X-Git-Url: https://git.pterodactylus.net/?a=blobdiff_plain;f=ETL%2Ftrunk%2FETL%2F_bezier.h;fp=ETL%2Ftrunk%2FETL%2F_bezier.h;h=d693fa4c97a1499fb3060cec28a595f7e82805a4;hb=b3016b249333ac0ab0008d8c6c4d9029b2ff30c9;hp=0000000000000000000000000000000000000000;hpb=7f4273493da74d7d5746a65551e20c7786d0f155;p=synfig.git

diff --git a/ETL/trunk/ETL/_bezier.h b/ETL/trunk/ETL/_bezier.h
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+/*! ========================================================================
+** Extended Template Library
+** Bezier Template Class Implementation
+** $Id: _bezier.h,v 1.1.1.1 2005/01/04 01:31:46 darco Exp $
+**
+** Copyright (c) 2002 Robert B. Quattlebaum Jr.
+**
+** This package is free software; you can redistribute it and/or
+** modify it under the terms of the GNU General Public License as
+** published by the Free Software Foundation; either version 2 of
+** the License, or (at your option) any later version.
+**
+** This package is distributed in the hope that it will be useful,
+** but WITHOUT ANY WARRANTY; without even the implied warranty of
+** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+** General Public License for more details.
+**
+** === N O T E S ===========================================================
+**
+** This is an internal header file, included by other ETL headers.
+** You should not attempt to use it directly.
+**
+** ========================================================================= */
+
+/* === S T A R T =========================================================== */
+
+#ifndef __ETL_BEZIER_H
+#define __ETL_BEZIER_H
+
+/* === H E A D E R S ======================================================= */
+
+#include "_curve_func.h"
+#include <ETL/fixed>
+
+/* === M A C R O S ========================================================= */
+
+/* === T Y P E D E F S ===================================================== */
+
+/* === C L A S S E S & S T R U C T S ======================================= */
+
+_ETL_BEGIN_NAMESPACE
+
+template<typename V,typename T> class bezier;
+
+//! Cubic Bezier Curve Base Class
+// This generic implementation uses the DeCasteljau algorithm.
+// Works for just about anything that has an affine combination function
+template <typename V,typename T=float>
+class bezier_base : public std::unary_function<T,V>
+{
+public:
+	typedef V value_type;
+	typedef T time_type;
+
+private:
+	value_type a,b,c,d;
+	time_type r,s;
+
+protected:
+	affine_combo<value_type,time_type> affine_func; 
+
+public:
+	bezier_base():r(0.0),s(1.0) { }
+	bezier_base(
+		const value_type &a, const value_type &b, const value_type &c, const value_type &d,
+		const time_type &r=0.0, const time_type &s=1.0):
+		a(a),b(b),c(c),d(d),r(r),s(s) { sync(); }
+		
+	void sync()
+	{
+	}
+
+	value_type
+	operator()(time_type t)const
+	{
+		t=(t-r)/(s-r);
+		return
+		affine_func(
+			affine_func(
+				affine_func(a,b,t),
+				affine_func(b,c,t)
+			,t),
+			affine_func(
+				affine_func(b,c,t),
+				affine_func(c,d,t)
+			,t)
+		,t);
+	}
+	
+	/*
+	void evaluate(time_type t, value_type &f, value_type &df) const
+	{
+		t=(t-r)/(s-r);
+		
+		value_type p1 = affine_func(
+							affine_func(a,b,t),
+							affine_func(b,c,t)
+							,t);
+		value_type p2 = affine_func(
+							affine_func(b,c,t),
+							affine_func(c,d,t)
+						,t);
+		
+		f = affine_func(p1,p2,t);
+		df = (p2-p1)*3;
+	}
+	*/
+	
+	void set_rs(time_type new_r, time_type new_s) { r=new_r; s=new_s; }
+	void set_r(time_type new_r) { r=new_r; }
+	void set_s(time_type new_s) { s=new_s; }
+	const time_type &get_r()const { return r; }
+	const time_type &get_s()const { return s; }
+	time_type get_dt()const { return s-r; }
+
+	bool intersect_hull(const bezier_base<value_type,time_type> &x)const
+	{
+		return 0;
+	}
+
+	//! Bezier curve intersection function
+	/*! Calculates the time of intersection
+	**	for the calling curve.
