#include <iostream>
#include <cassert>
#include <algorithm>
#include <iterator>
#include <vector>
#include <utility>
#include <math.h>
#include <bezierclip.hxx>
#include <gauss.hxx>

Include dependency graph for bezierclip.cxx:

Classes
struct	ClipBezierFunctor

struct	BezierTangencyFunctor

Macros
#define	WITH_ASSERTIONS

#define	WITH_BEZIERCLIP_TEST

Functions
int	fallFac (int n, int k)

int	fac (int n)

void	Impl_calcFatLine (FatLine &line, const Bezier &c)

void	Impl_calcBounds (Point2D &leftTop, Point2D &rightBottom, const Bezier &c1)

bool	Impl_doBBoxIntersect (const Bezier &c1, const Bezier &c2)

bool	Impl_calcSafeParams (double &t1, double &t2, const Polygon2D &rPoly, double lowerYBound, double upperYBound)

bool	Impl_calcSafeParams_clip (double &t1, double &t2, const FatLine &bounds, double c0, double c1, double c2, double c3)

void	Impl_deCasteljauAt (Bezier &part1, Bezier &part2, const Bezier &input, double t)

void	printCurvesWithSafeRange (const Bezier &c1, const Bezier &c2, double t1_c1, double t2_c1, const Bezier &c2_part, const FatLine &bounds_c2)

void	printResultWithFinalCurves (const Bezier &c1, const Bezier &c1_part, const Bezier &c2, const Bezier &c2_part, double t1_c1, double t2_c1)

bool	Impl_calcClipRange (double &t1, double &t2, const Bezier &c1_orig, const Bezier &c1_part, const Bezier &c2_orig, const Bezier &c2_part)
	determine parameter ranges [0,t1) and (t2,1] on c1, where c1 is guaranteed to lie outside c2. More...

void	Impl_calcFocus (Bezier &res, const Bezier &c)

bool	Impl_calcSafeParams_focus (double &t1, double &t2, const Bezier &curve, const Bezier &focus)

template<class Functor >
void	Impl_applySafeRanges_rec (std::back_insert_iterator< std::vector< std::pair< double, double > > > &result, double delta, const Functor &safeRangeFunctor, int recursionLevel, const Bezier &c1_orig, const Bezier &c1_part, double last_t1_c1, double last_t2_c1, const Bezier &c2_orig, const Bezier &c2_part, double last_t1_c2, double last_t2_c2)
	Calc all values t_i on c1, for which safeRanges functor does not give a safe range on c1 and c2. More...

void	clipBezier (std::back_insert_iterator< std::vector< std::pair< double, double > > > &result, double delta, const Bezier &c1, const Bezier &c2)
	Perform a bezier clip (curve against curve) More...

int	main (int argc, const char *argv[])

Macro Definition Documentation

◆ WITH_ASSERTIONS

#define WITH_ASSERTIONS

Definition at line 33 of file bezierclip.cxx.

◆ WITH_BEZIERCLIP_TEST

#define WITH_BEZIERCLIP_TEST

Definition at line 44 of file bezierclip.cxx.

Function Documentation

◆ clipBezier()

void clipBezier	(	std::back_insert_iterator< std::vector< std::pair< double, double > > > &	result,
		double	delta,
		const Bezier &	c1,
		const Bezier &	c2
	)

Perform a bezier clip (curve against curve)

Parameters

result	Output iterator where the final t values are added to. This iterator will remain empty, if there are no intersections.
delta	Maximal allowed distance to true intersection (measured in the original curve's coordinate system)

Definition at line 1162 of file bezierclip.cxx.

References first, i, Impl_applySafeRanges_rec(), Impl_deCasteljauAt(), and result.

Referenced by main().

◆ fac()

int fac ( int n )

Definition at line 71 of file bezierclip.cxx.

References fallFac(), and n.

Referenced by Impl_calcSafeParams_focus().

◆ fallFac()

int fallFac	(	int	n,
		int	k
	)

Definition at line 56 of file bezierclip.cxx.

References n.

Referenced by fac(), and Impl_calcSafeParams_focus().

◆ Impl_applySafeRanges_rec()

template<class Functor >

void Impl_applySafeRanges_rec	(	std::back_insert_iterator< std::vector< std::pair< double, double > > > &	result,
		double	delta,
		const Functor &	safeRangeFunctor,
		int	recursionLevel,
		const Bezier &	c1_orig,
		const Bezier &	c1_part,
		double	last_t1_c1,
		double	last_t2_c1,
		const Bezier &	c2_orig,
		const Bezier &	c2_part,
		double	last_t1_c2,
		double	last_t2_c2
	)

Calc all values t_i on c1, for which safeRanges functor does not give a safe range on c1 and c2.

This method is the workhorse of the bezier clipping. Because c1 and c2 must be alternatingly tested against each other (first determine safe parameter interval on c1 with regard to c2, then the other way around), we call this method recursively with c1 and c2 swapped.

Parameters

result	Output iterator where the final t values are added to. If curves don't intersect, nothing is added.
delta	Maximal allowed distance to true critical point (measured in the original curve's coordinate system)
safeRangeFunctor	Functor object, that must provide the following operator(): bool safeRangeFunctor( double& t1, double& t2, const Bezier& c1_orig, const Bezier& c1_part, const Bezier& c2_orig, const Bezier& c2_part ); This functor must calculate the safe ranges [0,t1] and [t2,1] on c1_orig, where c1_orig is 'safe' from c2_part. If the whole c1_orig is safe, false must be returned, true otherwise.

Definition at line 900 of file bezierclip.cxx.

References i, Impl_applySafeRanges_rec(), Impl_calcFocus(), Impl_deCasteljauAt(), printResultWithFinalCurves(), result, tolGreaterEqual(), and tolLessEqual().

Referenced by clipBezier(), and Impl_applySafeRanges_rec().

◆ Impl_calcBounds()

void Impl_calcBounds	(	Point2D &	leftTop,
		Point2D &	rightBottom,
		const Bezier &	c1
	)

Definition at line 121 of file bezierclip.cxx.

References Bezier::p0, Bezier::p1, Bezier::p2, Bezier::p3, Point2D::x, and Point2D::y.

Referenced by Impl_doBBoxIntersect().

◆ Impl_calcClipRange()

bool Impl_calcClipRange	(	double &	t1,
		double &	t2,
		const Bezier &	c1_orig,
		const Bezier &	c1_part,
		const Bezier &	c2_orig,
		const Bezier &	c2_part
	)

determine parameter ranges [0,t1) and (t2,1] on c1, where c1 is guaranteed to lie outside c2.

Returns false, if the two curves don't even intersect.

Parameters

t1	Range [0,t1) on c1 is guaranteed to lie outside c2
t2	Range (t2,1] on c1 is guaranteed to lie outside c2
c1_orig	Original curve c1
c1_part	Subdivided current part of c1
c2_orig	Original curve c2
c2_part	Subdivided current part of c2