1 | // |
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2 | // Lol Engine |
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3 | // |
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4 | // Copyright: (c) 2010-2012 Sam Hocevar <sam@hocevar.net> |
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5 | // This program is free software; you can redistribute it and/or |
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6 | // modify it under the terms of the Do What The Fuck You Want To |
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7 | // Public License, Version 2, as published by Sam Hocevar. See |
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8 | // http://www.wtfpl.net/ for more details. |
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9 | // |
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10 | |
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11 | #if defined HAVE_CONFIG_H |
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12 | # include "config.h" |
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13 | #endif |
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14 | |
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15 | #if defined _XBOX |
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16 | # define _USE_MATH_DEFINES /* for M_PI */ |
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17 | # include <xtl.h> |
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18 | # undef near /* Fuck Microsoft */ |
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19 | # undef far /* Fuck Microsoft again */ |
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20 | #elif defined _WIN32 |
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21 | # define _USE_MATH_DEFINES /* for M_PI */ |
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22 | # define WIN32_LEAN_AND_MEAN |
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23 | # include <windows.h> |
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24 | # undef near /* Fuck Microsoft */ |
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25 | # undef far /* Fuck Microsoft again */ |
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26 | #endif |
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27 | |
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28 | #include <cstdlib> /* free() */ |
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29 | #include <cstring> /* strdup() */ |
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30 | |
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31 | #include <ostream> /* std::ostream */ |
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32 | |
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33 | #include "core.h" |
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34 | |
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35 | using namespace std; |
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36 | |
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37 | namespace lol |
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38 | { |
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39 | |
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40 | static inline float det2(float a, float b, |
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41 | float c, float d) |
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42 | { |
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43 | return a * d - b * c; |
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44 | } |
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45 | |
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46 | static inline float det3(float a, float b, float c, |
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47 | float d, float e, float f, |
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48 | float g, float h, float i) |
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49 | { |
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50 | return a * (e * i - h * f) |
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51 | + b * (f * g - i * d) |
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52 | + c * (d * h - g * e); |
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53 | } |
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54 | |
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55 | static inline float cofact(mat2 const &mat, int i, int j) |
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56 | { |
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57 | return mat[(i + 1) & 1][(j + 1) & 1] * (((i + j) & 1) ? -1.0f : 1.0f); |
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58 | } |
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59 | |
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60 | static inline float cofact(mat3 const &mat, int i, int j) |
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61 | { |
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62 | return det2(mat[(i + 1) % 3][(j + 1) % 3], |
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63 | mat[(i + 2) % 3][(j + 1) % 3], |
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64 | mat[(i + 1) % 3][(j + 2) % 3], |
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65 | mat[(i + 2) % 3][(j + 2) % 3]); |
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66 | } |
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67 | |
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68 | static inline float cofact(mat4 const &mat, int i, int j) |
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69 | { |
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70 | return det3(mat[(i + 1) & 3][(j + 1) & 3], |
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71 | mat[(i + 2) & 3][(j + 1) & 3], |
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72 | mat[(i + 3) & 3][(j + 1) & 3], |
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73 | mat[(i + 1) & 3][(j + 2) & 3], |
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74 | mat[(i + 2) & 3][(j + 2) & 3], |
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75 | mat[(i + 3) & 3][(j + 2) & 3], |
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76 | mat[(i + 1) & 3][(j + 3) & 3], |
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77 | mat[(i + 2) & 3][(j + 3) & 3], |
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78 | mat[(i + 3) & 3][(j + 3) & 3]) * (((i + j) & 1) ? -1.0f : 1.0f); |
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79 | } |
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80 | |
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81 | template<> float determinant(mat2 const &mat) |
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82 | { |
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83 | return mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]; |
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84 | } |
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85 | |
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86 | template<> mat2 transpose(mat2 const &mat) |
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87 | { |
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88 | mat2 ret; |
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89 | for (int j = 0; j < 2; j++) |
