1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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_DIM2_H |
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20 | #define LEMON_DIM2_H |
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21 | |
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22 | #include <iostream> |
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23 | |
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24 | ///\ingroup misc |
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25 | ///\file |
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26 | ///\brief A simple two dimensional vector and a bounding box implementation |
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27 | /// |
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28 | /// The class \ref lemon::dim2::Point "dim2::Point" implements |
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29 | /// a two dimensional vector with the usual operations. |
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30 | /// |
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31 | /// The class \ref lemon::dim2::Box "dim2::Box" can be used to determine |
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32 | /// the rectangular bounding box of a set of |
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33 | /// \ref lemon::dim2::Point "dim2::Point"'s. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | ///Tools for handling two dimensional coordinates |
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38 | |
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39 | ///This namespace is a storage of several |
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40 | ///tools for handling two dimensional coordinates |
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41 | namespace dim2 { |
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42 | |
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43 | /// \addtogroup misc |
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44 | /// @{ |
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45 | |
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46 | /// Two dimensional vector (plain vector) |
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47 | |
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48 | /// A simple two dimensional vector (plain vector) implementation |
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49 | /// with the usual vector operations. |
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50 | template<typename T> |
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51 | class Point { |
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52 | |
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53 | public: |
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54 | |
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55 | typedef T Value; |
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56 | |
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57 | ///First coordinate |
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58 | T x; |
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59 | ///Second coordinate |
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60 | T y; |
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61 | |
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62 | ///Default constructor |
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63 | Point() {} |
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64 | |
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65 | ///Construct an instance from coordinates |
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66 | Point(T a, T b) : x(a), y(b) { } |
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67 | |
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68 | ///Returns the dimension of the vector (i.e. returns 2). |
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69 | |
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70 | ///The dimension of the vector. |
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71 | ///This function always returns 2. |
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72 | int size() const { return 2; } |
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73 | |
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74 | ///Subscripting operator |
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75 | |
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76 | ///\c p[0] is \c p.x and \c p[1] is \c p.y |
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77 | /// |
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78 | T& operator[](int idx) { return idx == 0 ? x : y; } |
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79 | |
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80 | ///Const subscripting operator |
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81 | |
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82 | ///\c p[0] is \c p.x and \c p[1] is \c p.y |
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83 | /// |
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84 | const T& operator[](int idx) const { return idx == 0 ? x : y; } |
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85 | |
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86 | ///Conversion constructor |
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87 | template<class TT> Point(const Point<TT> &p) : x(p.x), y(p.y) {} |
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88 | |
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89 | ///Give back the square of the norm of the vector |
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90 | T normSquare() const { |
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91 | return x*x+y*y; |
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92 | } |
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93 | |
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94 | ///Increment the left hand side by \c u |
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95 | Point<T>& operator +=(const Point<T>& u) { |
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96 | x += u.x; |
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97 | y += u.y; |
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98 | return *this; |
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99 | } |
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100 | |
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101 | ///Decrement the left hand side by \c u |
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102 | Point<T>& operator -=(const Point<T>& u) { |
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103 | x -= u.x; |
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104 | y -= u.y; |
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105 | return *this; |
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106 | } |
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107 | |
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108 | ///Multiply the left hand side with a scalar |
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109 | Point<T>& operator *=(const T &u) { |
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110 | x *= u; |
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111 | y *= u; |
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112 | return *this; |
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113 | } |
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114 | |
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115 | ///Divide the left hand side by a scalar |
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116 | Point<T>& operator /=(const T &u) { |
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117 | x /= u; |
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118 | y /= u; |
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119 | return *this; |
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120 | } |
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121 | |
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122 | ///Return the scalar product of two vectors |
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123 | T operator *(const Point<T>& u) const { |
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124 | return x*u.x+y*u.y; |
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125 | } |
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126 | |
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127 | ///Return the sum of two vectors |
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128 | Point<T> operator+(const Point<T> &u) const { |
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129 | Point<T> b=*this; |
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130 | return b+=u; |
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131 | } |
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132 | |
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133 | ///Return the negative of the vector |
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134 | Point<T> operator-() const { |
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135 | Point<T> b=*this; |
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136 | b.x=-b.x; b.y=-b.y; |
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137 | return b; |
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138 | } |
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139 | |
