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1 #ifndef __RIMATH_H |
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2 #define __RIMATH_H |
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3 |
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4 /*------------------------------------------------------------------------ |
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5 * |
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6 * OpenVG 1.1 Reference Implementation |
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7 * ----------------------------------- |
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8 * |
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9 * Copyright (c) 2007 The Khronos Group Inc. |
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10 * Portions copyright (c) 2010 Nokia Corporation and/or its subsidiary(-ies). |
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11 * |
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12 * Permission is hereby granted, free of charge, to any person obtaining a |
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13 * copy of this software and /or associated documentation files |
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14 * (the "Materials "), to deal in the Materials without restriction, |
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15 * including without limitation the rights to use, copy, modify, merge, |
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16 * publish, distribute, sublicense, and/or sell copies of the Materials, |
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17 * and to permit persons to whom the Materials are furnished to do so, |
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18 * subject to the following conditions: |
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19 * |
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20 * The above copyright notice and this permission notice shall be included |
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21 * in all copies or substantial portions of the Materials. |
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22 * |
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23 * THE MATERIALS ARE PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
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24 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF |
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25 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. |
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26 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, |
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27 * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR |
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28 * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE MATERIALS OR |
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29 * THE USE OR OTHER DEALINGS IN THE MATERIALS. |
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30 * |
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31 *//** |
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32 * \file |
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33 * \brief Math functions, Vector and Matrix classes. |
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34 * \note |
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35 *//*-------------------------------------------------------------------*/ |
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36 |
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37 #ifndef __RIDEFS_H |
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38 #include "riDefs.h" |
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39 #endif |
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40 |
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41 #include <math.h> |
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42 |
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43 namespace OpenVGRI |
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44 { |
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45 |
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46 /*-------------------------------------------------------------------*//*! |
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47 * \brief |
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48 * \param |
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49 * \return |
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50 * \note |
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51 *//*-------------------------------------------------------------------*/ |
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52 |
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53 RI_INLINE int RI_ISNAN(float a) |
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54 { |
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55 RIfloatInt p; |
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56 p.f = a; |
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57 unsigned int exponent = (p.i>>23) & 0xff; |
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58 unsigned int mantissa = p.i & 0x7fffff; |
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59 if(exponent == 255 && mantissa) |
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60 return 1; |
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61 return 0; |
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62 } |
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63 |
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64 #if (RI_MANTISSA_BITS > 23) |
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65 #error RI_MANTISSA_BITS is greater than 23 |
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66 #elif (RI_EXPONENT_BITS > 8) |
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67 #error RI_EXPONENT_BITS is greater than 8 |
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68 #elif (RI_MANTISSA_BITS != 23) || (RI_EXPONENT_BITS != 8) |
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69 |
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70 class RIfloat |
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71 { |
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72 public: |
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73 RIfloat() : v(0.0f) { removeBits(); } |
