1 | // =============================================================== // |
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2 | // // |
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3 | // File : aw_position.hxx // |
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4 | // Purpose : Positions, Vectors and Angles // |
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5 | // // |
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6 | // Coded by Ralf Westram (coder@reallysoft.de) in July 2007 // |
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7 | // Institute of Microbiology (Technical University Munich) // |
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8 | // http://www.arb-home.de/ // |
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9 | // // |
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10 | // =============================================================== // |
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11 | |
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12 | #ifndef AW_POSITION_HXX |
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13 | #define AW_POSITION_HXX |
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14 | |
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15 | #ifndef _CPP_CMATH |
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16 | #include <cmath> |
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17 | #endif |
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18 | |
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19 | #ifndef AW_ROOT_HXX |
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20 | #include <aw_root.hxx> |
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21 | #endif |
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22 | |
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23 | #ifndef aw_assert |
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24 | #ifndef ARB_ASSERT_H |
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25 | #include <arb_assert.h> |
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26 | #endif |
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27 | #define aw_assert(bed) arb_assert(bed) |
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28 | #endif |
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29 | |
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30 | // ------------------------ |
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31 | // validity checks |
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32 | // ------------------------ |
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33 | |
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34 | #if defined(DEBUG) |
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35 | #define ISVALID(a) aw_assert((a).valid()) |
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36 | #else |
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37 | #define ISVALID(a) |
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38 | #endif // DEBUG |
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39 | |
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40 | namespace AW { |
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41 | |
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42 | const double EPSILON = 0.001; // how equal is nearly equal |
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43 | |
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44 | inline bool nearlyEqual(const double& val1, const double& val2) { |
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45 | return std::abs(val1-val2) < EPSILON; |
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46 | } |
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47 | |
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48 | |
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49 | // ------------------------------------------------------- |
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50 | // class Position represents 2-dimensional positions |
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51 | // ------------------------------------------------------- |
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52 | |
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53 | // Note: orientation of drawn canvases is like shown in this figure: |
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54 | // |
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55 | // __________________\ +x |
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56 | // | / . |
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57 | // | |
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58 | // | |
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59 | // | |
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60 | // | |
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61 | // | |
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62 | // | |
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63 | // \|/ |
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64 | // +y |
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65 | // |
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66 | // i.e. rotating an angle by 90 degrees, means rotating it 3 hours in clockwise direction |
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67 | |
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68 | class Vector; |
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69 | |
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70 | class Position { |
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71 | double x, y; |
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72 | |
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73 | static bool is_between(const double& coord1, const double& between, const double& coord2) { |
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74 | return ((coord1-between)*(between-coord2)) >= 0.0; |
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75 | } |
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76 | |
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77 | public: |
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78 | |
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79 | bool valid() const { return (x == x) && (y == y); } // fails if one is NAN |
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80 | |
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81 | Position(double X, double Y) : x(X), y(Y) { ISVALID(*this); } |
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82 | Position() : x(NAN), y(NAN) {} // default is no position |
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83 | ~Position() {} |
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84 | |
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85 | inline Position& operator += (const Vector& v); |
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86 | inline Position& operator -= (const Vector& v); |
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87 | |
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88 | const double& xpos() const { return x; } |
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89 | const double& ypos() const { return y; } |
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90 | |
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91 | // void set(const double& X, const double& Y) { x = X; y = Y; } |
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92 | void setx(const double& X) { x = X; } |
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93 | void sety(const double& Y) { y = Y; } |
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94 | |
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95 | void movex(const double& X) { x += X; } |
