::tclinterp::approximation

Commands

bezier

Evaluates a Bezier polynomial on an interval.

bezier -n integer -a value -b value -x values -y values ?-input list|vector? ?-output list|vector? ?-namespace name? ?-name name? ?-names dictionary? ?-ifexists error|replace?

Parameters

-a value:

Start of the interval; must differ from -b.

-b value:

End of the interval; must differ from -a.

-ifexists error|replace:

Policy for existing destination vectors; uses the package default (initially error). With replace, an existing real vector is resized and overwritten.

-input list|vector:

Input representation for all array arguments: Tcl lists or real RBC vector names. Defaults to the package setting (initially list).

-n integer:

Polynomial degree; must be zero or greater.

-name name:

Destination vector name for yi; requires -output vector. Omit it or use #auto to create an automatically named vector.

-names dictionary:

Dictionary mapping output fields to destination vector names; requires -output vector. Valid fields: yi.

-namespace name:

Destination namespace for vector output; relative to the caller, created with missing parents.

-output list|vector:

Output representation for every numeric result array: Tcl list or RBC vector name. Defaults to the package setting (initially list); independent of -input.

-x values:

Evaluation positions; must not be empty.

-y values:

Control values; exactly n+1 values.

Description

Every array argument marked values uses the representation selected by -input. Scalar options remain ordinary Tcl numbers. Numeric inputs must be finite. RBC support must be enabled in the build to use vectors.

Omitted -input, -output and -ifexists use ::tclinterp::configure defaults at call time. Explicit options take precedence. Input vector names resolve in the caller’s namespace. Output names use -namespace, or the caller’s namespace when omitted. Empty namespace names are rejected; -namespace requires -output vector. Fully qualified output names override this location; their parent namespace must already exist. Each unnamed output, including fields omitted from -names, uses RBC’s #auto mechanism in the selected namespace. A final #auto component also works in qualified names; auto without # is an ordinary name. Returned vector names are fully qualified.

Do not specify both -name and the yi entry of -names. Unknown output fields and duplicate destinations are errors. The caller owns returned vectors and can release them with ::rbc::vector destroy $vectorName.

Return value

The interpolated values yi, as a Tcl list with list output or an RBC vector name with -output vector.

cubicBetaSpline1d

Evaluates a cubic beta-spline approximant.

cubicBetaSpline1d -beta1 value -beta2 value -t values -y values -ti values ?-input list|vector? ?-output list|vector? ?-namespace name? ?-name name? ?-names dictionary? ?-ifexists error|replace?

Parameters

-beta1 value:

Required skew or bias parameter; 1 means no skew or bias.

-beta2 value:

Required tension parameter; 0 means no tension.

-ifexists error|replace:

Policy for existing destination vectors; uses the package default (initially error). With replace, an existing real vector is resized and overwritten.

-input list|vector:

Input representation for all array arguments: Tcl lists or real RBC vector names. Defaults to the package setting (initially list).

-name name:

Destination vector name for yi; requires -output vector. Omit it or use #auto to create an automatically named vector.

-names dictionary:

Dictionary mapping output fields to destination vector names; requires -output vector. Valid fields: yi.

-namespace name:

Destination namespace for vector output; relative to the caller, created with missing parents.

-output list|vector:

Output representation for every numeric result array: Tcl list or RBC vector name. Defaults to the package setting (initially list); independent of -input.

-t values:

Strictly increasing sample positions; at least two values. Alias: -x.

-ti values:

Evaluation positions; must not be empty. Alias: -xi.

-y values:

Sample values; must have the same length as -t.

Description

Every array argument marked values uses the representation selected by -input. Scalar options remain ordinary Tcl numbers. Numeric inputs must be finite. RBC support must be enabled in the build to use vectors.

Omitted -input, -output and -ifexists use ::tclinterp::configure defaults at call time. Explicit options take precedence. Input vector names resolve in the caller’s namespace. Output names use -namespace, or the caller’s namespace when omitted. Empty namespace names are rejected; -namespace requires -output vector. Fully qualified output names override this location; their parent namespace must already exist. Each unnamed output, including fields omitted from -names, uses RBC’s #auto mechanism in the selected namespace. A final #auto component also works in qualified names; auto without # is an ordinary name. Returned vector names are fully qualified.

Do not specify both -name and the yi entry of -names. Unknown output fields and duplicate destinations are errors. The caller owns returned vectors and can release them with ::rbc::vector destroy $vectorName.

The parameters must produce a finite, nonzero beta-spline normalization.