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140 | ///Return the difference of two vectors |
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141 | Point<T> operator-(const Point<T> &u) const { |
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142 | Point<T> b=*this; |
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143 | return b-=u; |
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144 | } |
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145 | |
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146 | ///Return a vector multiplied by a scalar |
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147 | Point<T> operator*(const T &u) const { |
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148 | Point<T> b=*this; |
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149 | return b*=u; |
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150 | } |
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151 | |
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152 | ///Return a vector divided by a scalar |
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153 | Point<T> operator/(const T &u) const { |
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154 | Point<T> b=*this; |
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155 | return b/=u; |
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156 | } |
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157 | |
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158 | ///Test equality |
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159 | bool operator==(const Point<T> &u) const { |
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160 | return (x==u.x) && (y==u.y); |
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161 | } |
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162 | |
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163 | ///Test inequality |
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164 | bool operator!=(Point u) const { |
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165 | return (x!=u.x) || (y!=u.y); |
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166 | } |
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167 | |
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168 | }; |
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169 | |
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170 | ///Return a Point |
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171 | |
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172 | ///Return a Point. |
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173 | ///\relates Point |
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174 | template <typename T> |
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175 | inline Point<T> makePoint(const T& x, const T& y) { |
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176 | return Point<T>(x, y); |
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177 | } |
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178 | |
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179 | ///Return a vector multiplied by a scalar |
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180 | |
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181 | ///Return a vector multiplied by a scalar. |
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182 | ///\relates Point |
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183 | template<typename T> Point<T> operator*(const T &u,const Point<T> &x) { |
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184 | return x*u; |
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185 | } |
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186 | |
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187 | ///Read a plain vector from a stream |
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188 | |
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189 | ///Read a plain vector from a stream. |
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190 | ///\relates Point |
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191 | /// |
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192 | template<typename T> |
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193 | inline std::istream& operator>>(std::istream &is, Point<T> &z) { |
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194 | char c; |
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195 | if (is >> c) { |
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196 | if (c != '(') is.putback(c); |
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197 | } else { |
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198 | is.clear(); |
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199 | } |
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200 | if (!(is >> z.x)) return is; |
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201 | if (is >> c) { |
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202 | if (c != ',') is.putback(c); |
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203 | } else { |
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204 | is.clear(); |
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205 | } |
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206 | if (!(is >> z.y)) return is; |
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207 | if (is >> c) { |
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208 | if (c != ')') is.putback(c); |
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209 | } else { |
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210 | is.clear(); |
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211 | } |
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212 | return is; |
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213 | } |
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214 | |
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215 | ///Write a plain vector to a stream |
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216 | |
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217 | ///Write a plain vector to a stream. |
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218 | ///\relates Point |
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219 | /// |
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220 | template<typename T> |
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221 | inline std::ostream& operator<<(std::ostream &os, const Point<T>& z) |
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222 | { |
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223 | os << "(" << z.x << "," << z.y << ")"; |
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224 | return os; |
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225 | } |
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226 | |
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227 | ///Rotate by 90 degrees |
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228 | |
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229 | ///Returns the parameter rotated by 90 degrees in positive direction. |
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230 | ///\relates Point |
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231 | /// |
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232 | template<typename T> |
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233 | inline Point<T> rot90(const Point<T> &z) |
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234 | { |
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235 | return Point<T>(-z.y,z.x); |
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236 | } |
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237 | |
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238 | ///Rotate by 180 degrees |
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239 | |
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240 | ///Returns the parameter rotated by 180 degrees. |
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241 | ///\relates Point |
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242 | /// |
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243 | template<typename T> |
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244 | inline Point<T> rot180(const Point<T> &z) |
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245 | { |
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246 | return Point<T>(-z.x,-z.y); |
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247 | } |
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248 | |
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249 | ///Rotate by 270 degrees |
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250 | |
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251 | ///Returns the parameter rotated by 90 degrees in negative direction. |
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252 | ///\relates Point |
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253 | /// |
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254 | template<typename T> |
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255 | inline Point<T> rot270(const Point<T> &z) |
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256 | { |
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257 | return Point<T>(z.y,-z.x); |
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258 | } |
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259 | |
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260 | |
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261 | |