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96 | void movey(const double& Y) { y += Y; } |
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97 | |
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98 | void move(const Vector& movement) { *this += movement; } |
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99 | void moveTo(const Position& pos) { *this = pos; } |
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100 | |
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101 | inline bool is_between(const Position& p1, const Position& p2) const { |
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102 | return is_between(p1.x, x, p2.x) && is_between(p1.y, y, p2.y); |
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103 | } |
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104 | }; |
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105 | |
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106 | extern const Position Origin; |
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107 | |
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108 | // ------------------------------- |
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109 | // a 2D vector |
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110 | // ------------------------------- |
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111 | |
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112 | class Vector { |
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113 | Position end; // endpoint of vector (vector starts at Position::origin) |
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114 | // double x_, y_; |
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115 | mutable double len; // once calculated, length of vector is stored here (negative value means "not calculated") |
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116 | |
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117 | public: |
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118 | bool valid() const { return end.valid() && (len == len); } // len == len fails if len is NAN |
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119 | |
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120 | Vector() : len(NAN) {} // default is not a vector |
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121 | Vector(const double& X, const double& Y) : end(X, Y), len(-1) { ISVALID(*this); } // vector (0,0)->(X,Y) |
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122 | Vector(const double& X, const double& Y, const double& Length) : end(X, Y), len(Length) { ISVALID(*this); } // same with known length |
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123 | explicit Vector(const Position& to) : end(to), len(-1) { ISVALID(*this); } // vector origin->to |
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124 | Vector(const Position& from, const Position& to) : end(to.xpos()-from.xpos(), to.ypos()-from.ypos()), len(-1) { ISVALID(*this); } // vector from->to |
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125 | ~Vector() {} |
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126 | |
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127 | const double& x() const { return end.xpos(); } |
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128 | const double& y() const { return end.ypos(); } |
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129 | const Position& endpoint() { return end; } |
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130 | |
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131 | Vector& set(const double& X, const double& Y, double Length = -1) { end = Position(X, Y); len = Length; return *this; } |
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132 | Vector& setx(const double& X) { end.setx(X); len = -1; return *this; } |
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133 | Vector& sety(const double& Y) { end.sety(Y); len = -1; return *this; } |
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134 | |
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135 | const double& length() const { |
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136 | if (len<0.0) len = sqrt(x()*x() + y()*y()); |
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137 | return len; |
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138 | } |
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139 | |
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140 | // length-modifying members: |
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141 | |
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142 | Vector& operator *= (const double& factor) { return set(x()*factor, y()*factor, len*std::abs(factor)); } |
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143 | Vector& operator /= (const double& divisor) { return operator *= (1.0/divisor); } |
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144 | |
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145 | Vector& operator += (const Vector& other) { return set(x()+other.x(), y()+other.y()); } |
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146 | Vector& operator -= (const Vector& other) { return set(x()-other.x(), y()-other.y()); } |
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147 | |
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148 | Vector& normalize() { |
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149 | aw_assert(length()>0); // cannot normalize zero-Vector! |
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150 | return *this /= length(); |
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151 | } |
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152 | // bool is_normalized() const { return std::abs(length()-1.0) < EPSILON; } |
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153 | bool is_normalized() const { return nearlyEqual(length(), 1); } |
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154 | |
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155 | Vector& set_length(double new_length) { |
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156 | double factor = new_length/length(); |
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157 | return *this *= factor; |
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158 | } |
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159 | |
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160 | // length-constant members: |
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161 | |
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162 | Vector& neg() { end = Position(-x(), -y()); return *this; } |
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163 | Vector& negx() { end.setx(-x()); return *this; } |
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164 | Vector& negy() { end.sety(-y()); return *this; } |
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165 | |
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166 | Vector& flipxy() { end = Position(y(), x()); return *this; } |
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167 | |
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168 | Vector& rotate90deg() { return negy().flipxy(); } |
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169 | Vector& rotate180deg() { return neg(); } |
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170 | Vector& rotate270deg() { return negx().flipxy(); } |
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171 | |
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172 | Vector& rotate45deg(); |
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173 | Vector& rotate135deg() { return rotate45deg().rotate90deg(); } |