+	**
+	**	I still have not figured out a good generic
+	**	method of doing this for a bi-infinite
+	**	cubic bezier curve calculated with the DeCasteljau
+	**	algorithm.
+	**
+	**	One method, although it does not work for the
+	**	entire bi-infinite curve, is to iteratively
+	**	intersect the hulls. However, we would only detect
+	**	intersections that occur between R and S.
+	**	
+	**	It is entirely possible that a new construct similar
+	**	to the affine combination function will be necessary
+	**	for this to work properly.
+	**
+	**	For now, this function is BROKEN. (although it works
+	**	for the floating-point specializations, using newton's method)
+	*/
+	time_type intersect(const bezier_base<value_type,time_type> &x, time_type near=0.0)const
+	{
+		return 0;
+	}
+	
+	/* subdivide at some time t into 2 separate curves left and right
+	
+		b0 l1
+		*		0+1 l2
+		b1 		*		1+2*1+2 l3
+		*		1+2		*			0+3*1+3*2+3 l4,r1
+		b2 		*		1+2*2+2	r2	*
+		*		2+3	r3	*
+		b3 r4	*
+		*		
+		
+		0.1 2.3 ->	0.1 2 3 4 5.6
+	*/
+/*	void subdivide(bezier_base *left, bezier_base *right, const time_type &time = (time_type)0.5) const
+	{
+		time_type t = (time-r)/(s-r);
+		bezier_base lt,rt;
+		
+		value_type temp;
+
+		//1st stage points to keep		
+		lt.a = a;
+		rt.d = d;
+
+		//2nd stage calc
+		lt.b = affine_func(a,b,t);
+		temp = affine_func(b,c,t);
+		rt.c = affine_func(c,d,t);
+				
+		//3rd stage calc
+		lt.c = affine_func(lt.b,temp,t);
+		rt.b = affine_func(temp,rt.c,t);
+		
+		//last stage calc
+		lt.d = rt.a = affine_func(lt.c,rt.b,t);
+		
+		//set the time range for l,r (the inside values should be 1, 0 respectively)
+		lt.r = r;
+		rt.s = s;
+		
+		//give back the curves
+		if(left) *left = lt;
+		if(right) *right = rt; 
+	}
+	*/	
+	value_type &
+	operator[](int i)
+	{ return (&a)[i]; }
+
+	const value_type &
+	operator[](int i) const
+	{ return (&a)[i]; }
+};
+
+
+#if 1
+// Fast float implementation of a cubic bezier curve
+template <>
+class bezier_base<float,float> : public std::unary_function<float,float>
+{
+public:
+	typedef float value_type;
+	typedef float time_type;
+private:
+	affine_combo<value_type,time_type> affine_func; 
+	value_type a,b,c,d;
+	time_type r,s;
+
+	value_type _coeff[4];
+	time_type drs; // reciprocal of (s-r)
+public:
+	bezier_base():r(0.0),s(1.0),drs(1.0) { }
+	bezier_base(
+		const value_type &a, const value_type &b, const value_type &c, const value_type &d,
+		const time_type &r=0.0, const time_type &s=1.0):
+		a(a),b(b),c(c),d(d),r(r),s(s),drs(1.0/(s-r)) { sync(); }
+
+	void sync()
+	{
+//		drs=1.0/(s-r);
+		_coeff[0]=                 a;
+		_coeff[1]=           b*3 - a*3;
+		_coeff[2]=     c*3 - b*6 + a*3;
+		_coeff[3]= d - c*3 + b*3 - a;
+	}
+	
+	// Cost Summary: 4 products, 3 sums, and 1 difference.
+	inline value_type
+	operator()(time_type t)const
+	{ t-=r; t*=drs; return _coeff[0]+(_coeff[1]+(_coeff[2]+(_coeff[3])*t)*t)*t; }
+
+	void set_rs(time_type new_r, time_type new_s) { r=new_r; s=new_s; drs=1.0/(s-r); }
+	void set_r(time_type new_r) { r=new_r; drs=1.0/(s-r); }
+	void set_s(time_type new_s) { s=new_s; drs=1.0/(s-r); }
+	const time_type &get_r()const { return r; }
+	const time_type &get_s()const { return s; }
+	time_type get_dt()const { return s-r; }
+
+	//! Bezier curve intersection function
+	/*! Calculates the time of intersection
+	**	for the calling curve.