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262 | /// Bounding box of plain vectors (points). |
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263 | |
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264 | /// A class to calculate or store the bounding box of plain vectors |
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265 | /// (\ref Point "points"). |
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266 | template<typename T> |
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267 | class Box { |
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268 | Point<T> _bottom_left, _top_right; |
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269 | bool _empty; |
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270 | public: |
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271 | |
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272 | ///Default constructor: creates an empty box |
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273 | Box() { _empty = true; } |
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274 | |
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275 | ///Construct a box from one point |
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276 | Box(Point<T> a) { |
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277 | _bottom_left = _top_right = a; |
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278 | _empty = false; |
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279 | } |
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280 | |
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281 | ///Construct a box from two points |
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282 | |
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283 | ///Construct a box from two points. |
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284 | ///\param a The bottom left corner. |
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285 | ///\param b The top right corner. |
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286 | ///\warning The coordinates of the bottom left corner must be no more |
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287 | ///than those of the top right one. |
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288 | Box(Point<T> a,Point<T> b) |
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289 | { |
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290 | _bottom_left = a; |
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291 | _top_right = b; |
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292 | _empty = false; |
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293 | } |
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294 | |
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295 | ///Construct a box from four numbers |
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296 | |
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297 | ///Construct a box from four numbers. |
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298 | ///\param l The left side of the box. |
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299 | ///\param b The bottom of the box. |
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300 | ///\param r The right side of the box. |
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301 | ///\param t The top of the box. |
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302 | ///\warning The left side must be no more than the right side and |
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303 | ///bottom must be no more than the top. |
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304 | Box(T l,T b,T r,T t) |
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305 | { |
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306 | _bottom_left=Point<T>(l,b); |
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307 | _top_right=Point<T>(r,t); |
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308 | _empty = false; |
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309 | } |
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310 | |
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311 | ///Return \c true if the box is empty. |
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312 | |
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313 | ///Return \c true if the box is empty (i.e. return \c false |
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314 | ///if at least one point was added to the box or the coordinates of |
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315 | ///the box were set). |
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316 | /// |
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317 | ///The coordinates of an empty box are not defined. |
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318 | bool empty() const { |
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319 | return _empty; |
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320 | } |
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321 | |
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322 | ///Make the box empty |
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323 | void clear() { |
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324 | _empty = true; |
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325 | } |
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326 | |
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327 | ///Give back the bottom left corner of the box |
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328 | |
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329 | ///Give back the bottom left corner of the box. |
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330 | ///If the box is empty, then the return value is not defined. |
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331 | Point<T> bottomLeft() const { |
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332 | return _bottom_left; |
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333 | } |
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334 | |
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335 | ///Set the bottom left corner of the box |
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336 | |
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337 | ///Set the bottom left corner of the box. |
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338 | ///\pre The box must not be empty. |
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339 | void bottomLeft(Point<T> p) { |
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340 | _bottom_left = p; |
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341 | } |
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342 | |
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343 | ///Give back the top right corner of the box |
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344 | |
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345 | ///Give back the top right corner of the box. |
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346 | ///If the box is empty, then the return value is not defined. |
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347 | Point<T> topRight() const { |
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348 | return _top_right; |
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349 | } |
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350 | |
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351 | ///Set the top right corner of the box |
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352 | |
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353 | ///Set the top right corner of the box. |
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354 | ///\pre The box must not be empty. |
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355 | void topRight(Point<T> p) { |
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356 | _top_right = p; |
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357 | } |
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358 | |
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359 | ///Give back the bottom right corner of the box |
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360 | |
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361 | ///Give back the bottom right corner of the box. |
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362 | ///If the box is empty, then the return value is not defined. |
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363 | Point<T> bottomRight() const { |
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364 | return Point<T>(_top_right.x,_bottom_left.y); |
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365 | } |
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366 | |
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367 | ///Set the bottom right corner of the box |
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368 | |
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369 | ///Set the bottom right corner of the box. |
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370 | ///\pre The box must not be empty. |
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371 | void bottomRight(Point<T> p) { |
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372 | _top_right.x = p.x; |
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373 | _bottom_left.y = p.y; |
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374 | } |
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375 | |