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74 RIfloat(float a) : v(a) { removeBits(); } |
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75 RIfloat(double a) : v((float)a) { removeBits(); } |
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76 RIfloat(int a) : v((float)a) { removeBits(); } |
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77 RIfloat(unsigned int a) : v((float)a) { removeBits(); } |
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78 RIfloat& operator=(const RIfloat &a) { v = a.v; removeBits(); return *this; } |
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79 RIfloat& operator+=(const RIfloat &a){ v += a.v; removeBits(); return *this; } |
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80 RIfloat& operator-=(const RIfloat &a){ v -= a.v; removeBits(); return *this; } |
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81 RIfloat& operator*=(const RIfloat &a){ v *= a.v; removeBits(); return *this; } |
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82 RIfloat& operator/=(const RIfloat &a){ v /= a.v; removeBits(); return *this; } |
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83 RIfloat operator-() const { return -v; } |
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84 operator float() const { return v; } |
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85 operator double() const { return (double)v; } |
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86 operator int() const { return (int)v; } |
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87 |
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88 friend RIfloat operator+(const RIfloat &a, const RIfloat &b); |
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89 friend RIfloat operator+(float a, const RIfloat &b); |
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90 friend RIfloat operator+(const RIfloat &a, float b); |
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91 friend RIfloat operator-(const RIfloat &a, const RIfloat &b); |
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92 friend RIfloat operator-(float a, const RIfloat &b); |
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93 friend RIfloat operator-(const RIfloat &a, float b); |
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94 friend RIfloat operator*(const RIfloat &a, const RIfloat &b); |
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95 friend RIfloat operator*(float a, const RIfloat &b); |
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96 friend RIfloat operator*(const RIfloat &a, float b); |
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97 friend RIfloat operator/(const RIfloat &a, const RIfloat &b); |
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98 friend RIfloat operator/(float a, const RIfloat &b); |
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99 friend RIfloat operator/(const RIfloat &a, float b); |
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100 |
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101 friend bool operator<(const RIfloat &a, const RIfloat &b); |
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102 friend bool operator<(float a, const RIfloat &b); |
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103 friend bool operator<(const RIfloat &a, float b); |
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104 friend bool operator>(const RIfloat &a, const RIfloat &b); |
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105 friend bool operator>(float a, const RIfloat &b); |
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106 friend bool operator>(const RIfloat &a, float b); |
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107 friend bool operator<=(const RIfloat &a, const RIfloat &b); |
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108 friend bool operator<=(float a, const RIfloat &b); |
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109 friend bool operator<=(const RIfloat &a, float b); |
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110 friend bool operator>=(const RIfloat &a, const RIfloat &b); |
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111 friend bool operator>=(float a, const RIfloat &b); |
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112 friend bool operator>=(const RIfloat &a, float b); |
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113 friend bool operator==(const RIfloat &a, const RIfloat &b); |
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114 friend bool operator==(float a, const RIfloat &b); |
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115 friend bool operator==(const RIfloat &a, float b); |
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116 friend bool operator!=(const RIfloat &a, const RIfloat &b); |
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117 friend bool operator!=(float a, const RIfloat &b); |
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118 friend bool operator!=(const RIfloat &a, float b); |
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119 private: |
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120 void removeBits() |
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121 { |
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122 RIfloatInt p; |
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123 p.f = v; |
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124 unsigned int exponent = (p.i>>23) & 0xff; |
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125 if(exponent == 0 || exponent == 255) |
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126 return; //zero, denormal, infinite, or NaN |
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127 |
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128 p.i &= ~((1<<(23-RI_MANTISSA_BITS))-1); |
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129 |
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130 #if (RI_EXPONENT_BITS != 8) |
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131 if (exponent > 127 + (1 << (RI_EXPONENT_BITS-1))) |
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132 exponent = 127 + (1 << (RI_EXPONENT_BITS-1)); |
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133 |
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134 if (exponent < 127 + 1 - (1 << (RI_EXPONENT_BITS-1))) |
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135 exponent = 127 + 1 - (1 << (RI_EXPONENT_BITS-1)); |
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136 |