+	*/
+	time_type intersect(const bezier_base<value_type,time_type> &x, time_type t=0.0,int i=15)const
+	{
+		//BROKEN - the time values of the 2 curves should be independent
+		value_type system[4];
+		system[0]=_coeff[0]-x._coeff[0];
+		system[1]=_coeff[1]-x._coeff[1];
+		system[2]=_coeff[2]-x._coeff[2];
+		system[3]=_coeff[3]-x._coeff[3];
+
+		t-=r;
+		t*=drs;
+
+		// Newton's method
+		// Inner loop cost summary: 7 products, 5 sums, 1 difference
+		for(;i;i--)
+			t-= (system[0]+(system[1]+(system[2]+(system[3])*t)*t)*t)/
+				(system[1]+(system[2]*2+(system[3]*3)*t)*t);
+
+		t*=(s-r);
+		t+=r;
+
+		return t;
+	}
+
+	value_type &
+	operator[](int i)
+	{ return (&a)[i]; }
+
+	const value_type &
+	operator[](int i) const
+	{ return (&a)[i]; }
+};
+
+
+// Fast double implementation of a cubic bezier curve
+template <>
+class bezier_base<double,float> : public std::unary_function<float,double>
+{
+public:
+	typedef double value_type;
+	typedef float time_type;
+private:
+	affine_combo<value_type,time_type> affine_func;
+	value_type a,b,c,d;
+	time_type r,s;
+
+	value_type _coeff[4];
+	time_type drs; // reciprocal of (s-r)
+public:
+	bezier_base():r(0.0),s(1.0),drs(1.0) { }
+	bezier_base(
+		const value_type &a, const value_type &b, const value_type &c, const value_type &d,
+		const time_type &r=0.0, const time_type &s=1.0):
+		a(a),b(b),c(c),d(d),r(r),s(s),drs(1.0/(s-r)) { sync(); }
+
+	void sync()
+	{
+//		drs=1.0/(s-r);
+		_coeff[0]=                 a;
+		_coeff[1]=           b*3 - a*3;
+		_coeff[2]=     c*3 - b*6 + a*3;
+		_coeff[3]= d - c*3 + b*3 - a;
+	}
+
+	// 4 products, 3 sums, and 1 difference.
+	inline value_type
+	operator()(time_type t)const
+	{ t-=r; t*=drs; return _coeff[0]+(_coeff[1]+(_coeff[2]+(_coeff[3])*t)*t)*t; }
+
+	void set_rs(time_type new_r, time_type new_s) { r=new_r; s=new_s; drs=1.0/(s-r); }
+	void set_r(time_type new_r) { r=new_r; drs=1.0/(s-r); }
+	void set_s(time_type new_s) { s=new_s; drs=1.0/(s-r); }
+	const time_type &get_r()const { return r; }
+	const time_type &get_s()const { return s; }
+	time_type get_dt()const { return s-r; }
+
+	//! Bezier curve intersection function
+	/*! Calculates the time of intersection
+	**	for the calling curve.
+	*/
+	time_type intersect(const bezier_base<value_type,time_type> &x, time_type t=0.0,int i=15)const
+	{
+		//BROKEN - the time values of the 2 curves should be independent
+		value_type system[4];
+		system[0]=_coeff[0]-x._coeff[0];
+		system[1]=_coeff[1]-x._coeff[1];
+		system[2]=_coeff[2]-x._coeff[2];
+		system[3]=_coeff[3]-x._coeff[3];
+
+		t-=r;
+		t*=drs;
+
+		// Newton's method
+		// Inner loop: 7 products, 5 sums, 1 difference
+		for(;i;i--)
+			t-= (system[0]+(system[1]+(system[2]+(system[3])*t)*t)*t)/
+				(system[1]+(system[2]*2+(system[3]*3)*t)*t);
+
+		t*=(s-r);
+		t+=r;
+
+		return t;
+	}
+
+	value_type &
+	operator[](int i)
+	{ return (&a)[i]; }
+
+	const value_type &
+	operator[](int i) const
+	{ return (&a)[i]; }
+};
+
+//#ifdef __FIXED__
+
+// Fast double implementation of a cubic bezier curve
+/*
+template <>
+template <class T,unsigned int FIXED_BITS>
+class bezier_base<fixed_base<T,FIXED_BITS> > : std::unary_function<fixed_base<T,FIXED_BITS>,fixed_base<T,FIXED_BITS> >
+{
+public:
+	typedef fixed_base<T,FIXED_BITS> value_type;
+	typedef fixed_base<T,FIXED_BITS> time_type;
+
+private:
+	affine_combo<value_type,time_type> affine_func;
+	value_type a,b,c,d;
+	time_type r,s;
+
+	value_type _coeff[4];
+	time_type drs; // reciprocal of (s-r)
+public:
+	bezier_base():r(0.0),s(1.0),drs(1.0) { }
+	bezier_base(
+		const value_type &a, const value_type &b, const value_type &c, const value_type &d,
+		const time_type &r=0, const time_type &s=1):
+		a(a),b(b),c(c),d(d),r(r),s(s),drs(1.0/(s-r)) { sync(); }
+
+	void sync()
+	{
+		drs=time_type(1)/(s-r);
+		_coeff[0]=                 a;
+		_coeff[1]=           b*3 - a*3;
+		_coeff[2]=     c*3 - b*6 + a*3;
+		_coeff[3]= d - c*3 + b*3 - a;
+	}
+
+	// 4 products, 3 sums, and 1 difference.