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376 | ///Give back the top left corner of the box |
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377 | |
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378 | ///Give back the top left corner of the box. |
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379 | ///If the box is empty, then the return value is not defined. |
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380 | Point<T> topLeft() const { |
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381 | return Point<T>(_bottom_left.x,_top_right.y); |
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382 | } |
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383 | |
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384 | ///Set the top left corner of the box |
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385 | |
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386 | ///Set the top left corner of the box. |
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387 | ///\pre The box must not be empty. |
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388 | void topLeft(Point<T> p) { |
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389 | _top_right.y = p.y; |
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390 | _bottom_left.x = p.x; |
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391 | } |
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392 | |
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393 | ///Give back the bottom of the box |
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394 | |
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395 | ///Give back the bottom of the box. |
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396 | ///If the box is empty, then the return value is not defined. |
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397 | T bottom() const { |
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398 | return _bottom_left.y; |
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399 | } |
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400 | |
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401 | ///Set the bottom of the box |
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402 | |
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403 | ///Set the bottom of the box. |
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404 | ///\pre The box must not be empty. |
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405 | void bottom(T t) { |
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406 | _bottom_left.y = t; |
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407 | } |
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408 | |
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409 | ///Give back the top of the box |
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410 | |
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411 | ///Give back the top of the box. |
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412 | ///If the box is empty, then the return value is not defined. |
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413 | T top() const { |
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414 | return _top_right.y; |
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415 | } |
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416 | |
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417 | ///Set the top of the box |
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418 | |
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419 | ///Set the top of the box. |
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420 | ///\pre The box must not be empty. |
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421 | void top(T t) { |
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422 | _top_right.y = t; |
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423 | } |
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424 | |
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425 | ///Give back the left side of the box |
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426 | |
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427 | ///Give back the left side of the box. |
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428 | ///If the box is empty, then the return value is not defined. |
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429 | T left() const { |
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430 | return _bottom_left.x; |
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431 | } |
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432 | |
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433 | ///Set the left side of the box |
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434 | |
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435 | ///Set the left side of the box. |
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436 | ///\pre The box must not be empty. |
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437 | void left(T t) { |
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438 | _bottom_left.x = t; |
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439 | } |
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440 | |
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441 | /// Give back the right side of the box |
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442 | |
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443 | /// Give back the right side of the box. |
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444 | ///If the box is empty, then the return value is not defined. |
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445 | T right() const { |
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446 | return _top_right.x; |
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447 | } |
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448 | |
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449 | ///Set the right side of the box |
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450 | |
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451 | ///Set the right side of the box. |
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452 | ///\pre The box must not be empty. |
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453 | void right(T t) { |
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454 | _top_right.x = t; |
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455 | } |
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456 | |
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457 | ///Give back the height of the box |
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458 | |
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459 | ///Give back the height of the box. |
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460 | ///If the box is empty, then the return value is not defined. |
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461 | T height() const { |
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462 | return _top_right.y-_bottom_left.y; |
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463 | } |
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464 | |
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465 | ///Give back the width of the box |
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466 | |
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467 | ///Give back the width of the box. |
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468 | ///If the box is empty, then the return value is not defined. |
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469 | T width() const { |
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470 | return _top_right.x-_bottom_left.x; |
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471 | } |
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472 | |
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473 | ///Checks whether a point is inside the box |
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474 | bool inside(const Point<T>& u) const { |
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475 | if (_empty) |
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476 | return false; |
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477 | else { |
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478 | return ( (u.x-_bottom_left.x)*(_top_right.x-u.x) >= 0 && |
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479 | (u.y-_bottom_left.y)*(_top_right.y-u.y) >= 0 ); |
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480 | } |
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481 | } |
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482 | |
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483 | ///Increments the box with a point |
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484 | |
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485 | ///Increments the box with a point. |
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486 | /// |
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487 | Box& add(const Point<T>& u){ |
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488 | if (_empty) { |
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489 | _bottom_left = _top_right = u; |
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490 | _empty = false; |
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491 | } |
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492 | else { |
