An interpolation model is a means of converting a set of input points into some general function. For example, a linear regression is one type of model that does not necessarily evaluate to all points exactly. Another type of model is a cubic spline interpolator, which does evaluate to all points exactly, but provides smoothed curves between them. Through all model types are available in all contexts, they may not necessarily make sense in some.

Interpolation models provide multi-dimensional interpolation, but many of the specific types simply operate with each dimension independently. For example, a model used in a gradient definition may simply use linear interpolation of each component of the color independently. In most cases, the first dimension is used as the independent variable.

The model in use is selected by the enumeration value Type:

LeastSquares or LSQ

A least squares linear regression of the input points.

ZeroLeastSquares or ZLSQ

A least squares linear regression of the input points, with the intercept forced through zero.

NPolynomial or NPoly

An N-th order polynomial, fitted with non-linear least squares (Levenberg-Marquardt).

Order

The integer order of the polynomial. For example, two gives a polynomial of the form \$a + b*x + c*x^2\$

ZeroNPolynomial or ZNPoly

An N-th order polynomial with no intercept term, fitted with non-linear least squares (Levenberg-Marquardt).

Order

The integer order of the polynomial. For example, two gives a polynomial of the form \$a*x + b*x^2\$

Linear

A linear interpolator between all input data points. This creates a piecewise function that starts with a linear interpolation between each point and then (optionally) applies a transfer function.

Transfer

An enumeration specifying the transfer function applies to each segment.

Linear

Use the default of no transfer function. The output is simply the input line segment.

Sin

A sin based function of the form \$(sin(x))^n\$. This creates a "concave" form of interpolation, with the greatest rate of change near the start.

Cos

A cos based function of the form \$(1-cos(x))^n\$. This creates a "convex" form of interpolation, with the greatest rate of change near the end.

Sigmoid

A sigmoid shaped function. The sigmoid created is symmetric around the middle of the range with the parameter in [-1,1] with negative values causing increased rate of change at the start end end.

TransferParameter

The real number of the parameter to the transfer function. This is the power in the sin and cos variants and the tunable input in the sigmoid.

CubicSpline or CSpline

A cubic spline interpolator between all points. This produces a smooth interpolator between each point.

Clamp

The real number slope of the interpolator at the endpoints, if neither is overridden. If set to undefined, a natural spline is used; meaning that the slope is set such that the second derivative is zero.

ClampStart

The real number slope of the interpolator at the first point. If set to undefined, a natural spline is used; meaning that the slope is set such that the second derivative is zero.

ClampEnd

The real number slope of the interpolator at the last point. If set to undefined, a natural spline is used; meaning that the slope is set such that the second derivative is zero.

CDF or NormalCDF

A fit line suitable for data that has been transformed into a CDF. The fine line assumes a normal distribution and calculates the mean and standard deviation. If the data are truely normal, the result would be an exactly straight line in the CDF with those parameters.

Allan

A fit line suitable for data that has been transformed into an Allan plot. The fine line is generated between a minimum and maximum averaging intervals and its slope is the reduction in standard deviation from more averaging.

Start

The real number of averaging seconds to start the fitting at.

End

The real number of averaging seconds to end the fitting at.

Intercept

The real number of averaging seconds to report the intercept at in graph legends.

Density

A density plot filling interpolator. This interpolator takes the input points and produces a field that can be evaluated to generate an image of the relative desnity of points. The field itself is created by creating gaussian shaped kernels around each point and adding the results together.

Density

The real number density parameter. Smaller values give larger spots around each point.

Limit

The real number limit factor. From zero to one, this determines the weight limit of a point in the field. Smaller values "clip" peaks in the field.

Constant

A model that always evaluates to a constant value. It can optionally calculate this constant value as the mean of the input values.

Value

The real number output. When undefined, the mean of the input values is calculated instead.

GeometricAverage

A boolean value that when set causes the mean to be calculated with a geometric average, instead of an arithmetic one.

Composite

This creates a composite model, allowing for the selection of different models for each component or dimension.

DefaultComponent

A model definition that sets the default for the composite model when a dimension is not explicitly defined.

Components

An array of model definitions for the components or dimensions of the input.

Least squares regression
/Type,"LeastSquares"
Clamped cubic spline interpolation
/Type,"CubicSpline"
/Clamp,0.0
CDF fit line
/Type,"CDF"
Composite model
/Model,"Composite"
/DefaultComponent/Type,"Linear"
/Components/#0/Type,"Linear"
/Components/#1/Type,"CubicSpline"