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137 p.i &= ~(0xff<<23); |
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138 p.i |= exponent<<23; |
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139 #endif |
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140 v = p.f; |
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141 } |
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142 |
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143 float v; |
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144 }; |
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145 |
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146 RI_INLINE RIfloat operator+(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v+b.v); } |
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147 RI_INLINE RIfloat operator+(float a, const RIfloat &b) { return RIfloat(a+b.v); } |
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148 RI_INLINE RIfloat operator+(const RIfloat &a, float b) { return RIfloat(a.v+b); } |
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149 RI_INLINE RIfloat operator-(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v-b.v); } |
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150 RI_INLINE RIfloat operator-(float a, const RIfloat &b) { return RIfloat(a-b.v); } |
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151 RI_INLINE RIfloat operator-(const RIfloat &a, float b) { return RIfloat(a.v-b); } |
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152 RI_INLINE RIfloat operator*(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v*b.v); } |
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153 RI_INLINE RIfloat operator*(float a, const RIfloat &b) { return RIfloat(a*b.v); } |
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154 RI_INLINE RIfloat operator*(const RIfloat &a, float b) { return RIfloat(a.v*b); } |
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155 RI_INLINE RIfloat operator/(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v/b.v); } |
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156 RI_INLINE RIfloat operator/(float a, const RIfloat &b) { return RIfloat(a/b.v); } |
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157 RI_INLINE RIfloat operator/(const RIfloat &a, float b) { return RIfloat(a.v/b); } |
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158 |
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159 RI_INLINE bool operator<(const RIfloat &a, const RIfloat &b) { return a.v < b.v ? true : false; } |
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160 RI_INLINE bool operator<(float a, const RIfloat &b) { return a < b.v ? true : false; } |
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161 RI_INLINE bool operator<(const RIfloat &a, float b) { return a.v < b ? true : false; } |
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162 RI_INLINE bool operator>(const RIfloat &a, const RIfloat &b) { return a.v > b.v ? true : false; } |
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163 RI_INLINE bool operator>(float a, const RIfloat &b) { return a > b.v ? true : false; } |
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164 RI_INLINE bool operator>(const RIfloat &a, float b) { return a.v > b ? true : false; } |
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165 RI_INLINE bool operator<=(const RIfloat &a, const RIfloat &b) { return a.v <= b.v ? true : false; } |
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166 RI_INLINE bool operator<=(float a, const RIfloat &b) { return a <= b.v ? true : false; } |
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167 RI_INLINE bool operator<=(const RIfloat &a, float b) { return a.v <= b ? true : false; } |
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168 RI_INLINE bool operator>=(const RIfloat &a, const RIfloat &b) { return a.v >= b.v ? true : false; } |
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169 RI_INLINE bool operator>=(float a, const RIfloat &b) { return a >= b.v ? true : false; } |
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170 RI_INLINE bool operator>=(const RIfloat &a, float b) { return a.v >= b ? true : false; } |
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171 RI_INLINE bool operator==(const RIfloat &a, const RIfloat &b) { return a.v == b.v ? true : false; } |
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172 RI_INLINE bool operator==(float a, const RIfloat &b) { return a == b.v ? true : false; } |
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173 RI_INLINE bool operator==(const RIfloat &a, float b) { return a.v == b ? true : false; } |
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174 RI_INLINE bool operator!=(const RIfloat &a, const RIfloat &b) { return a.v != b.v ? true : false; } |
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175 RI_INLINE bool operator!=(float a, const RIfloat &b) { return a != b.v ? true : false; } |
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176 RI_INLINE bool operator!=(const RIfloat &a, float b) { return a.v != b ? true : false; } |
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177 |
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178 #else |
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179 typedef float RIfloat; |
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180 #endif |
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181 |
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182 #define RI_PI 3.141592654f |
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183 |
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184 RI_INLINE RIfloat RI_FRAC(RIfloat f) { return f - (RIfloat)(int)f; } |
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185 RI_INLINE int RI_ROUND_TO_INT(RIfloat v) { return (v >= 0.0f) ? (int)(v+0.5f) : (int)(v-0.5f); } |
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186 RI_INLINE RIfloat RI_MAX(RIfloat a, RIfloat b) { return (a > b) ? a : b; } |
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187 RI_INLINE int RI_MAX(int a, int b) { return (a > b) ? a : b; } |
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188 RI_INLINE RIfloat RI_MIN(RIfloat a, RIfloat b) { return (a < b) ? a : b; } |
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189 RI_INLINE int RI_MIN(int a, int b) { return (a < b) ? a : b; } |