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174 | Vector& rotate225deg() { return rotate45deg().rotate180deg(); } |
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175 | Vector& rotate315deg() { return rotate45deg().rotate270deg(); } |
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176 | |
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177 | Vector operator-() const { return Vector(-x(), -y(), len); } // unary minus |
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178 | }; |
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179 | |
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180 | extern const Vector ZeroVector; |
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181 | |
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182 | // ----------------------------------------- |
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183 | // inline Position members |
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184 | // ----------------------------------------- |
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185 | |
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186 | inline Position& Position::operator += (const Vector& v) { x += v.x(); y += v.y(); ISVALID(*this); return *this; } |
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187 | inline Position& Position::operator -= (const Vector& v) { x -= v.x(); y -= v.y(); ISVALID(*this); return *this; } |
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188 | |
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189 | // ------------------------------------------ |
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190 | // basic Position / Vector functions |
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191 | // ------------------------------------------ |
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192 | |
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193 | // Difference between Positions |
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194 | inline Vector operator-(const Position& to, const Position& from) { return Vector(from, to); } |
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195 | |
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196 | // Position +- Vector -> new Position |
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197 | inline Position operator+(const Position& p, const Vector& v) { return Position(p) += v; } |
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198 | inline Position operator+(const Vector& v, const Position& p) { return Position(p) += v; } |
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199 | inline Position operator-(const Position& p, const Vector& v) { return Position(p) -= v; } |
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200 | |
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201 | // Vector addition |
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202 | inline Vector operator+(const Vector& v1, const Vector& v2) { return Vector(v1) += v2; } |
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203 | inline Vector operator-(const Vector& v1, const Vector& v2) { return Vector(v1) -= v2; } |
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204 | |
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205 | // stretch/shrink Vector |
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206 | inline Vector operator*(const Vector& v, const double& f) { return Vector(v) *= f; } |
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207 | inline Vector operator*(const double& f, const Vector& v) { return Vector(v) *= f; } |
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208 | inline Vector operator/(const Vector& v, const double& d) { return Vector(v) /= d; } |
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209 | |
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210 | inline Position centroid(const Position& p1, const Position& p2) { return Position((p1.xpos()+p2.xpos())*0.5, (p1.ypos()+p2.ypos())*0.5); } |
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211 | |
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212 | inline double Distance(const Position& from, const Position& to) { return Vector(from, to).length(); } |
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213 | inline double scalarProduct(const Vector& v1, const Vector& v2) { return v1.x()*v2.x() + v1.y()*v2.y(); } |
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214 | |
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215 | // ------------------------------------------------- |
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216 | // a positioned vector, representing a line |
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217 | // ------------------------------------------------- |
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218 | |
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219 | class LineVector { |
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220 | Position Start; // start point |
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221 | Vector ToEnd; // vector to end point |
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222 | |
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223 | protected: |
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224 | void standardize(); |
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225 | |
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226 | public: |
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227 | bool valid() const { return Start.valid() && ToEnd.valid(); } |
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228 | |
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229 | LineVector(const Position& startpos, const Position& end) : Start(startpos), ToEnd(startpos, end) { ISVALID(*this); } |
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230 | LineVector(const Position& startpos, const Vector& to_end) : Start(startpos), ToEnd(to_end) { ISVALID(*this); } |
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231 | LineVector(double X1, double Y1, double X2, double Y2) : Start(X1, Y1), ToEnd(X2-X1, Y2-Y1) { ISVALID(*this); } |
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232 | LineVector(const AW_rectangle& r) : Start(r.l, r.t), ToEnd(r.r-r.l-1, r.b-r.t-1) { ISVALID(*this); } |
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233 | LineVector() {} |
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234 | |
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235 | const Vector& line_vector() const { return ToEnd; } |
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236 | const Position& start() const { return Start; } |
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237 | Position head() const { return Start+ToEnd; } |
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238 | |
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239 | Position centroid() const { return Start+ToEnd*0.5; } |
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240 | double length() const { return line_vector().length(); } |
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241 | |
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242 | const double& xpos() const { return Start.xpos(); } |
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243 | const double& ypos() const { return Start.ypos(); } |
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244 | |
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245 | void move(const Vector& movement) { Start += movement; } |
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246 | void moveTo(const Position& pos) { Start = pos; } |
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247 | }; |
