1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_BEZIER_H |
---|
20 | #define LEMON_BEZIER_H |
---|
21 | |
---|
22 | //\ingroup misc |
---|
23 | //\file |
---|
24 | //\brief Classes to compute with Bezier curves. |
---|
25 | // |
---|
26 | //Up to now this file is used internally by \ref graph_to_eps.h |
---|
27 | |
---|
28 | #include<lemon/dim2.h> |
---|
29 | |
---|
30 | namespace lemon { |
---|
31 | namespace dim2 { |
---|
32 | |
---|
33 | class BezierBase { |
---|
34 | public: |
---|
35 | typedef lemon::dim2::Point<double> Point; |
---|
36 | protected: |
---|
37 | static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;} |
---|
38 | }; |
---|
39 | |
---|
40 | class Bezier1 : public BezierBase |
---|
41 | { |
---|
42 | public: |
---|
43 | Point p1,p2; |
---|
44 | |
---|
45 | Bezier1() {} |
---|
46 | Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} |
---|
47 | |
---|
48 | Point operator()(double t) const |
---|
49 | { |
---|
50 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
---|
51 | return conv(p1,p2,t); |
---|
52 | } |
---|
53 | Bezier1 before(double t) const |
---|
54 | { |
---|
55 | return Bezier1(p1,conv(p1,p2,t)); |
---|
56 | } |
---|
57 | |
---|
58 | Bezier1 after(double t) const |
---|
59 | { |
---|
60 | return Bezier1(conv(p1,p2,t),p2); |
---|
61 | } |
---|
62 | |
---|
63 | Bezier1 revert() const { return Bezier1(p2,p1);} |
---|
64 | Bezier1 operator()(double a,double b) const { return before(b).after(a/b); } |
---|
65 | Point grad() const { return p2-p1; } |
---|
66 | Point norm() const { return rot90(p2-p1); } |
---|
67 | Point grad(double) const { return grad(); } |
---|
68 | Point norm(double t) const { return rot90(grad(t)); } |
---|
69 | }; |
---|
70 | |
---|
71 | class Bezier2 : public BezierBase |
---|
72 | { |
---|
73 | public: |
---|
74 | Point p1,p2,p3; |
---|
75 | |
---|
76 | Bezier2() {} |
---|
77 | Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {} |
---|
78 | Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} |
---|
79 | Point operator()(double t) const |
---|
80 | { |
---|
81 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
---|
82 | return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; |
---|
83 | } |
---|
84 | Bezier2 before(double t) const |
---|
85 | { |
---|
86 | Point q(conv(p1,p2,t)); |
---|
87 | Point r(conv(p2,p3,t)); |
---|
88 | return Bezier2(p1,q,conv(q,r,t)); |
---|
89 | } |
---|
90 | |
---|
91 | Bezier2 after(double t) const |
---|
92 | { |
---|
93 | Point q(conv(p1,p2,t)); |
---|
94 | Point r(conv(p2,p3,t)); |
---|
95 | return Bezier2(conv(q,r,t),r,p3); |
---|
96 | } |
---|
97 | Bezier2 revert() const { return Bezier2(p3,p2,p1);} |
---|
98 | Bezier2 operator()(double a,double b) const { return before(b).after(a/b); } |
---|
99 | Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } |
---|
100 | Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); } |
---|
101 | Point grad(double t) const { return grad()(t); } |
---|
102 | Point norm(double t) const { return rot90(grad(t)); } |
---|
103 | }; |
---|
104 | |
---|
105 | class Bezier3 : public BezierBase |
---|
106 | { |
---|
107 | public: |
---|
108 | Point p1,p2,p3,p4; |
---|
109 | |
---|
110 | Bezier3() {} |
---|
111 | Bezier3(Point _p1, Point _p2, Point _p3, Point _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)), |
---|
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)), |
---|
116 | p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
---|
117 | |
---|
118 | Point operator()(double t) const |
---|
119 | { |
---|
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+ |
---|
122 | (3*t*t*(1-t))*p3+(t*t*t)*p4; |
---|
123 | } |
---|
124 | Bezier3 before(double t) const |
---|
125 | { |
---|
126 | Point p(conv(p1,p2,t)); |
---|
127 | Point q(conv(p2,p3,t)); |
---|
128 | Point r(conv(p3,p4,t)); |
---|
129 | Point a(conv(p,q,t)); |
---|
130 | Point b(conv(q,r,t)); |
---|
131 | Point c(conv(a,b,t)); |
---|
132 | return Bezier3(p1,p,a,c); |
---|
133 | } |
---|
134 | |
---|
135 | Bezier3 after(double t) const |
---|
136 | { |
---|
137 | Point p(conv(p1,p2,t)); |
---|
138 | Point q(conv(p2,p3,t)); |
---|
139 | Point r(conv(p3,p4,t)); |
---|
140 | Point a(conv(p,q,t)); |
---|
141 | Point b(conv(q,r,t)); |
---|
142 | Point c(conv(a,b,t)); |
---|
143 | return Bezier3(c,b,r,p4); |
---|
144 | } |
---|
145 | Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} |
---|
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)); } |
---|
148 | Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), |
---|
149 | 3.0*rot90(p3-p2), |
---|
150 | 3.0*rot90(p4-p3)); } |
---|
151 | Point grad(double t) const { return grad()(t); } |
---|
152 | Point norm(double t) const { return rot90(grad(t)); } |
---|
153 | |
---|
154 | template<class R,class F,class S,class D> |
---|
155 | R recSplit(F &_f,const S &_s,D _d) const |
---|
156 | { |
---|
157 | const Point a=(p1+p2)/2; |
---|
158 | const Point b=(p2+p3)/2; |
---|
159 | const Point c=(p3+p4)/2; |
---|
160 | const Point d=(a+b)/2; |
---|
161 | const Point e=(b+c)/2; |
---|
162 | const Point f=(d+e)/2; |
---|
163 | R f1=_f(Bezier3(p1,a,d,e),_d); |
---|
164 | R f2=_f(Bezier3(e,d,c,p4),_d); |
---|
165 | return _s(f1,f2); |
---|
166 | } |
---|
167 | |
---|
168 | }; |
---|
169 | |
---|
170 | |
---|
171 | } //END OF NAMESPACE dim2 |
---|
172 | } //END OF NAMESPACE lemon |
---|
173 | |
---|
174 | #endif // LEMON_BEZIER_H |
---|