1 /* -*- C++ -*- |
1 /* -*- mode: C++; indent-tabs-mode: nil; -*- |
2 * |
2 * |
3 * This file is a part of LEMON, a generic C++ optimization library |
3 * This file is a part of LEMON, a generic C++ optimization library. |
4 * |
4 * |
5 * Copyright (C) 2003-2008 |
5 * Copyright (C) 2003-2008 |
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
7 * (Egervary Research Group on Combinatorial Optimization, EGRES). |
7 * (Egervary Research Group on Combinatorial Optimization, EGRES). |
8 * |
8 * |
42 public: |
42 public: |
43 Point p1,p2; |
43 Point p1,p2; |
44 |
44 |
45 Bezier1() {} |
45 Bezier1() {} |
46 Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} |
46 Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} |
47 |
47 |
48 Point operator()(double t) const |
48 Point operator()(double t) const |
49 { |
49 { |
50 // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
50 // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
51 return conv(p1,p2,t); |
51 return conv(p1,p2,t); |
52 } |
52 } |
53 Bezier1 before(double t) const |
53 Bezier1 before(double t) const |
54 { |
54 { |
55 return Bezier1(p1,conv(p1,p2,t)); |
55 return Bezier1(p1,conv(p1,p2,t)); |
56 } |
56 } |
57 |
57 |
58 Bezier1 after(double t) const |
58 Bezier1 after(double t) const |
59 { |
59 { |
60 return Bezier1(conv(p1,p2,t),p2); |
60 return Bezier1(conv(p1,p2,t),p2); |
61 } |
61 } |
62 |
62 |
85 { |
85 { |
86 Point q(conv(p1,p2,t)); |
86 Point q(conv(p1,p2,t)); |
87 Point r(conv(p2,p3,t)); |
87 Point r(conv(p2,p3,t)); |
88 return Bezier2(p1,q,conv(q,r,t)); |
88 return Bezier2(p1,q,conv(q,r,t)); |
89 } |
89 } |
90 |
90 |
91 Bezier2 after(double t) const |
91 Bezier2 after(double t) const |
92 { |
92 { |
93 Point q(conv(p1,p2,t)); |
93 Point q(conv(p1,p2,t)); |
94 Point r(conv(p2,p3,t)); |
94 Point r(conv(p2,p3,t)); |
95 return Bezier2(conv(q,r,t),r,p3); |
95 return Bezier2(conv(q,r,t),r,p3); |
108 Point p1,p2,p3,p4; |
108 Point p1,p2,p3,p4; |
109 |
109 |
110 Bezier3() {} |
110 Bezier3() {} |
111 Bezier3(Point _p1, Point _p2, Point _p3, Point _p4) |
111 Bezier3(Point _p1, Point _p2, Point _p3, Point _p4) |
112 : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
112 : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
113 Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
113 Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
114 p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
114 p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
115 Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
115 Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
116 p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
116 p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
117 |
117 |
118 Point operator()(double t) const |
118 Point operator()(double t) const |
119 { |
119 { |
120 // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
120 // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
121 return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
121 return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
122 (3*t*t*(1-t))*p3+(t*t*t)*p4; |
122 (3*t*t*(1-t))*p3+(t*t*t)*p4; |
123 } |
123 } |
124 Bezier3 before(double t) const |
124 Bezier3 before(double t) const |
125 { |
125 { |
126 Point p(conv(p1,p2,t)); |
126 Point p(conv(p1,p2,t)); |
127 Point q(conv(p2,p3,t)); |
127 Point q(conv(p2,p3,t)); |
129 Point a(conv(p,q,t)); |
129 Point a(conv(p,q,t)); |
130 Point b(conv(q,r,t)); |
130 Point b(conv(q,r,t)); |
131 Point c(conv(a,b,t)); |
131 Point c(conv(a,b,t)); |
132 return Bezier3(p1,p,a,c); |
132 return Bezier3(p1,p,a,c); |
133 } |
133 } |
134 |
134 |
135 Bezier3 after(double t) const |
135 Bezier3 after(double t) const |
136 { |
136 { |
137 Point p(conv(p1,p2,t)); |
137 Point p(conv(p1,p2,t)); |
138 Point q(conv(p2,p3,t)); |
138 Point q(conv(p2,p3,t)); |
139 Point r(conv(p3,p4,t)); |
139 Point r(conv(p3,p4,t)); |
144 } |
144 } |
145 Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} |
145 Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} |
146 Bezier3 operator()(double a,double b) const { return before(b).after(a/b); } |
146 Bezier3 operator()(double a,double b) const { return before(b).after(a/b); } |
147 Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
147 Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
148 Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), |
148 Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), |
149 3.0*rot90(p3-p2), |
149 3.0*rot90(p3-p2), |
150 3.0*rot90(p4-p3)); } |
150 3.0*rot90(p4-p3)); } |
151 Point grad(double t) const { return grad()(t); } |
151 Point grad(double t) const { return grad()(t); } |
152 Point norm(double t) const { return rot90(grad(t)); } |
152 Point norm(double t) const { return rot90(grad(t)); } |
153 |
153 |
154 template<class R,class F,class S,class D> |
154 template<class R,class F,class S,class D> |
155 R recSplit(F &_f,const S &_s,D _d) const |
155 R recSplit(F &_f,const S &_s,D _d) const |
156 { |
156 { |
157 const Point a=(p1+p2)/2; |
157 const Point a=(p1+p2)/2; |
158 const Point b=(p2+p3)/2; |
158 const Point b=(p2+p3)/2; |
159 const Point c=(p3+p4)/2; |
159 const Point c=(p3+p4)/2; |
160 const Point d=(a+b)/2; |
160 const Point d=(a+b)/2; |
162 const Point f=(d+e)/2; |
162 const Point f=(d+e)/2; |
163 R f1=_f(Bezier3(p1,a,d,e),_d); |
163 R f1=_f(Bezier3(p1,a,d,e),_d); |
164 R f2=_f(Bezier3(e,d,c,p4),_d); |
164 R f2=_f(Bezier3(e,d,c,p4),_d); |
165 return _s(f1,f2); |
165 return _s(f1,f2); |
166 } |
166 } |
167 |
167 |
168 }; |
168 }; |
169 |
169 |
170 |
170 |
171 } //END OF NAMESPACE dim2 |
171 } //END OF NAMESPACE dim2 |
172 } //END OF NAMESPACE lemon |
172 } //END OF NAMESPACE lemon |