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90 | for (int i = 0; i < 2; i++) |
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91 | ret[j][i] = mat[i][j]; |
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92 | return ret; |
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93 | } |
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94 | |
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95 | template<> mat2 inverse(mat2 const &mat) |
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96 | { |
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97 | mat2 ret; |
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98 | float d = determinant(mat); |
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99 | if (d) |
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100 | { |
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101 | d = 1.0f / d; |
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102 | for (int j = 0; j < 2; j++) |
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103 | for (int i = 0; i < 2; i++) |
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104 | ret[j][i] = cofact(mat, i, j) * d; |
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105 | } |
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106 | return ret; |
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107 | } |
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108 | |
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109 | template<> float determinant(mat3 const &mat) |
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110 | { |
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111 | return det3(mat[0][0], mat[0][1], mat[0][2], |
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112 | mat[1][0], mat[1][1], mat[1][2], |
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113 | mat[2][0], mat[2][1], mat[2][2]); |
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114 | } |
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115 | |
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116 | template<> mat3 transpose(mat3 const &mat) |
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117 | { |
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118 | mat3 ret; |
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119 | for (int j = 0; j < 3; j++) |
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120 | for (int i = 0; i < 3; i++) |
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121 | ret[j][i] = mat[i][j]; |
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122 | return ret; |
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123 | } |
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124 | |
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125 | template<> mat3 inverse(mat3 const &mat) |
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126 | { |
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127 | mat3 ret; |
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128 | float d = determinant(mat); |
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129 | if (d) |
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130 | { |
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131 | d = 1.0f / d; |
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132 | for (int j = 0; j < 3; j++) |
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133 | for (int i = 0; i < 3; i++) |
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134 | ret[j][i] = cofact(mat, i, j) * d; |
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135 | } |
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136 | return ret; |
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137 | } |
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138 | |
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139 | template<> float determinant(mat4 const &mat) |
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140 | { |
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141 | float ret = 0; |
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142 | for (int n = 0; n < 4; n++) |
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143 | ret += mat[n][0] * cofact(mat, n, 0); |
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144 | return ret; |
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145 | } |
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146 | |
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147 | template<> mat4 transpose(mat4 const &mat) |
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148 | { |
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149 | mat4 ret; |
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150 | for (int j = 0; j < 4; j++) |
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151 | for (int i = 0; i < 4; i++) |
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152 | ret[j][i] = mat[i][j]; |
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153 | return ret; |
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154 | } |
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155 | |
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156 | template<> mat4 inverse(mat4 const &mat) |
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157 | { |
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158 | mat4 ret; |
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159 | float d = determinant(mat); |
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160 | if (d) |
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161 | { |
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162 | d = 1.0f / d; |
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163 | for (int j = 0; j < 4; j++) |
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164 | for (int i = 0; i < 4; i++) |
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165 | ret[j][i] = cofact(mat, i, j) * d; |
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166 | } |
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167 | return ret; |
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168 | } |
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169 | |
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170 | template<> void vec2::printf() const |
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171 | { |
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172 | Log::Debug("[ %6.6f %6.6f ]\n", x, y); |
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173 | } |
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174 | |
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175 | template<> void ivec2::printf() const |
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176 | { |
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177 | Log::Debug("[ %i %i ]\n", x, y); |
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178 | } |
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179 | |
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180 | template<> void cmplx::printf() const |
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181 | { |
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182 | Log::Debug("[ %6.6f %6.6f ]\n", x, y); |
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183 | } |