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493 | if (_bottom_left.x > u.x) _bottom_left.x = u.x; |
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494 | if (_bottom_left.y > u.y) _bottom_left.y = u.y; |
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495 | if (_top_right.x < u.x) _top_right.x = u.x; |
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496 | if (_top_right.y < u.y) _top_right.y = u.y; |
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497 | } |
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498 | return *this; |
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499 | } |
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500 | |
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501 | ///Increments the box to contain another box |
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502 | |
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503 | ///Increments the box to contain another box. |
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504 | /// |
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505 | Box& add(const Box &u){ |
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506 | if ( !u.empty() ){ |
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507 | add(u._bottom_left); |
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508 | add(u._top_right); |
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509 | } |
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510 | return *this; |
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511 | } |
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512 | |
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513 | ///Intersection of two boxes |
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514 | |
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515 | ///Intersection of two boxes. |
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516 | /// |
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517 | Box operator&(const Box& u) const { |
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518 | Box b; |
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519 | if (_empty || u._empty) { |
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520 | b._empty = true; |
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521 | } else { |
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522 | b._bottom_left.x = std::max(_bottom_left.x, u._bottom_left.x); |
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523 | b._bottom_left.y = std::max(_bottom_left.y, u._bottom_left.y); |
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524 | b._top_right.x = std::min(_top_right.x, u._top_right.x); |
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525 | b._top_right.y = std::min(_top_right.y, u._top_right.y); |
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526 | b._empty = b._bottom_left.x > b._top_right.x || |
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527 | b._bottom_left.y > b._top_right.y; |
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528 | } |
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529 | return b; |
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530 | } |
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531 | |
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532 | };//class Box |
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533 | |
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534 | |
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535 | ///Read a box from a stream |
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536 | |
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537 | ///Read a box from a stream. |
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538 | ///\relates Box |
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539 | template<typename T> |
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540 | inline std::istream& operator>>(std::istream &is, Box<T>& b) { |
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541 | char c; |
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542 | Point<T> p; |
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543 | if (is >> c) { |
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544 | if (c != '(') is.putback(c); |
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545 | } else { |
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546 | is.clear(); |
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547 | } |
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548 | if (!(is >> p)) return is; |
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549 | b.bottomLeft(p); |
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550 | if (is >> c) { |
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551 | if (c != ',') is.putback(c); |
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552 | } else { |
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553 | is.clear(); |
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554 | } |
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555 | if (!(is >> p)) return is; |
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556 | b.topRight(p); |
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557 | if (is >> c) { |
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558 | if (c != ')') is.putback(c); |
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559 | } else { |
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560 | is.clear(); |
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561 | } |
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562 | return is; |
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563 | } |
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564 | |
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565 | ///Write a box to a stream |
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566 | |
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567 | ///Write a box to a stream. |
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568 | ///\relates Box |
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569 | template<typename T> |
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570 | inline std::ostream& operator<<(std::ostream &os, const Box<T>& b) |
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571 | { |
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572 | os << "(" << b.bottomLeft() << "," << b.topRight() << ")"; |
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573 | return os; |
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574 | } |
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575 | |
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576 | ///Map of x-coordinates of a <tt>Point</tt>-map |
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577 | |
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578 | ///Map of x-coordinates of a \ref Point "Point"-map. |
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579 | /// |
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580 | template<class M> |
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581 | class XMap |
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582 | { |
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583 | M& _map; |
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584 | public: |
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585 | |
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586 | typedef typename M::Value::Value Value; |
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587 | typedef typename M::Key Key; |
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588 | ///\e |
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589 | XMap(M& map) : _map(map) {} |
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590 | Value operator[](Key k) const {return _map[k].x;} |
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591 | void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));} |
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592 | }; |
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593 | |
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594 | ///Returns an XMap class |
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595 | |
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596 | ///This function just returns an XMap class. |
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597 | ///\relates XMap |
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598 | template<class M> |
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599 | inline XMap<M> xMap(M &m) |
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600 | { |
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601 | return XMap<M>(m); |
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602 | } |
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603 | |
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604 | template<class M> |
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605 | inline XMap<M> xMap(const M &m) |
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606 | { |
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607 | return XMap<M>(m); |
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608 | } |
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609 | |
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610 | ///Constant (read only) version of XMap |
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611 | |
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612 | ///Constant (read only) version of XMap. |