Return value

The approximated values yi, as a Tcl list with list output or an RBC vector name with -output vector.

cubicBSpline1d

Evaluates a cubic B-spline approximant.

cubicBSpline1d -t values -y values -ti values ?-input list|vector? ?-output list|vector? ?-namespace name? ?-name name? ?-names dictionary? ?-ifexists error|replace?

Parameters

-ifexists error|replace:

Policy for existing destination vectors; uses the package default (initially error). With replace, an existing real vector is resized and overwritten.

-input list|vector:

Input representation for all array arguments: Tcl lists or real RBC vector names. Defaults to the package setting (initially list).

-name name:

Destination vector name for yi; requires -output vector. Omit it or use #auto to create an automatically named vector.

-names dictionary:

Dictionary mapping output fields to destination vector names; requires -output vector. Valid fields: yi.

-namespace name:

Destination namespace for vector output; relative to the caller, created with missing parents.

-output list|vector:

Output representation for every numeric result array: Tcl list or RBC vector name. Defaults to the package setting (initially list); independent of -input.

-t values:

Strictly increasing sample positions; at least two values. Alias: -x.

-ti values:

Evaluation positions; must not be empty. Alias: -xi.

-y values:

Sample values; must have the same length as -t.

Description

Every array argument marked values uses the representation selected by -input. Scalar options remain ordinary Tcl numbers. Numeric inputs must be finite. RBC support must be enabled in the build to use vectors.

Omitted -input, -output and -ifexists use ::tclinterp::configure defaults at call time. Explicit options take precedence. Input vector names resolve in the caller’s namespace. Output names use -namespace, or the caller’s namespace when omitted. Empty namespace names are rejected; -namespace requires -output vector. Fully qualified output names override this location; their parent namespace must already exist. Each unnamed output, including fields omitted from -names, uses RBC’s #auto mechanism in the selected namespace. A final #auto component also works in qualified names; auto without # is an ordinary name. Returned vector names are fully qualified.

Do not specify both -name and the yi entry of -names. Unknown output fields and duplicate destinations are errors. The caller owns returned vectors and can release them with ::rbc::vector destroy $vectorName.

Return value

The approximated values yi, as a Tcl list with list output or an RBC vector name with -output vector.

genBezier

Evaluates a parametric Bezier curve.

genBezier -n integer -x values -y values -t values ?-input list|vector? ?-output list|vector? ?-namespace name? ?-name name? ?-names dictionary? ?-ifexists error|replace?

Parameters

-ifexists error|replace:

Policy for existing destination vectors; uses the package default (initially error). With replace, an existing real vector is resized and overwritten.

-input list|vector:

Input representation for all array arguments: Tcl lists or real RBC vector names. Defaults to the package setting (initially list).

-n integer:

Curve degree; must be zero or greater.

-name name:

Destination vector name for yi; requires -output vector. Omit it or use #auto to create an automatically named vector.

-names dictionary:

Dictionary mapping output fields to destination vector names; requires -output vector. Valid fields: xi, yi.

-namespace name:

Destination namespace for vector output; relative to the caller, created with missing parents.

-output list|vector:

Output representation for every numeric result array: Tcl list or RBC vector name. Defaults to the package setting (initially list); independent of -input.

-t values:

Nonempty evaluation parameters; normally between 0 and 1.

-x values:

X control coordinates; exactly n+1 values.

-y values:

Y control coordinates; exactly n+1 values.

Description

Every array argument marked values uses the representation selected by -input. Scalar options remain ordinary Tcl numbers. Numeric inputs must be finite. RBC support must be enabled in the build to use vectors.

Omitted -input, -output and -ifexists use ::tclinterp::configure defaults at call time. Explicit options take precedence. Input vector names resolve in the caller’s namespace. Output names use -namespace, or the caller’s namespace when omitted. Empty namespace names are rejected; -namespace requires -output vector. Fully qualified output names override this location; their parent namespace must already exist. Each unnamed output, including fields omitted from -names, uses RBC’s #auto mechanism in the selected namespace. A final #auto component also works in qualified names; auto without # is an ordinary name. Returned vector names are fully qualified.

Do not specify both -name and the yi entry of -names. Unknown output fields and duplicate destinations are errors. The caller owns returned vectors and can release them with ::rbc::vector destroy $vectorName.

Return value

A dictionary with xi and yi coordinates. Each numeric array is a Tcl list with list output or an RBC vector name with -output vector.

Copyright (c) George Yashin