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184 | |
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185 | template<> void vec3::printf() const |
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186 | { |
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187 | Log::Debug("[ %6.6f %6.6f %6.6f ]\n", x, y, z); |
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188 | } |
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189 | |
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190 | template<> void ivec3::printf() const |
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191 | { |
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192 | Log::Debug("[ %i %i %i ]\n", x, y, z); |
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193 | } |
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194 | |
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195 | template<> void vec4::printf() const |
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196 | { |
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197 | Log::Debug("[ %6.6f %6.6f %6.6f %6.6f ]\n", x, y, z, w); |
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198 | } |
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199 | |
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200 | template<> void ivec4::printf() const |
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201 | { |
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202 | Log::Debug("[ %i %i %i %i ]\n", x, y, z, w); |
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203 | } |
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204 | |
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205 | template<> void quat::printf() const |
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206 | { |
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207 | Log::Debug("[ %6.6f %6.6f %6.6f %6.6f ]\n", w, x, y, z); |
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208 | } |
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209 | |
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210 | template<> void mat2::printf() const |
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211 | { |
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212 | mat2 const &p = *this; |
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213 | |
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214 | Log::Debug("[ %6.6f %6.6f\n", p[0][0], p[1][0]); |
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215 | Log::Debug(" %6.6f %6.6f ]\n", p[0][1], p[1][1]); |
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216 | } |
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217 | |
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218 | template<> void mat3::printf() const |
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219 | { |
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220 | mat3 const &p = *this; |
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221 | |
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222 | Log::Debug("[ %6.6f %6.6f %6.6f\n", p[0][0], p[1][0], p[2][0]); |
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223 | Log::Debug(" %6.6f %6.6f %6.6f\n", p[0][1], p[1][1], p[2][1]); |
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224 | Log::Debug(" %6.6f %6.6f %6.6f ]\n", p[0][2], p[1][2], p[2][2]); |
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225 | } |
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226 | |
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227 | template<> void mat4::printf() const |
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228 | { |
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229 | mat4 const &p = *this; |
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230 | |
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231 | Log::Debug("[ %6.6f %6.6f %6.6f %6.6f\n", |
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232 | p[0][0], p[1][0], p[2][0], p[3][0]); |
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233 | Log::Debug(" %6.6f %6.6f %6.6f %6.6f\n", |
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234 | p[0][1], p[1][1], p[2][1], p[3][1]); |
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235 | Log::Debug(" %6.6f %6.6f %6.6f %6.6f\n", |
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236 | p[0][2], p[1][2], p[2][2], p[3][2]); |
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237 | Log::Debug(" %6.6f %6.6f %6.6f %6.6f ]\n", |
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238 | p[0][3], p[1][3], p[2][3], p[3][3]); |
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239 | } |
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240 | |
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241 | template<> std::ostream &operator<<(std::ostream &stream, ivec2 const &v) |
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242 | { |
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243 | return stream << "(" << v.x << ", " << v.y << ")"; |
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244 | } |
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245 | |
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246 | template<> std::ostream &operator<<(std::ostream &stream, icmplx const &v) |
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247 | { |
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248 | return stream << "(" << v.x << ", " << v.y << ")"; |
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249 | } |
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250 | |
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251 | template<> std::ostream &operator<<(std::ostream &stream, ivec3 const &v) |
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252 | { |
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253 | return stream << "(" << v.x << ", " << v.y << ", " << v.z << ")"; |
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254 | } |
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255 | |
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256 | template<> std::ostream &operator<<(std::ostream &stream, ivec4 const &v) |
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257 | { |
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258 | return stream << "(" << v.x << ", " << v.y << ", " |
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259 | << v.z << ", " << v.w << ")"; |
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260 | } |
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261 | |
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262 | template<> std::ostream &operator<<(std::ostream &stream, iquat const &v) |
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263 | { |
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264 | return stream << "(" << v.x << ", " << v.y << ", " |
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265 | << v.z << ", " << v.w << ")"; |
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266 | } |
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267 | |
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268 | template<> std::ostream &operator<<(std::ostream &stream, vec2 const &v) |
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269 | { |
