CartoType::Spline Class Reference

#include <cartotype_spline.h>

List of all members.

Public Types
enum	{ EStackSize = 32 * 3 + 1 }
Static Public Member Functions
static void	SplitQuadratic (TPoint *aStack)
static void	SplitCubic (TPoint *aStack)
static void	SplitQuadratic (TPointFP *aStack)
static void	SplitCubic (TPointFP *aStack)
static CT_IMPORT void	EquidistantParabola (const TPoint &aFocus, const TPoint &aLineStart, const TPoint &aLineEnd, TOutlinePoint &aStart, TOutlinePoint &aControl, TOutlinePoint &aEnd)
static CT_IMPORT void	ExtendParabola (TOutlinePoint &aStart, TOutlinePoint &aControl, TOutlinePoint &aEnd)
static CT_IMPORT int32	QuadraticCurveLineIntersection (TFixed &aT1, TFixed &aT2, const TPoint &aLineStart, const TPoint &aLineEnd, const TPoint &aStart, const TPoint &aControl, const TPoint &aEnd)
static CT_IMPORT bool	PointToT (TFixed &aT, const TPoint &aPoint, const TPoint &aStart, const TPoint &aControl, const TPoint &aEnd)
static CT_IMPORT void	TToPoint (TPoint &aPoint, const TFixed &aT, const TPoint &aStart, const TPoint &aControl, const TPoint &aEnd)
static CT_IMPORT void	CutQuadraticCurveAt (const TFixed &aT, TPoint &aStart, TPoint &aControl, TPoint &aEnd, bool aKeepStart)

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Detailed Description

The Spline class is a wrapper for static functions concerned with Bezier splines.

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Member Enumeration Documentation

anonymous enum

Enumerator:

EStackSize

The size of a stack of points used for calculating a quadratic or cubic Bezier spline by repeated bisection. Cubic splines are defined by 4 points but the first point of the current curve is the last point of the previous one, hence the multiplication by 3. Quadratic splines need only 3 points.

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Member Function Documentation

CT_EXPORT void Spline::CutQuadraticCurveAt	(	const TFixed &	aT,
		TPoint &	aStart,
		TPoint &	aControl,
		TPoint &	aEnd,
		bool	aKeepStart
	)		[static]

Split the quadratic curve at the specified value for t and updates start, control and end point such that they are the curve segment starting or ending at the point implied by t. If aKeepStart is true, this segment corresponds to the 0..t interval, otherwise the segment corresponds to the t..1 interval. Algorithm based on comp.graphics.algorithms FAQ 4.02 simplified for quadratic where f0t = s f00 + t f01 f1t = s f01 + t f11 ftt = s f0t + t f1t Low precision implementation in 64ths for speed.

CT_EXPORT void Spline::EquidistantParabola	(	const TPoint &	aFocus,
		const TPoint &	aLineStart,
		const TPoint &	aLineEnd,
		TOutlinePoint &	aStart,
		TOutlinePoint &	aControl,
		TOutlinePoint &	aEnd
	)		[static]

Generate quadratic bezier curve that is a segment of the parabola of points equidistant to a point and a line. The end points of this segment are the intersections of the parabola with the line through the point parallel to the line segment.

CT_EXPORT void Spline::ExtendParabola	(	TOutlinePoint &	aStart,
		TOutlinePoint &	aControl,
		TOutlinePoint &	aEnd
	)		[static]

Take a quadratic bezier curve assumed to represent a parabola segment and extend the segment by computing the points at -1 and 2 and recomputing the control point.

CT_EXPORT bool Spline::PointToT	(	TFixed &	aT,
		const TPoint &	aPoint,
		const TPoint &	aStart,
		const TPoint &	aControl,
		const TPoint &	aEnd
	)		[static]

Convert point on quadratic curve to a value for t. It is assumed that the point is on or near the curve. This method uses an approximation method where a line perpendicular to the line between start and end point is constructed through the point and this line is intersected with the bezier curve. Return true if the point is on the curve, false otherwise.

CT_EXPORT int32 Spline::QuadraticCurveLineIntersection	(	TFixed &	aT1,
		TFixed &	aT2,
		const TPoint &	aLineStart,
		const TPoint &	aLineEnd,
		const TPoint &	aStart,
		const TPoint &	aControl,
		const TPoint &	aEnd
	)		[static]

Compute t's for intersection between quadratic bezier and a line. Return number of solutions. If there is one solution it is returned in aT1. Algorithm: transform coordinates such that the line aligns with the x axis. Then solve the blending function equation y = 0 for t. Values of t between 0 and 1 (both inclusive) are valid solutions.

CT_EXPORT void Spline::TToPoint	(	TPoint &	aPoint,
		const TFixed &	aT,
		const TPoint &	aStart,
		const TPoint &	aControl,
		const TPoint &	aEnd
	)		[static]

Convert t value to a point on quadratic curve. Low precision implementation in 64ths for speed.

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The documentation for this class was generated from the following files:

• cartotype_spline.h
• cartotype_spline.cpp