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248 | |
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249 | Position crosspoint(const LineVector& l1, const LineVector& l2, double& factor_l1, double& factor_l2); |
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250 | double Distance(const Position pos, const LineVector line); |
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251 | |
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252 | // --------------------- |
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253 | // a rectangle |
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254 | // --------------------- |
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255 | |
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256 | class Rectangle : public LineVector { // the LineVector describes one corner and the diagonal |
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257 | public: |
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258 | explicit Rectangle(const LineVector& Diagonal) : LineVector(Diagonal) { standardize(); } |
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259 | Rectangle(const Position& corner, const Position& opposite_corner) : LineVector(corner, opposite_corner) { standardize(); } |
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260 | Rectangle(const Position& corner, const Vector& to_opposite_corner) : LineVector(corner, to_opposite_corner) { standardize(); } |
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261 | Rectangle(double X1, double Y1, double X2, double Y2) : LineVector(X1, Y1, X2, Y2) { standardize(); } |
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262 | Rectangle(const AW_rectangle& r) : LineVector(r) { standardize(); } |
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263 | Rectangle() {}; |
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264 | |
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265 | const Vector& diagonal() const { return line_vector(); } |
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266 | |
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267 | const Position& upper_left_corner() const { return start(); } |
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268 | Position lower_left_corner() const { return Position(start().xpos(), start().ypos()+line_vector().y()); } |
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269 | Position upper_right_corner() const { return Position(start().xpos()+line_vector().x(), start().ypos()); } |
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270 | Position lower_right_corner() const { return head(); } |
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271 | |
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272 | double width() const { return diagonal().x(); } |
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273 | double height() const { return diagonal().y(); } |
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274 | |
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275 | void standardize() { LineVector::standardize(); } |
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276 | |
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277 | bool contains(const Position& pos) const { return pos.is_between(upper_left_corner(), lower_right_corner()); } |
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278 | bool contains(const LineVector& lvec) const { return contains(lvec.start()) && contains(lvec.head()); } |
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279 | }; |
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280 | |
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281 | // ------------------------------------------------------------------ |
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282 | // class angle represents an angle using a normalized vector |
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283 | // ------------------------------------------------------------------ |
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284 | |
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285 | class Angle { |
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286 | mutable Vector Normal; // the normal vector representing the angle (x = cos(angle), y = sin(angle)) |
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287 | mutable double Radian; // the radian of the angle |
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288 | |
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289 | void recalcRadian() const; |
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290 | void recalcNormal() const; |
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291 | |
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292 | public: |
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293 | bool valid() const { return Normal.valid() && (Radian == Radian); } // Radian == Radian fails if Radian is NAN |
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294 | |
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295 | static const double rad2deg; |
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296 | static const double deg2rad; |
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297 | |
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298 | Angle(double Radian_) : Radian(Radian_) { recalcNormal(); ISVALID(*this); } |
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299 | Angle(double x, double y) : Normal(x, y) { Normal.normalize(); recalcRadian(); ISVALID(*this); } |
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300 | explicit Angle(const Vector& v) : Normal(v) { Normal.normalize(); recalcRadian(); ISVALID(*this); } |
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301 | Angle(const Vector& n, double r) : Normal(n), Radian(r) { aw_assert(n.is_normalized()); ISVALID(*this); } |
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302 | Angle(const Position& p1, const Position& p2) : Normal(p1, p2) { Normal.normalize(); recalcRadian(); ISVALID(*this); } |
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303 | Angle() : Radian(NAN) { } // default is not an angle |
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304 | |
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305 | Angle& operator = (const Angle& other) { Normal = other.Normal; Radian = other.Radian; return *this; } |
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306 | Angle& operator = (const Vector& vec) { Normal = vec; Normal.normalize(); recalcRadian(); return *this; } |
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307 | |
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308 | void fixRadian() const { // force radian into range [0, 2*M_PI[ |
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309 | while (Radian<0.0) Radian += 2*M_PI; |
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310 | while (Radian >= 2*M_PI) Radian -= 2*M_PI; |
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311 | } |
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312 | |
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313 | const double& radian() const { fixRadian(); return Radian; } |
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314 | double degrees() const { fixRadian(); return rad2deg*Radian; } |
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315 | const Vector& normal() const { return Normal; } |
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316 | |
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317 | const double& sin() const { return Normal.y(); } |
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318 | const double& cos() const { return Normal.x(); } |
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319 | |