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270 | return stream << "(" << v.x << ", " << v.y << ")"; |
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271 | } |
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272 | |
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273 | template<> std::ostream &operator<<(std::ostream &stream, cmplx const &v) |
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274 | { |
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275 | return stream << "(" << v.x << ", " << v.y << ")"; |
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276 | } |
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277 | |
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278 | template<> std::ostream &operator<<(std::ostream &stream, vec3 const &v) |
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279 | { |
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280 | return stream << "(" << v.x << ", " << v.y << ", " << v.z << ")"; |
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281 | } |
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282 | |
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283 | template<> std::ostream &operator<<(std::ostream &stream, vec4 const &v) |
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284 | { |
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285 | return stream << "(" << v.x << ", " << v.y << ", " |
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286 | << v.z << ", " << v.w << ")"; |
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287 | } |
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288 | |
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289 | template<> std::ostream &operator<<(std::ostream &stream, quat const &v) |
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290 | { |
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291 | return stream << "(" << v.x << ", " << v.y << ", " |
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292 | << v.z << ", " << v.w << ")"; |
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293 | } |
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294 | |
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295 | template<> std::ostream &operator<<(std::ostream &stream, mat4 const &m) |
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296 | { |
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297 | stream << "((" << m[0][0] << ", " << m[1][0] |
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298 | << ", " << m[2][0] << ", " << m[3][0] << "), "; |
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299 | stream << "(" << m[0][1] << ", " << m[1][1] |
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300 | << ", " << m[2][1] << ", " << m[3][1] << "), "; |
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301 | stream << "(" << m[0][2] << ", " << m[1][2] |
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302 | << ", " << m[2][2] << ", " << m[3][2] << "), "; |
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303 | stream << "(" << m[0][3] << ", " << m[1][3] |
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304 | << ", " << m[2][3] << ", " << m[3][3] << "))"; |
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305 | return stream; |
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306 | } |
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307 | |
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308 | template<> mat3 mat3::scale(float x) |
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309 | { |
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310 | mat3 ret(1.0f); |
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311 | |
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312 | ret[0][0] = x; |
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313 | ret[1][1] = x; |
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314 | ret[2][2] = x; |
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315 | |
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316 | return ret; |
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317 | } |
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318 | |
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319 | template<> mat3 mat3::scale(float x, float y, float z) |
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320 | { |
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321 | mat3 ret(1.0f); |
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322 | |
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323 | ret[0][0] = x; |
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324 | ret[1][1] = y; |
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325 | ret[2][2] = z; |
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326 | |
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327 | return ret; |
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328 | } |
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329 | |
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330 | template<> mat3 mat3::scale(vec3 v) |
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331 | { |
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332 | return scale(v.x, v.y, v.z); |
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333 | } |
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334 | |
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335 | template<> mat4 mat4::translate(float x, float y, float z) |
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336 | { |
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337 | mat4 ret(1.0f); |
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338 | ret[3][0] = x; |
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339 | ret[3][1] = y; |
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340 | ret[3][2] = z; |
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341 | return ret; |
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342 | } |
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343 | |
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344 | template<> mat4 mat4::translate(vec3 v) |
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345 | { |
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346 | return translate(v.x, v.y, v.z); |
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347 | } |
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348 | |
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349 | template<> mat2 mat2::rotate(float angle) |
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350 | { |
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351 | angle *= (M_PI / 180.0f); |
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352 | |
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353 | float st = sin(angle); |
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354 | float ct = cos(angle); |
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355 | |
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356 | mat2 ret; |
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357 | |
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358 | ret[0][0] = ct; |
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359 | ret[0][1] = st; |