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190 RI_INLINE RIfloat RI_CLAMP(RIfloat a, RIfloat l, RIfloat h) { if(RI_ISNAN(a)) return l; RI_ASSERT(l <= h); return (a < l) ? l : (a > h) ? h : a; } |
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191 RI_INLINE int RI_CEIL(RIfloat a) {return (int)ceilf(a);} |
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192 RI_INLINE int RI_FLOOR(RIfloat a) { return (int)floorf(a); } |
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193 RI_INLINE void RI_SWAP(RIfloat &a, RIfloat &b) { RIfloat tmp = a; a = b; b = tmp; } |
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194 RI_INLINE RIfloat RI_ABS(RIfloat a) { return (a < 0.0f) ? -a : a; } |
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195 RI_INLINE RIfloat RI_SQR(RIfloat a) { return a * a; } |
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196 RI_INLINE RIfloat RI_DEG_TO_RAD(RIfloat a) { return a * RI_PI / 180.0f; } |
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197 RI_INLINE RIfloat RI_RAD_TO_DEG(RIfloat a) { return a * 180.0f/ RI_PI; } |
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198 RI_INLINE RIfloat RI_MOD(RIfloat a, RIfloat b) { if(RI_ISNAN(a) || RI_ISNAN(b)) return 0.0f; RI_ASSERT(b >= 0.0f); if(b == 0.0f) return 0.0f; RIfloat f = (RIfloat)fmod(a, b); if(f < 0.0f) f += b; RI_ASSERT(f >= 0.0f && f <= b); return f; } |
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199 |
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200 #define RI_ANY_SWAP(type, a, b) {type tmp = a; a = b; b = tmp;} |
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201 |
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202 RI_INLINE void RI_INT16_SWAP(RIint16 &a, RIint16 &b) {RIint16 tmp = a; a = b; b = tmp;} |
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203 RI_INLINE int RI_INT_ABS(int a) { return (a >= 0) ? a : -a; } |
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204 RI_INLINE int RI_INT_MAX(int a, int b) { return (a > b) ? a : b; } |
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205 RI_INLINE int RI_INT_MIN(int a, int b) { return (a < b) ? a : b; } |
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206 RI_INLINE int RI_INT_CLAMP(int a, int l, int h) { return (a < l) ? l : (a > h) ? h : a; } |
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207 RI_INLINE void RI_INT_SWAP(int &a, int &b) { int tmp = a; a = b; b = tmp; } |
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208 RI_INLINE int RI_INT_MOD(int a, int b) { RI_ASSERT(b >= 0); if(!b) return 0; int i = a % b; if(i < 0) i += b; RI_ASSERT(i >= 0 && i < b); return i; } |
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209 RI_INLINE int RI_INT_ADDSATURATE(int a, int b) { RI_ASSERT(b >= 0); int r = a + b; return (r >= a) ? r : RI_INT32_MAX; } |
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210 |
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211 RI_INLINE RIfloat validateFloat(RIfloat f) |
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212 { |
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213 //this function is used for all floating point input values |
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214 if(RI_ISNAN(f)) return 0.0f; //convert NaN to zero |
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215 return RI_CLAMP(f, -RI_FLOAT_MAX, RI_FLOAT_MAX); //clamp +-inf to +-RIfloat max |
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216 } |
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217 |
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218 |
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219 |
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220 RI_INLINE int RI_SHL(int a, int sh) |
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221 { |
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222 RI_ASSERT(sh >= 0 && sh <= 31); |
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223 int r = a << sh; |
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224 RI_ASSERT(a >= 0 ? (r >= 0) : (r < 0)); |
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225 return r; |
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226 } |
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227 |
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228 RI_INLINE int RI_SAT_SHL(RIint32 a, int sh) |
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229 { |
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230 RI_ASSERT(sh >= 0 && sh <= 31); |
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231 |
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232 RIint64 r = ((RIint64)a) << sh; |
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233 |
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234 if (r > 0x7fffffff) |
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235 return 0x7fffffff; |
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236 else if (r < (long long)(int)0x80000000) |
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237 return 0x80000000; |
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238 |
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239 return (RIint32)r; |
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240 } |
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241 |
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242 RI_INLINE int RI_SHR(int a, int sh) |
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243 { |
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244 RI_ASSERT(sh >= 0 && sh <= 31); |
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245 int r = a >> sh; |
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246 return r; |
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247 } |
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248 |
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249 RI_INLINE RIfloat RI_FLOAT_TO_FX(RIfloat f, unsigned int n) { return (RIfloat)RI_ROUND_TO_INT(f * (RIfloat)RI_SHL(1, n)); } |
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250 |
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251 class Matrix3x3; |
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252 class Vector2; |
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253 class Vector3; |
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254 |
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255 //============================================================================================== |
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256 |
