
Taylor Series P3D: z = a + b/ln(x) + c/ln(y) + d/ln(x)² + f/ln(y)² + g/(ln(x)*ln(y))

3D Trigonometric

Cosh X Plus Cosh Y [radians]3D: z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y)
Cosh X Plus Sine Y [radians]3D: z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y)
Cosh X Plus Tangent Y [radians]3D: z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y)
Cosh X Times Cosh Y[radians]3D: z = amplitude * cosh(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y)
Cosh X Times Sine Y [radians]3D: z = amplitude * cosh(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y)
Cosh X Times Tangent Y [radians]3D: z = amplitude * cosh(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y)
Cosh XY [radians]3D: z = amplitude * cosh(pi * (xy - center) / width)
Reza's Custom Equation One [radians]3D: z = (cos(a*x - b*y) + sin(c*x - d*y))ⁿ - (cos(f*x - g*y) + sin(h*x- i*y))ⁿ
Reza's Custom Equation Two [radians]3D: 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
Sine X Plus Cosh Y [radians]3D: z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y)
Sine X Plus Sine Y [radians]3D: z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y)
Sine X Plus Tangent Y [radians]3D: z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y)
Sine X Times Cosh Y [radians]3D: z = amplitude * sine(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y)
Sine X Times Sine Y [radians]3D: z = amplitude * sin(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y)
Sine X Times Tangent Y [radians]3D: z = amplitude * sin(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y)
Sine XY [radians]3D: z = amplitude * sin(pi * (xy - center) / width)
Tangent X Plus Cosh Y [radians]3D: z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y)
Tangent X Plus Sine Y [radians]3D: z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y)
Tangent X Plus Tangent Y [radians]3D: z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y)
Tangent X Times Cosh Y [radians]3D: z = amplitude * tan(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y)
Tangent X Times Sine Y [radians]3D: z = amplitude * tan(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y)
Tangent X Times Tangent Y [radians]3D: z = amplitude * tan(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y)
Tangent XY [radians]3D: z = amplitude * tan(pi * (xy - center) / width)

Cosh X Plus Cosh Y [radians] With Offset3D: z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y) + Offset
Cosh X Plus Sine Y [radians] With Offset3D: z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y) + Offset
Cosh X Plus Tangent Y [radians] With Offset3D: z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y) + Offset
Cosh X Times Cosh Y[radians] With Offset3D: z = amplitude * cosh(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y) + Offset
Cosh X Times Sine Y [radians] With Offset3D: z = amplitude * cosh(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y) + Offset
Cosh X Times Tangent Y [radians] With Offset3D: z = amplitude * cosh(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y) + Offset
Cosh XY [radians] With Offset3D: z = amplitude * cosh(pi * (xy - center) / width) + Offset
Reza's Custom Equation One [radians] With Offset3D: z = (cos(a*x - b*y) + sin(c*x - d*y))ⁿ - (cos(f*x - g*y) + sin(h*x- i*y))ⁿ + Offset
Reza's Custom Equation Two [radians] With Offset3D: 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 + Offset
Sine X Plus Cosh Y [radians] With Offset3D: z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y) + Offset
Sine X Plus Sine Y [radians] With Offset3D: z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y) + Offset
Sine X Plus Tangent Y [radians] With Offset3D: z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y) + Offset
Sine X Times Cosh Y [radians] With Offset3D: z = amplitude * sine(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y) + Offset
Sine X Times Sine Y [radians] With Offset3D: z = amplitude * sin(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y) + Offset
Sine X Times Tangent Y [radians] With Offset3D: z = amplitude * sin(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y) + Offset
Sine XY [radians] With Offset3D: z = amplitude * sin(pi * (xy - center) / width) + Offset
Tangent X Plus Cosh Y [radians] With Offset3D: z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y) + Offset
Tangent X Plus Sine Y [radians] With Offset3D: z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y) + Offset
Tangent X Plus Tangent Y [radians] With Offset3D: z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y) + Offset
Tangent X Times Cosh Y [radians] With Offset3D: z = amplitude * tan(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y) + Offset
Tangent X Times Sine Y [radians] With Offset3D: z = amplitude * tan(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y) + Offset
Tangent X Times Tangent Y [radians] With Offset3D: z = amplitude * tan(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y) + Offset
Tangent XY [radians] With Offset3D: z = amplitude * tan(pi * (xy - center) / width) + Offset

Cosh XY [radians] Plus Plane3D: z = amplitude * cosh(pi * (xy - center) / width)
z = z + (d * x) + (f * y) + g
Sine XY [radians] Plus Plane3D: z = amplitude * sin(pi * (xy - center) / width)
z = z + (d * x) + (f * y) + g
Tangent XY [radians] Plus Plane3D: z = amplitude * tan(pi * (xy - center) / width)
z = z + (d * x) + (f * y) + g

All 2D Equations

List Of All 2D Equations: Standard Versions Only
List Of All 2D Equations: Including Extended Versions

All 3D Equations

List Of All 3D Equations: Standard Versions Only
List Of All 3D Equations: Including Extended Versions