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1 /* -*- C++ -*- |
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2 * |
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3 * This file is a part of LEMON, a generic C++ optimization library |
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4 * |
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5 * Copyright (C) 2003-2008 |
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6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 * |
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9 * Permission to use, modify and distribute this software is granted |
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10 * provided that this copyright notice appears in all copies. For |
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11 * precise terms see the accompanying LICENSE file. |
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12 * |
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13 * This software is provided "AS IS" with no warranty of any kind, |
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14 * express or implied, and with no claim as to its suitability for any |
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15 * purpose. |
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16 * |
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17 */ |
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18 |
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19 #ifndef LEMON_BEZIER_H |
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20 #define LEMON_BEZIER_H |
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21 |
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22 ///\ingroup misc |
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23 ///\file |
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24 ///\brief Classes to compute with Bezier curves. |
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25 /// |
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26 ///Up to now this file is used internally by \ref graph_to_eps.h |
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27 /// |
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28 ///\author Alpar Juttner |
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29 |
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30 #include<lemon/dim2.h> |
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31 |
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32 namespace lemon { |
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33 namespace dim2 { |
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34 |
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35 class BezierBase { |
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36 public: |
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37 typedef Point<double> Point; |
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38 protected: |
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39 static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;} |
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40 }; |
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41 |
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42 class Bezier1 : public BezierBase |
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43 { |
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44 public: |
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45 Point p1,p2; |
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46 |
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47 Bezier1() {} |
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48 Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} |
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49 |
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50 Point operator()(double t) const |
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51 { |
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52 // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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53 return conv(p1,p2,t); |
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54 } |
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55 Bezier1 before(double t) const |
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56 { |
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57 return Bezier1(p1,conv(p1,p2,t)); |
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58 } |
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59 |
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60 Bezier1 after(double t) const |
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61 { |
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62 return Bezier1(conv(p1,p2,t),p2); |
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63 } |
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64 |
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65 Bezier1 revert() const { return Bezier1(p2,p1);} |
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66 Bezier1 operator()(double a,double b) const { return before(b).after(a/b); } |
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67 Point grad() const { return p2-p1; } |
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68 Point norm() const { return rot90(p2-p1); } |
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69 Point grad(double) const { return grad(); } |
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70 Point norm(double t) const { return rot90(grad(t)); } |
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71 }; |
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72 |
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73 class Bezier2 : public BezierBase |
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74 { |
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75 public: |
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76 Point p1,p2,p3; |
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77 |
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78 Bezier2() {} |
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79 Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {} |
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80 Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} |
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81 Point operator()(double t) const |
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82 { |
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83 // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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84 return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; |
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85 } |
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86 Bezier2 before(double t) const |
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87 { |
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88 Point q(conv(p1,p2,t)); |
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89 Point r(conv(p2,p3,t)); |
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90 return Bezier2(p1,q,conv(q,r,t)); |
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91 } |
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92 |
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93 Bezier2 after(double t) const |
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94 { |
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95 Point q(conv(p1,p2,t)); |
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96 Point r(conv(p2,p3,t)); |
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97 return Bezier2(conv(q,r,t),r,p3); |
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98 } |
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99 Bezier2 revert() const { return Bezier2(p3,p2,p1);} |
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100 Bezier2 operator()(double a,double b) const { return before(b).after(a/b); } |
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101 Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } |
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102 Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); } |
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103 Point grad(double t) const { return grad()(t); } |
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104 Point norm(double t) const { return rot90(grad(t)); } |
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105 }; |
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106 |
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107 class Bezier3 : public BezierBase |
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108 { |
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109 public: |
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110 Point p1,p2,p3,p4; |
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111 |
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112 Bezier3() {} |
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113 Bezier3(Point _p1, Point _p2, Point _p3, Point _p4) |
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114 : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
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115 Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
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116 p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
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117 Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
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118 p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
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119 |
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120 Point operator()(double t) const |
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121 { |
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122 // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
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123 return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
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124 (3*t*t*(1-t))*p3+(t*t*t)*p4; |
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125 } |
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126 Bezier3 before(double t) const |
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127 { |
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128 Point p(conv(p1,p2,t)); |
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129 Point q(conv(p2,p3,t)); |
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130 Point r(conv(p3,p4,t)); |
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131 Point a(conv(p,q,t)); |
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132 Point b(conv(q,r,t)); |
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133 Point c(conv(a,b,t)); |
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134 return Bezier3(p1,p,a,c); |
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135 } |
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136 |
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137 Bezier3 after(double t) const |
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138 { |
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139 Point p(conv(p1,p2,t)); |
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140 Point q(conv(p2,p3,t)); |
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141 Point r(conv(p3,p4,t)); |
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142 Point a(conv(p,q,t)); |
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143 Point b(conv(q,r,t)); |
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144 Point c(conv(a,b,t)); |
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145 return Bezier3(c,b,r,p4); |
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146 } |
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147 Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} |
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148 Bezier3 operator()(double a,double b) const { return before(b).after(a/b); } |
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149 Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
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150 Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), |
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151 3.0*rot90(p3-p2), |
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152 3.0*rot90(p4-p3)); } |
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153 Point grad(double t) const { return grad()(t); } |
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154 Point norm(double t) const { return rot90(grad(t)); } |
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155 |
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156 template<class R,class F,class S,class D> |
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157 R recSplit(F &_f,const S &_s,D _d) const |
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158 { |
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159 const Point a=(p1+p2)/2; |
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160 const Point b=(p2+p3)/2; |
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161 const Point c=(p3+p4)/2; |
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162 const Point d=(a+b)/2; |
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163 const Point e=(b+c)/2; |
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164 const Point f=(d+e)/2; |
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165 R f1=_f(Bezier3(p1,a,d,e),_d); |
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166 R f2=_f(Bezier3(e,d,c,p4),_d); |
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167 return _s(f1,f2); |
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168 } |
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169 |
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170 }; |
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171 |
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172 |
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173 } //END OF NAMESPACE dim2 |
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174 } //END OF NAMESPACE lemon |
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175 |
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176 #endif // LEMON_BEZIER_H |