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257 //MatrixRxC, R = number of rows, C = number of columns |
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258 //indexing: matrix[row][column] |
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259 //Matrix3x3 inline functions cannot be inside the class because Vector3 is not defined yet when Matrix3x3 is defined |
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260 |
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261 class Matrix3x3 |
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262 { |
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263 public: |
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264 RI_INLINE Matrix3x3 (); //initialized to identity |
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265 RI_INLINE Matrix3x3 ( const Matrix3x3& m ); |
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266 RI_INLINE Matrix3x3 ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ); |
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267 RI_INLINE ~Matrix3x3 (); |
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268 RI_INLINE Matrix3x3& operator= ( const Matrix3x3& m ); |
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269 RI_INLINE Vector3& operator[] ( int i ); //returns a row vector |
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270 RI_INLINE const Vector3& operator[] ( int i ) const; |
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271 RI_INLINE void set ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ); |
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272 RI_INLINE const Vector3 getRow ( int i ) const; |
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273 RI_INLINE const Vector3 getColumn ( int i ) const; |
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274 RI_INLINE void setRow ( int i, const Vector3& v ); |
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275 RI_INLINE void setColumn ( int i, const Vector3& v ); |
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276 RI_INLINE void operator*= ( const Matrix3x3& m ); |
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277 RI_INLINE void operator*= ( RIfloat f ); |
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278 RI_INLINE void operator+= ( const Matrix3x3& m ); |
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279 RI_INLINE void operator-= ( const Matrix3x3& m ); |
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280 RI_INLINE const Matrix3x3 operator- () const; |
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281 RI_INLINE void identity (); |
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282 RI_INLINE void transpose (); |
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283 bool invert (); //if the matrix is singular, returns false and leaves it unmodified |
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284 RI_INLINE RIfloat det () const; |
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285 RI_INLINE bool isAffine () const; |
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286 RI_INLINE void assertValid () const; |
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287 RI_INLINE void validate (); |
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288 |
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289 private: |
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290 RIfloat matrix[3][3]; |
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291 }; |
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292 |
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293 //============================================================================================== |
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294 |
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295 class Vector2 |
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296 { |
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297 public: |
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298 RI_INLINE Vector2 () : x(0.0f), y(0.0f) {} |
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299 RI_INLINE Vector2 ( const Vector2& v ) : x(v.x), y(v.y) {} |
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300 RI_INLINE Vector2 ( RIfloat fx, RIfloat fy ) : x(fx), y(fy) {} |
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301 RI_INLINE ~Vector2 () {} |
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302 RI_INLINE Vector2& operator= ( const Vector2& v ) { x = v.x; y = v.y; return *this; } |
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303 RI_INLINE RIfloat& operator[] ( int i ) { RI_ASSERT(i>=0&&i<2); return (&x)[i]; } |
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304 RI_INLINE const RIfloat& operator[] ( int i ) const { RI_ASSERT(i>=0&&i<2); return (&x)[i]; } |
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305 RI_INLINE void set ( RIfloat fx, RIfloat fy ) { x = fx; y = fy; } |
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306 RI_INLINE void operator*= ( RIfloat f ) { x *= f; y *= f; } |
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307 RI_INLINE void operator+= ( const Vector2& v ) { x += v.x; y += v.y; } |
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308 RI_INLINE void operator-= ( const Vector2& v ) { x -= v.x; y -= v.y; } |
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309 RI_INLINE const Vector2 operator- () const { return Vector2(-x,-y); } |
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310 //if the vector is zero, returns false and leaves it unmodified |
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311 RI_INLINE bool normalize () { double l = (double)x*(double)x+(double)y*(double)y; if( l == 0.0 ) return false; l = 1.0 / sqrt(l); x = (RIfloat)((double)x * l); y = (RIfloat)((double)y * l); return true; } |
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312 RI_INLINE RIfloat length () const { return (RIfloat)sqrt((double)x*(double)x+(double)y*(double)y); } |
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313 RI_INLINE void scale ( const Vector2& v ) { x *= v.x; y *= v.y; } //component-wise scale |
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314 RI_INLINE void negate () { x = -x; y = -y; } |
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315 |
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316 RIfloat x,y; |
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317 }; |