+	inline value_type
+	operator()(time_type t)const
+	{ t-=r; t*=drs; return _coeff[0]+(_coeff[1]+(_coeff[2]+(_coeff[3])*t)*t)*t; }
+
+	void set_rs(time_type new_r, time_type new_s) { r=new_r; s=new_s; drs=time_type(1)/(s-r); }
+	void set_r(time_type new_r) { r=new_r; drs=time_type(1)/(s-r); }
+	void set_s(time_type new_s) { s=new_s; drs=time_type(1)/(s-r); }
+	const time_type &get_r()const { return r; }
+	const time_type &get_s()const { return s; }
+	time_type get_dt()const { return s-r; }
+
+	//! Bezier curve intersection function
+	//! Calculates the time of intersection
+	//	for the calling curve.
+	//
+	time_type intersect(const bezier_base<value_type,time_type> &x, time_type t=0,int i=15)const
+	{
+		value_type system[4];
+		system[0]=_coeff[0]-x._coeff[0];
+		system[1]=_coeff[1]-x._coeff[1];
+		system[2]=_coeff[2]-x._coeff[2];
+		system[3]=_coeff[3]-x._coeff[3];
+
+		t-=r;
+		t*=drs;
+
+		// Newton's method
+		// Inner loop: 7 products, 5 sums, 1 difference
+		for(;i;i--)
+			t-=(time_type) ( (system[0]+(system[1]+(system[2]+(system[3])*t)*t)*t)/
+				(system[1]+(system[2]*2+(system[3]*3)*t)*t) );
+
+		t*=(s-r);
+		t+=r;
+
+		return t;
+	}
+
+	value_type &
+	operator[](int i)
+	{ return (&a)[i]; }
+
+	const value_type &
+	operator[](int i) const
+	{ return (&a)[i]; }
+};
+*/
+//#endif
+
+#endif
+
+
+
+template <typename V, typename T>
+class bezier_iterator
+{
+public:
+
+	struct iterator_category {};
+	typedef V value_type;
+	typedef T difference_type;
+	typedef V reference;
+	
+private:
+	difference_type t;
+	difference_type dt;
+	bezier_base<V,T>	curve;
+
+public:
+
+/*
+	reference
+	operator*(void)const { return curve(t); }
+	const surface_iterator&
+
+	operator++(void)
+	{ t+=dt; return &this; }
+
+	const surface_iterator&
+	operator++(int)
+	{ hermite_iterator _tmp=*this; t+=dt; return _tmp; }
+
+	const surface_iterator&
+	operator--(void)
+	{ t-=dt; return &this; }
+
+	const surface_iterator&
+	operator--(int)
+	{ hermite_iterator _tmp=*this; t-=dt; return _tmp; }
+
+	
+	surface_iterator
+	operator+(difference_type __n) const
+	{ return surface_iterator(data+__n[0]+__n[1]*pitch,pitch); }
+
+	surface_iterator
+	operator-(difference_type __n) const
+	{ return surface_iterator(data-__n[0]-__n[1]*pitch,pitch); }
+*/
+	
+};
+
+template <typename V,typename T=float>
+class bezier : public bezier_base<V,T>
+{
+public:
+	typedef V value_type;
+	typedef T time_type;
+	typedef float distance_type;
+	typedef bezier_iterator<V,T> iterator;
+	typedef bezier_iterator<V,T> const_iterator;
+	
+	distance_func<value_type> dist;
+	
+	using bezier_base<V,T>::get_r;
+	using bezier_base<V,T>::get_s;
+	using bezier_base<V,T>::get_dt;
+
+public:	
+	bezier() { }
+	bezier(const value_type &a, const value_type &b, const value_type &c, const value_type &d):
