Unit CastleCurves

Description

3D curves (TCurve and basic descendants).

Uses

Overview

Classes, Interfaces, Objects and Records

Name Description
Class ECurveFileInvalid  
Class TCurve 3D curve, a set of points defined by a continuous function Point for arguments within [TBegin, TEnd].
Class TCurveList  
Class TCasScriptCurve Curve defined by explicitly giving functions for Point(t) = x(t), y(t), z(t) as CastleScript expressions.
Class TControlPointsCurve A basic abstract class for curves determined my some set of ControlPoints.
Class TPiecewiseCubicBezier Piecewise (composite) cubic Bezier curve.

Functions and Procedures

function CubicBezier1D(T: Single; const Points: TVector4): Single;
function CubicBezier2D(T: Single; const Points: TCubicBezier2DPoints): TVector2;
function CubicBezier3D(T: Single; const Points: TCubicBezier3DPoints): TVector3;
function CatmullRomSpline(const X: Single; const Loop: boolean; const Arguments: TSingleList; const Values: TSingleList): Single;
function CatmullRom(const V0, V1, V2, V3, X: Single): Single;
function HermiteSpline(const X: Single; const Loop: boolean; const Arguments, Values, Tangents: TSingleList): Single;
function HermiteTenseSpline(const X: Single; const Loop: boolean; const Arguments, Values: TSingleList): Single;

Types

TControlPointsCurveClass = class of TControlPointsCurve;
TControlPointsCurveList = specialize TObjectList<TControlPointsCurve>;
TCubicBezier2DPoints = array [0..3] of TVector2;
TCubicBezier3DPoints = array [0..3] of TVector3;

Description

Functions and Procedures

function CubicBezier1D(T: Single; const Points: TVector4): Single;

Cubic (4 control points) Bezier curve (with all weights equal) in 1D.

function CubicBezier2D(T: Single; const Points: TCubicBezier2DPoints): TVector2;

Cubic (4 control points) Bezier curve (with all weights equal) in 2D.

function CubicBezier3D(T: Single; const Points: TCubicBezier3DPoints): TVector3;

Cubic (4 control points) Bezier curve (with all weights equal) in 3D.

function CatmullRomSpline(const X: Single; const Loop: boolean; const Arguments: TSingleList; const Values: TSingleList): Single;

Catmull-Rom spline. Nice way to have a function that for certain arguments reaches certain values, and between interpolates smoothly.

Catmull-Rom splines are a special case of cubic Hermite splines, see https://en.wikipedia.org/wiki/Cubic_Hermite_spline .

function CatmullRom(const V0, V1, V2, V3, X: Single): Single;

Catmull-Rom spline low-level function. For X in [0..1], the curve values change from V1 to V2. V0 and V3 are curve values outside the [0..1] range, used to calculate tangents.

See http://www.mvps.org/directx/articles/catmull/.

See also
CatmullRomSpline
Catmull-Rom spline.
function HermiteSpline(const X: Single; const Loop: boolean; const Arguments, Values, Tangents: TSingleList): Single;

Hermite spline. Nice way to have a function that for certain arguments reaches certain values, and between interpolates smoothly. Requires specifying tangent values (use CatmullRomSpline or HermiteTenseSpline to use automatic tangents).

function HermiteTenseSpline(const X: Single; const Loop: boolean; const Arguments, Values: TSingleList): Single;

Hermite spline with tangents zero (it will be horizontal at control points). Nice way to have a function that for certain arguments reaches certain values, and between interpolates smoothly.

This is equivalent (for faster) to using HermiteSpline with all tangents equal to zero.

This is called a "cardinal spline", a special case of Hermite spline, with all tangents calculated with "tension" parameter equal to 1 (maximum), which means that all tangents are simply zero (horizontal). See https://en.wikipedia.org/wiki/Cubic_Hermite_spline for math behind this.

Types

TControlPointsCurveClass = class of TControlPointsCurve;
 
TControlPointsCurveList = specialize TObjectList<TControlPointsCurve>;
 
TCubicBezier2DPoints = array [0..3] of TVector2;
 
TCubicBezier3DPoints = array [0..3] of TVector3;
 

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