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318 |
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319 //============================================================================================== |
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320 |
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321 class Vector3 |
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322 { |
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323 public: |
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324 RI_INLINE Vector3 () : x(0.0f), y(0.0f), z(0.0f) {} |
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325 RI_INLINE Vector3 ( const Vector3& v ) : x(v.x), y(v.y), z(v.z) {} |
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326 RI_INLINE Vector3 ( RIfloat fx, RIfloat fy, RIfloat fz ) : x(fx), y(fy), z(fz) {} |
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327 RI_INLINE ~Vector3 () {} |
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328 RI_INLINE Vector3& operator= ( const Vector3& v ) { x = v.x; y = v.y; z = v.z; return *this; } |
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329 RI_INLINE RIfloat& operator[] ( int i ) { RI_ASSERT(i>=0&&i<3); return (&x)[i]; } |
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330 RI_INLINE const RIfloat& operator[] ( int i ) const { RI_ASSERT(i>=0&&i<3); return (&x)[i]; } |
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331 RI_INLINE void set ( RIfloat fx, RIfloat fy, RIfloat fz ){ x = fx; y = fy; z = fz; } |
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332 RI_INLINE void operator*= ( RIfloat f ) { x *= f; y *= f; z *= f; } |
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333 RI_INLINE void operator+= ( const Vector3& v ) { x += v.x; y += v.y; z += v.z; } |
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334 RI_INLINE void operator-= ( const Vector3& v ) { x -= v.x; y -= v.y; z -= v.z; } |
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335 RI_INLINE const Vector3 operator- () const { return Vector3(-x,-y,-z); } |
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336 //if the vector is zero, returns false and leaves it unmodified |
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337 RI_INLINE bool normalize () { double l = (double)x*(double)x+(double)y*(double)y+(double)z*(double)z; if( l == 0.0 ) return false; l = 1.0 / sqrt(l); x = (RIfloat)((double)x * l); y = (RIfloat)((double)y * l); z = (RIfloat)((double)z * l); return true; } |
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338 RI_INLINE RIfloat length () const { return (RIfloat)sqrt((double)x*(double)x+(double)y*(double)y+(double)z*(double)z); } |
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339 RI_INLINE void scale ( const Vector3& v ) { x *= v.x; y *= v.y; z *= v.z; } //component-wise scale |
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340 RI_INLINE void negate () { x = -x; y = -y; z = -z; } |
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341 |
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342 RIfloat x,y,z; |
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343 }; |
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344 |
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345 //============================================================================================== |
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346 |
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347 //Vector2 global functions |
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348 RI_INLINE bool operator== ( const Vector2& v1, const Vector2& v2 ) { return (v1.x == v2.x) && (v1.y == v2.y); } |
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349 RI_INLINE bool operator!= ( const Vector2& v1, const Vector2& v2 ) { return (v1.x != v2.x) || (v1.y != v2.y); } |
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350 RI_INLINE bool isEqual ( const Vector2& v1, const Vector2& v2, RIfloat epsilon ) { return RI_SQR(v2.x-v1.x) + RI_SQR(v2.y-v1.y) <= epsilon*epsilon; } |
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351 RI_INLINE bool isZero ( const Vector2& v ) { return (v.x == 0.0f) && (v.y == 0.0f); } |
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352 RI_INLINE const Vector2 operator* ( RIfloat f, const Vector2& v ) { return Vector2(v.x*f,v.y*f); } |
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353 RI_INLINE const Vector2 operator* ( const Vector2& v, RIfloat f ) { return Vector2(v.x*f,v.y*f); } |
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354 RI_INLINE const Vector2 operator+ ( const Vector2& v1, const Vector2& v2 ) { return Vector2(v1.x+v2.x, v1.y+v2.y); } |
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355 RI_INLINE const Vector2 operator- ( const Vector2& v1, const Vector2& v2 ) { return Vector2(v1.x-v2.x, v1.y-v2.y); } |
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356 RI_INLINE RIfloat dot ( const Vector2& v1, const Vector2& v2 ) { return v1.x*v2.x+v1.y*v2.y; } |
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357 //if v is a zero vector, returns a zero vector |
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358 RI_INLINE const Vector2 normalize ( const Vector2& v ) { double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y; if( l != 0.0 ) l = 1.0 / sqrt(l); return Vector2((RIfloat)((double)v.x * l), (RIfloat)((double)v.y * l)); } |
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359 //if onThis is a zero vector, returns a zero vector |
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360 RI_INLINE const Vector2 project ( const Vector2& v, const Vector2& onThis ) { RIfloat l = dot(onThis,onThis); if( l != 0.0f ) l = dot(v, onThis)/l; return onThis * l; } |
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361 RI_INLINE const Vector2 lerp ( const Vector2& v1, const Vector2& v2, RIfloat ratio ) { return v1 + ratio * (v2 - v1); } |
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362 RI_INLINE const Vector2 scale ( const Vector2& v1, const Vector2& v2 ) { return Vector2(v1.x*v2.x, v1.y*v2.y); } |
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363 //matrix * column vector. The input vector2 is implicitly expanded to (x,y,1) |
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364 RI_INLINE const Vector2 affineTransform( const Matrix3x3& m, const Vector2& v ) { RI_ASSERT(m.isAffine()); return Vector2(v.x * m[0][0] + v.y * m[0][1] + m[0][2], v.x * m[1][0] + v.y * m[1][1] + m[1][2]); } |
