Castle Game Engine

Unit CastleCurves

Description
Uses
Classes, Interfaces, Objects and Records
Functions and Procedures
Types
Constants
Variables

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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