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320 | Angle& operator += (const Angle& o) { |
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321 | Radian += o.Radian; |
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322 | |
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323 | double norm = normal().length()*o.normal().length(); |
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324 | if (nearlyEqual(norm, 1)) { // fast method |
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325 | Vector newNormal(cos()*o.cos() - sin()*o.sin(), |
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326 | sin()*o.cos() + cos()*o.sin()); |
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327 | aw_assert(newNormal.is_normalized()); |
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328 | Normal = newNormal; |
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329 | } |
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330 | else { |
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331 | recalcNormal(); |
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332 | } |
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333 | return *this; |
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334 | } |
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335 | Angle& operator -= (const Angle& o) { |
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336 | Radian -= o.Radian; |
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337 | |
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338 | double norm = normal().length()*o.normal().length(); |
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339 | if (nearlyEqual(norm, 1)) { // fast method |
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340 | Vector newNormal(cos()*o.cos() + sin()*o.sin(), |
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341 | sin()*o.cos() - cos()*o.sin()); |
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342 | aw_assert(newNormal.is_normalized()); |
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343 | |
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344 | Normal = newNormal; |
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345 | } |
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346 | else { |
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347 | recalcNormal(); |
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348 | } |
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349 | return *this; |
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350 | } |
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351 | |
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352 | Angle& operator *= (const double& fact) { |
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353 | fixRadian(); |
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354 | Radian *= fact; |
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355 | recalcNormal(); |
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356 | return *this; |
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357 | } |
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358 | |
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359 | Angle& rotate90deg() { Normal.rotate90deg(); Radian += 0.5*M_PI; return *this; } |
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360 | Angle& rotate180deg() { Normal.rotate180deg(); Radian += M_PI; return *this; } |
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361 | Angle& rotate270deg() { Normal.rotate270deg(); Radian += 1.5*M_PI; return *this; } |
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362 | |
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363 | Angle operator-() const { return Angle(Vector(Normal).negy(), 2*M_PI-Radian); } // unary minus |
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364 | }; |
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365 | |
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366 | inline Angle operator+(const Angle& a1, const Angle& a2) { return Angle(a1) += a2; } |
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367 | inline Angle operator-(const Angle& a1, const Angle& a2) { return Angle(a1) -= a2; } |
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368 | |
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369 | inline Angle operator*(const Angle& a, const double& fact) { return Angle(a) *= fact; } |
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370 | inline Angle operator/(const Angle& a, const double& divi) { return Angle(a) *= (1.0/divi); } |
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371 | |
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372 | // --------------------- |
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373 | // some helpers |
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374 | // --------------------- |
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375 | |
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376 | // pythagoras: |
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377 | |
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378 | inline double hypotenuse(double cath1, double cath2) { return sqrt(cath1*cath1 + cath2*cath2); } |
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379 | inline double cathetus(double hypotenuse, double cathetus) { |
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380 | aw_assert(hypotenuse>cathetus); |
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381 | return sqrt(hypotenuse*hypotenuse - cathetus*cathetus); |
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382 | } |
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383 | |
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384 | #if defined(DEBUG) |
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385 | // dont use these in release code - they are only approximizations! |
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386 | |
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387 | // test whether two doubles are "equal" (slow - use for assertions only!) |
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388 | inline bool are_equal(const double& d1, const double& d2) { |
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389 | double diff = std::abs(d1-d2); |
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390 | return diff < 0.000001; |
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391 | } |
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392 | |
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393 | inline bool are_orthographic(const Vector& v1, const Vector& v2) { |
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394 | return are_equal(scalarProduct(v1, v2), 0); |
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395 | } |
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396 | #endif // DEBUG |
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397 | |
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398 | inline bool isOrigin(const Position& p) { |
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399 | return p.xpos() == 0 && p.ypos() == 0; |
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400 | } |
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401 | |
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402 | |
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403 | }; |
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404 | |
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405 | #else |
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406 | #error aw_position.hxx included twice |
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407 | #endif // AW_POSITION_HXX |
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