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365 //matrix * column vector. The input vector2 is implicitly expanded to (x,y,0) |
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366 RI_INLINE const Vector2 affineTangentTransform(const Matrix3x3& m, const Vector2& v) { RI_ASSERT(m.isAffine()); return Vector2(v.x * m[0][0] + v.y * m[0][1], v.x * m[1][0] + v.y * m[1][1]); } |
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367 RI_INLINE const Vector2 perpendicularCW(const Vector2& v) { return Vector2(v.y, -v.x); } |
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368 RI_INLINE const Vector2 perpendicularCCW(const Vector2& v) { return Vector2(-v.y, v.x); } |
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369 RI_INLINE const Vector2 perpendicular(const Vector2& v, bool cw) { if(cw) return Vector2(v.y, -v.x); return Vector2(-v.y, v.x); } |
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370 |
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371 //============================================================================================== |
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372 |
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373 //Vector3 global functions |
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374 RI_INLINE bool operator== ( const Vector3& v1, const Vector3& v2 ) { return (v1.x == v2.x) && (v1.y == v2.y) && (v1.z == v2.z); } |
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375 RI_INLINE bool operator!= ( const Vector3& v1, const Vector3& v2 ) { return (v1.x != v2.x) || (v1.y != v2.y) || (v1.z != v2.z); } |
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376 RI_INLINE bool isEqual ( const Vector3& v1, const Vector3& v2, RIfloat epsilon ) { return RI_SQR(v2.x-v1.x) + RI_SQR(v2.y-v1.y) + RI_SQR(v2.z-v1.z) <= epsilon*epsilon; } |
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377 RI_INLINE const Vector3 operator* ( RIfloat f, const Vector3& v ) { return Vector3(v.x*f,v.y*f,v.z*f); } |
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378 RI_INLINE const Vector3 operator* ( const Vector3& v, RIfloat f ) { return Vector3(v.x*f,v.y*f,v.z*f); } |
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379 RI_INLINE const Vector3 operator+ ( const Vector3& v1, const Vector3& v2 ) { return Vector3(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z); } |
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380 RI_INLINE const Vector3 operator- ( const Vector3& v1, const Vector3& v2 ) { return Vector3(v1.x-v2.x, v1.y-v2.y, v1.z-v2.z); } |
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381 RI_INLINE RIfloat dot ( const Vector3& v1, const Vector3& v2 ) { return v1.x*v2.x+v1.y*v2.y+v1.z*v2.z; } |
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382 RI_INLINE const Vector3 cross ( const Vector3& v1, const Vector3& v2 ) { return Vector3( v1.y*v2.z-v1.z*v2.y, v1.z*v2.x-v1.x*v2.z, v1.x*v2.y-v1.y*v2.x ); } |
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383 //if v is a zero vector, returns a zero vector |
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384 RI_INLINE const Vector3 normalize ( const Vector3& v ) { double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y+(double)v.z*(double)v.z; if( l != 0.0 ) l = 1.0 / sqrt(l); return Vector3((RIfloat)((double)v.x * l), (RIfloat)((double)v.y * l), (RIfloat)((double)v.z * l)); } |
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385 RI_INLINE const Vector3 lerp ( const Vector3& v1, const Vector3& v2, RIfloat ratio ) { return v1 + ratio * (v2 - v1); } |
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386 RI_INLINE const Vector3 scale ( const Vector3& v1, const Vector3& v2 ) { return Vector3(v1.x*v2.x, v1.y*v2.y, v1.z*v2.z); } |
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387 |
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388 //============================================================================================== |
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389 |
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390 //matrix * column vector |
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391 RI_INLINE const Vector3 operator* ( const Matrix3x3& m, const Vector3& v) { return Vector3( v.x*m[0][0]+v.y*m[0][1]+v.z*m[0][2], v.x*m[1][0]+v.y*m[1][1]+v.z*m[1][2], v.x*m[2][0]+v.y*m[2][1]+v.z*m[2][2] ); } |
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392 |
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393 //============================================================================================== |
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394 |
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395 //Matrix3x3 global functions |
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396 RI_INLINE bool operator== ( const Matrix3x3& m1, const Matrix3x3& m2 ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) if( m1[i][j] != m2[i][j] ) return false; return true; } |
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397 RI_INLINE bool operator!= ( const Matrix3x3& m1, const Matrix3x3& m2 ) { return !(m1 == m2); } |
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398 RI_INLINE const Matrix3x3 operator* ( const Matrix3x3& m1, const Matrix3x3& m2 ) { Matrix3x3 t; for(int i=0;i<3;i++) for(int j=0;j<3;j++) t[i][j] = m1[i][0] * m2[0][j] + m1[i][1] * m2[1][j] + m1[i][2] * m2[2][j]; return t; } |
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399 RI_INLINE const Matrix3x3 operator* ( RIfloat f, const Matrix3x3& m ) { Matrix3x3 t(m); t *= f; return t; } |
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400 RI_INLINE const Matrix3x3 operator* ( const Matrix3x3& m, RIfloat f ) { Matrix3x3 t(m); t *= f; return t; } |
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401 RI_INLINE const Matrix3x3 operator+ ( const Matrix3x3& m1, const Matrix3x3& m2 ) { Matrix3x3 t(m1); t += m2; return t; } |
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402 RI_INLINE const Matrix3x3 operator- ( const Matrix3x3& m1, const Matrix3x3& m2 ) { Matrix3x3 t(m1); t -= m2; return t; } |
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403 RI_INLINE const Matrix3x3 transpose ( const Matrix3x3& m ) { Matrix3x3 t(m); t.transpose(); return t; } |
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404 // if the matrix is singular, returns it unmodified |