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360 | |
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361 | ret[1][0] = -st; |
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362 | ret[1][1] = ct; |
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363 | |
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364 | return ret; |
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365 | } |
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366 | |
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367 | template<> mat3 mat3::rotate(float angle, float x, float y, float z) |
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368 | { |
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369 | angle *= (M_PI / 180.0f); |
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370 | |
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371 | float st = sin(angle); |
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372 | float ct = cos(angle); |
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373 | |
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374 | float len = std::sqrt(x * x + y * y + z * z); |
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375 | float invlen = len ? 1.0f / len : 0.0f; |
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376 | x *= invlen; |
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377 | y *= invlen; |
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378 | z *= invlen; |
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379 | |
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380 | float mtx = (1.0f - ct) * x; |
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381 | float mty = (1.0f - ct) * y; |
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382 | float mtz = (1.0f - ct) * z; |
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383 | |
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384 | mat3 ret; |
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385 | |
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386 | ret[0][0] = x * mtx + ct; |
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387 | ret[0][1] = x * mty + st * z; |
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388 | ret[0][2] = x * mtz - st * y; |
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389 | |
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390 | ret[1][0] = y * mtx - st * z; |
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391 | ret[1][1] = y * mty + ct; |
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392 | ret[1][2] = y * mtz + st * x; |
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393 | |
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394 | ret[2][0] = z * mtx + st * y; |
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395 | ret[2][1] = z * mty - st * x; |
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396 | ret[2][2] = z * mtz + ct; |
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397 | |
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398 | return ret; |
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399 | } |
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400 | |
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401 | template<> mat3 mat3::rotate(float angle, vec3 v) |
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402 | { |
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403 | return rotate(angle, v.x, v.y, v.z); |
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404 | } |
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405 | |
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406 | template<> mat3::Mat3(quat const &q) |
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407 | { |
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408 | float n = norm(q); |
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409 | |
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410 | if (!n) |
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411 | { |
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412 | for (int j = 0; j < 3; j++) |
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413 | for (int i = 0; i < 3; i++) |
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414 | (*this)[i][j] = (i == j) ? 1.f : 0.f; |
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415 | return; |
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416 | } |
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417 | |
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418 | float s = 2.0f / n; |
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419 | |
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420 | v0[0] = 1.0f - s * (q.y * q.y + q.z * q.z); |
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421 | v0[1] = s * (q.x * q.y + q.z * q.w); |
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422 | v0[2] = s * (q.x * q.z - q.y * q.w); |
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423 | |
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424 | v1[0] = s * (q.x * q.y - q.z * q.w); |
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425 | v1[1] = 1.0f - s * (q.z * q.z + q.x * q.x); |
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426 | v1[2] = s * (q.y * q.z + q.x * q.w); |
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427 | |
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428 | v2[0] = s * (q.x * q.z + q.y * q.w); |
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429 | v2[1] = s * (q.y * q.z - q.x * q.w); |
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430 | v2[2] = 1.0f - s * (q.x * q.x + q.y * q.y); |
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431 | } |
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432 | |
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433 | template<> mat4::Mat4(quat const &q) |
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434 | { |
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435 | *this = mat4(mat3(q), 1.f); |
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436 | } |
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437 | |
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438 | static inline void MatrixToQuat(quat &that, mat3 const &m) |
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439 | { |
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440 | /* See http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/christian.htm for a version with no branches */ |
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441 | float t = m[0][0] + m[1][1] + m[2][2]; |
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442 | if (t > 0) |
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443 | { |
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444 | that.w = 0.5f * std::sqrt(1.0f + t); |
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445 | float s = 0.25f / that.w; |
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446 | that.x = s * (m[1][2] - m[2][1]); |
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447 | that.y = s * (m[2][0] - m[0][2]); |
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448 | that.z = s * (m[0][1] - m[1][0]); |
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449 | } |
