1 | /* -*- C++ -*- |
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2 | * lemon/bezier.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_BEZIER_H |
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18 | #define LEMON_BEZIER_H |
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19 | |
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20 | ///\ingroup misc |
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21 | ///\file |
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22 | ///\brief Classes to compute with Bezier curves. |
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23 | /// |
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24 | ///Up to now this file is used internally by \ref graph_to_eps.h |
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25 | /// |
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26 | ///\author Alpar Juttner |
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27 | |
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28 | #include<lemon/xy.h> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | class BezierBase { |
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33 | public: |
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34 | typedef xy<double> xy; |
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35 | protected: |
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36 | static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;} |
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37 | }; |
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38 | |
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39 | class Bezier1 : public BezierBase |
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40 | { |
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41 | public: |
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42 | xy p1,p2; |
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43 | |
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44 | Bezier1() {} |
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45 | Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {} |
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46 | |
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47 | xy operator()(double t) const |
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48 | { |
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49 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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50 | return conv(p1,p2,t); |
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51 | } |
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52 | Bezier1 before(double t) const |
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53 | { |
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54 | return Bezier1(p1,conv(p1,p2,t)); |
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55 | } |
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56 | |
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57 | Bezier1 after(double t) const |
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58 | { |
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59 | return Bezier1(conv(p1,p2,t),p2); |
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60 | } |
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61 | Bezier1 revert() { return Bezier1(p2,p1);} |
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62 | Bezier1 operator()(double a,double b) { return before(b).after(a/b); } |
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63 | xy grad() { return p2-p1; } |
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64 | xy grad(double t) { return grad(); } |
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65 | |
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66 | }; |
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67 | |
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68 | class Bezier2 : public BezierBase |
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69 | { |
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70 | public: |
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71 | xy p1,p2,p3; |
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72 | |
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73 | Bezier2() {} |
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74 | Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {} |
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75 | Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} |
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76 | xy operator()(double t) const |
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77 | { |
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78 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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79 | return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; |
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80 | } |
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81 | Bezier2 before(double t) const |
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82 | { |
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83 | xy q(conv(p1,p2,t)); |
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84 | xy r(conv(p2,p3,t)); |
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85 | return Bezier2(p1,q,conv(q,r,t)); |
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86 | } |
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87 | |
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88 | Bezier2 after(double t) const |
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89 | { |
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90 | xy q(conv(p1,p2,t)); |
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91 | xy r(conv(p2,p3,t)); |
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92 | return Bezier2(conv(q,r,t),r,p3); |
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93 | } |
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94 | Bezier2 revert() { return Bezier2(p3,p2,p1);} |
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95 | Bezier2 operator()(double a,double b) { return before(b).after(a/b); } |
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96 | Bezier1 grad() { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } |
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97 | xy grad(double t) { return grad()(t); } |
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98 | }; |
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99 | |
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100 | class Bezier3 : public BezierBase |
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101 | { |
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102 | public: |
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103 | xy p1,p2,p3,p4; |
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104 | |
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105 | Bezier3() {} |
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106 | Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
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107 | Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
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108 | p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
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109 | Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
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110 | p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
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111 | |
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112 | xy operator()(double t) const |
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113 | { |
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114 | // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
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115 | return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
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116 | (3*t*t*(1-t))*p3+(t*t*t)*p4; |
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117 | } |
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118 | Bezier3 before(double t) const |
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119 | { |
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120 | xy p(conv(p1,p2,t)); |
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121 | xy q(conv(p2,p3,t)); |
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122 | xy r(conv(p3,p4,t)); |
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123 | xy a(conv(p,q,t)); |
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124 | xy b(conv(q,r,t)); |
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125 | xy c(conv(a,b,t)); |
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126 | return Bezier3(p1,p,a,c); |
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127 | } |
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128 | |
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129 | Bezier3 after(double t) const |
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130 | { |
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131 | xy p(conv(p1,p2,t)); |
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132 | xy q(conv(p2,p3,t)); |
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133 | xy r(conv(p3,p4,t)); |
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134 | xy a(conv(p,q,t)); |
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135 | xy b(conv(q,r,t)); |
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136 | xy c(conv(a,b,t)); |
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137 | return Bezier3(c,b,r,p4); |
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138 | } |
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139 | Bezier3 revert() { return Bezier3(p4,p3,p2,p1);} |
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140 | Bezier3 operator()(double a,double b) { return before(b).after(a/b); } |
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141 | Bezier2 grad() { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
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142 | xy grad(double t) { return grad()(t); } |
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143 | }; |
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144 | |
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145 | } //END OF NAMESPACE LEMON |
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146 | |
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147 | #endif // LEMON_BEZIER_H |
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