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405 RI_INLINE const Matrix3x3 invert ( const Matrix3x3& m ) { Matrix3x3 t(m); t.invert(); return t; } |
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406 |
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407 //============================================================================================== |
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408 |
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409 //Matrix3x3 inline functions (cannot be inside the class because Vector3 is not defined yet when Matrix3x3 is defined) |
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410 RI_INLINE Matrix3x3::Matrix3x3 () { identity(); } |
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411 RI_INLINE Matrix3x3::Matrix3x3 ( const Matrix3x3& m ) { *this = m; } |
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412 RI_INLINE Matrix3x3::Matrix3x3 ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ) { set(m00,m01,m02,m10,m11,m12,m20,m21,m22); } |
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413 RI_INLINE Matrix3x3::~Matrix3x3 () {} |
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414 RI_INLINE Matrix3x3& Matrix3x3::operator= ( const Matrix3x3& m ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] = m.matrix[i][j]; return *this; } |
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415 RI_INLINE Vector3& Matrix3x3::operator[] ( int i ) { RI_ASSERT(i>=0&&i<3); return (Vector3&)matrix[i][0]; } |
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416 RI_INLINE const Vector3& Matrix3x3::operator[] ( int i ) const { RI_ASSERT(i>=0&&i<3); return (const Vector3&)matrix[i][0]; } |
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417 RI_INLINE void Matrix3x3::set ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ) { matrix[0][0] = m00; matrix[0][1] = m01; matrix[0][2] = m02; matrix[1][0] = m10; matrix[1][1] = m11; matrix[1][2] = m12; matrix[2][0] = m20; matrix[2][1] = m21; matrix[2][2] = m22; } |
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418 RI_INLINE const Vector3 Matrix3x3::getRow ( int i ) const { RI_ASSERT(i>=0&&i<3); return Vector3(matrix[i][0], matrix[i][1], matrix[i][2]); } |
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419 RI_INLINE const Vector3 Matrix3x3::getColumn ( int i ) const { RI_ASSERT(i>=0&&i<3); return Vector3(matrix[0][i], matrix[1][i], matrix[2][i]); } |
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420 RI_INLINE void Matrix3x3::setRow ( int i, const Vector3& v ) { RI_ASSERT(i>=0&&i<3); matrix[i][0] = v.x; matrix[i][1] = v.y; matrix[i][2] = v.z; } |
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421 RI_INLINE void Matrix3x3::setColumn ( int i, const Vector3& v ) { RI_ASSERT(i>=0&&i<3); matrix[0][i] = v.x; matrix[1][i] = v.y; matrix[2][i] = v.z; } |
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422 RI_INLINE void Matrix3x3::operator*= ( const Matrix3x3& m ) { *this = *this * m; } |
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423 RI_INLINE void Matrix3x3::operator*= ( RIfloat f ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] *= f; } |
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424 RI_INLINE void Matrix3x3::operator+= ( const Matrix3x3& m ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] += m.matrix[i][j]; } |
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425 RI_INLINE void Matrix3x3::operator-= ( const Matrix3x3& m ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] -= m.matrix[i][j]; } |
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426 RI_INLINE const Matrix3x3 Matrix3x3::operator- () const { return Matrix3x3( -matrix[0][0],-matrix[0][1],-matrix[0][2], -matrix[1][0],-matrix[1][1],-matrix[1][2], -matrix[2][0],-matrix[2][1],-matrix[2][2]); } |
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427 RI_INLINE void Matrix3x3::identity () { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] = (i == j) ? 1.0f : 0.0f; } |
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428 RI_INLINE void Matrix3x3::transpose () { RI_SWAP(matrix[1][0], matrix[0][1]); RI_SWAP(matrix[2][0], matrix[0][2]); RI_SWAP(matrix[2][1], matrix[1][2]); } |
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429 RI_INLINE RIfloat Matrix3x3::det () const { return matrix[0][0] * (matrix[1][1]*matrix[2][2] - matrix[2][1]*matrix[1][2]) + matrix[0][1] * (matrix[2][0]*matrix[1][2] - matrix[1][0]*matrix[2][2]) + matrix[0][2] * (matrix[1][0]*matrix[2][1] - matrix[2][0]*matrix[1][1]); } |
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430 RI_INLINE bool Matrix3x3::isAffine () const { if(matrix[2][0] == 0.0f && matrix[2][1] == 0.0f && matrix[2][2] == 1.0f) return true; return false; } |
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431 |
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432 RI_INLINE void Matrix3x3::validate() |
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433 { |
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434 for (int i = 0; i < 3; i++) |
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435 for (int j = 0; j < 3; j++) |
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436 matrix[i][j] = validateFloat(matrix[i][j]); |
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437 } |
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438 |
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439 RI_INLINE void Matrix3x3::assertValid() const |
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440 { |
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441 #if defined(RI_DEBUG) |
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442 for (int i = 0; i < 3; i++) |
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443 for (int j = 0; j < 3; j++) |
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444 RI_ASSERT(!RI_ISNAN(matrix[i][j])); |
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445 #endif |
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446 } |
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447 |
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448 //============================================================================================== |
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449 |
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450 } //namespace OpenVGRI |
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451 |
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452 #endif /* __RIMATH_H */ |