+		bezier_base<V,T>(a,b,c,d) { }
+
+
+	const_iterator begin()const;
+	const_iterator end()const;
+	
+	time_type find_closest(const value_type& x, int i=7, time_type r=(0), time_type s=(1))const
+	{
+		float t((r+s)*0.5);
+		for(;i;i--)
+		{						
+			if(dist(operator()((s-r)*(1.0/3.0)+r),x) < dist(operator()((s-r)*(2.0/3.0)+r),x))
+				s=t;
+			else
+				r=t;
+			t=((r+s)*0.5);
+		}
+		return t;
+	}
+
+	
+	distance_type find_distance(time_type r, time_type s, int steps=7)const
+	{
+		const time_type inc((s-r)/steps);
+		distance_type ret(0);
+		value_type last(operator()(r));
+		
+		for(r+=inc;r<s;r+=inc)
+		{
+			const value_type n(operator()(r));
+			ret+=dist.uncook(dist(last,n));
+			last=n;
+		}
+		ret+=dist.uncook(dist(last,operator()(r)))*(s-(r-inc))/inc;
+		
+		return ret;
+	}
+	
+	distance_type length()const { return find_distance(get_r(),get_s()); }
+	
+	/* subdivide at some time t into 2 separate curves left and right
+	
+		b0 l1
+		*		0+1 l2
+		b1 		*		1+2*1+2 l3
+		*		1+2		*			0+3*1+3*2+3 l4,r1
+		b2 		*		1+2*2+2	r2	*
+		*		2+3	r3	*
+		b3 r4	*
+		*		
+		
+		0.1 2.3 ->	0.1 2 3 4 5.6
+	*/
+	void subdivide(bezier *left, bezier *right, const time_type &time = (time_type)0.5) const
+	{
+		time_type t=(t-get_r())/get_dt();
+		bezier lt,rt;
+		
+		value_type temp;
+		const value_type& a((*this)[0]);
+		const value_type& b((*this)[1]);
+		const value_type& c((*this)[2]);
+		const value_type& d((*this)[3]);
+
+		//1st stage points to keep		
+		lt[0] = a;
+		rt[3] = d;
+
+		//2nd stage calc
+		lt[1] = affine_func(a,b,t);
+		temp = affine_func(b,c,t);
+		rt[2] = affine_func(c,d,t);
+				
+		//3rd stage calc
+		lt[2] = affine_func(lt[1],temp,t);
+		rt[1] = affine_func(temp,rt[2],t);
+		
+		//last stage calc
+		lt[3] = rt[0] = affine_func(lt[2],rt[1],t);
+		
+		//set the time range for l,r (the inside values should be 1, 0 respectively)
+		lt.set_r(get_r());
+		rt.set_s(get_s());
+		
+		lt.sync();
+		rt.sync();
+		
+		//give back the curves
+		if(left) *left = lt;
+		if(right) *right = rt; 
+	}
+
+	
+	void evaluate(time_type t, value_type &f, value_type &df) const
+	{
+		t=(t-get_r())/get_dt();
+
+		const value_type& a((*this)[0]);
+		const value_type& b((*this)[1]);
+		const value_type& c((*this)[2]);
+		const value_type& d((*this)[3]);
+		
+		const value_type p1 = affine_func(
+							affine_func(a,b,t),
+							affine_func(b,c,t)
+							,t);
+		const value_type p2 = affine_func(
+							affine_func(b,c,t),
+							affine_func(c,d,t)
+						,t);
+		
+		f = affine_func(p1,p2,t);
+		df = (p2-p1)*3;
+	}
+};
+
+_ETL_END_NAMESPACE
+
+/* === E X T E R N S ======================================================= */
+
+/* === E N D =============================================================== */
+
+#endif