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613 | /// |
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614 | template<class M> |
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615 | class ConstXMap |
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616 | { |
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617 | const M& _map; |
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618 | public: |
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619 | |
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620 | typedef typename M::Value::Value Value; |
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621 | typedef typename M::Key Key; |
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622 | ///\e |
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623 | ConstXMap(const M &map) : _map(map) {} |
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624 | Value operator[](Key k) const {return _map[k].x;} |
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625 | }; |
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626 | |
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627 | ///Returns a ConstXMap class |
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628 | |
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629 | ///This function just returns a ConstXMap class. |
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630 | ///\relates ConstXMap |
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631 | template<class M> |
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632 | inline ConstXMap<M> xMap(const M &m) |
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633 | { |
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634 | return ConstXMap<M>(m); |
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635 | } |
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636 | |
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637 | ///Map of y-coordinates of a <tt>Point</tt>-map |
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638 | |
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639 | ///Map of y-coordinates of a \ref Point "Point"-map. |
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640 | /// |
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641 | template<class M> |
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642 | class YMap |
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643 | { |
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644 | M& _map; |
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645 | public: |
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646 | |
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647 | typedef typename M::Value::Value Value; |
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648 | typedef typename M::Key Key; |
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649 | ///\e |
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650 | YMap(M& map) : _map(map) {} |
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651 | Value operator[](Key k) const {return _map[k].y;} |
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652 | void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));} |
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653 | }; |
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654 | |
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655 | ///Returns a YMap class |
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656 | |
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657 | ///This function just returns a YMap class. |
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658 | ///\relates YMap |
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659 | template<class M> |
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660 | inline YMap<M> yMap(M &m) |
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661 | { |
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662 | return YMap<M>(m); |
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663 | } |
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664 | |
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665 | template<class M> |
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666 | inline YMap<M> yMap(const M &m) |
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667 | { |
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668 | return YMap<M>(m); |
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669 | } |
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670 | |
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671 | ///Constant (read only) version of YMap |
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672 | |
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673 | ///Constant (read only) version of YMap. |
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674 | /// |
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675 | template<class M> |
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676 | class ConstYMap |
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677 | { |
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678 | const M& _map; |
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679 | public: |
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680 | |
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681 | typedef typename M::Value::Value Value; |
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682 | typedef typename M::Key Key; |
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683 | ///\e |
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684 | ConstYMap(const M &map) : _map(map) {} |
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685 | Value operator[](Key k) const {return _map[k].y;} |
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686 | }; |
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687 | |
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688 | ///Returns a ConstYMap class |
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689 | |
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690 | ///This function just returns a ConstYMap class. |
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691 | ///\relates ConstYMap |
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692 | template<class M> |
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693 | inline ConstYMap<M> yMap(const M &m) |
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694 | { |
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695 | return ConstYMap<M>(m); |
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696 | } |
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697 | |
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698 | |
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699 | ///\brief Map of the normSquare() of a <tt>Point</tt>-map |
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700 | /// |
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701 | ///Map of the \ref Point::normSquare() "normSquare()" |
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702 | ///of a \ref Point "Point"-map. |
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703 | template<class M> |
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704 | class NormSquareMap |
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705 | { |
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706 | const M& _map; |
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707 | public: |
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708 | |
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709 | typedef typename M::Value::Value Value; |
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710 | typedef typename M::Key Key; |
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711 | ///\e |
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712 | NormSquareMap(const M &map) : _map(map) {} |
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713 | Value operator[](Key k) const {return _map[k].normSquare();} |
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714 | }; |
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715 | |
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716 | ///Returns a NormSquareMap class |
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717 | |
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718 | ///This function just returns a NormSquareMap class. |
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719 | ///\relates NormSquareMap |
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720 | template<class M> |
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721 | inline NormSquareMap<M> normSquareMap(const M &m) |
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722 | { |
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723 | return NormSquareMap<M>(m); |
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724 | } |
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725 | |
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726 | /// @} |
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727 | |
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728 | } //namespce dim2 |
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729 | |
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730 | } //namespace lemon |
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731 | |
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732 | #endif //LEMON_DIM2_H |
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