1 /* -*- C++ -*- |
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2 * src/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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