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450 | else if (m[0][0] > m[1][1] && m[0][0] > m[2][2]) |
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451 | { |
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452 | that.x = 0.5f * std::sqrt(1.0f + m[0][0] - m[1][1] - m[2][2]); |
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453 | float s = 0.25f / that.x; |
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454 | that.y = s * (m[0][1] + m[1][0]); |
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455 | that.z = s * (m[2][0] + m[0][2]); |
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456 | that.w = s * (m[1][2] - m[2][1]); |
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457 | } |
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458 | else if (m[1][1] > m[2][2]) |
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459 | { |
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460 | that.y = 0.5f * std::sqrt(1.0f - m[0][0] + m[1][1] - m[2][2]); |
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461 | float s = 0.25f / that.y; |
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462 | that.x = s * (m[0][1] + m[1][0]); |
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463 | that.z = s * (m[1][2] + m[2][1]); |
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464 | that.w = s * (m[2][0] - m[0][2]); |
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465 | } |
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466 | else |
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467 | { |
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468 | that.z = 0.5f * std::sqrt(1.0f - m[0][0] - m[1][1] + m[2][2]); |
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469 | float s = 0.25f / that.z; |
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470 | that.x = s * (m[2][0] + m[0][2]); |
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471 | that.y = s * (m[1][2] + m[2][1]); |
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472 | that.w = s * (m[0][1] - m[1][0]); |
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473 | } |
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474 | } |
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475 | |
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476 | template<> quat::Quat(mat3 const &m) |
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477 | { |
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478 | MatrixToQuat(*this, m); |
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479 | } |
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480 | |
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481 | template<> quat::Quat(mat4 const &m) |
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482 | { |
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483 | MatrixToQuat(*this, mat3(m)); |
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484 | } |
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485 | |
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486 | template<> quat quat::rotate(float angle, vec3 const &v) |
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487 | { |
---|
488 | angle *= (M_PI / 360.0f); |
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489 | |
---|
490 | vec3 tmp = normalize(v) * sin(angle); |
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491 | |
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492 | return quat(cos(angle), tmp.x, tmp.y, tmp.z); |
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493 | } |
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494 | |
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495 | template<> quat quat::rotate(float angle, float x, float y, float z) |
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496 | { |
---|
497 | return quat::rotate(angle, vec3(x, y, z)); |
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498 | } |
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499 | |
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500 | template<> quat slerp(quat const &qa, quat const &qb, float f) |
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501 | { |
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502 | float const magnitude = lol::sqrt(sqlength(qa) * sqlength(qb)); |
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503 | float const product = lol::dot(qa, qb) / magnitude; |
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504 | |
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505 | /* If quaternions are equal or opposite, there is no need |
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506 | * to slerp anything, just return qa. */ |
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507 | if (std::abs(product) >= 1.0f) |
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508 | return qa; |
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509 | |
---|
510 | float const sign = (product < 0.0f) ? -1.0f : 1.0f; |
---|
511 | float const theta = lol::acos(sign * product); |
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512 | float const s1 = lol::sin(sign * f * theta); |
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513 | float const s0 = lol::sin((1.0f - f) * theta); |
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514 | |
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515 | /* This is the same as 1/sin(theta) */ |
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516 | float const d = 1.0f / lol::sqrt(1.f - product * product); |
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517 | |
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518 | return qa * (s0 * d) + qb * (s1 * d); |
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519 | } |
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520 | |
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521 | template<> vec3 vec3::toeuler(quat const &q) |
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522 | { |
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523 | float n = norm(q); |
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524 | |
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525 | if (!n) |
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526 | return vec3(0.f); |
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527 | |
---|
528 | vec3 ret(atan2(2.f * (q.w * q.x + q.y * q.z), |
---|
529 | 1.f - 2.f * (q.x * q.x + q.y * q.y)), |
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530 | asin(2.f * (q.w * q.y - q.z * q.x)), |
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531 | atan2(2.f * (q.w * q.z + q.y * q.x), |
---|
532 | 1.f - 2.f * (q.z * q.z + q.y * q.y))); |
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533 | |
---|
534 | return (180.0f / M_PI / n) * ret; |
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535 | } |
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536 | |
---|
537 | static inline mat3 mat3_fromeuler_generic(vec3 const &v, int i, int j, int k) |
---|
538 | { |
---|
539 | mat3 ret; |
---|
540 | |
---|
541 | vec3 radians = (M_PI / 180.0f) * v; |
---|
542 | float s0 = sin(radians[0]), c0 = cos(radians[0]); |
---|
543 | float s1 = sin(radians[1]), c1 = cos(radians[1]); |
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544 | float s2 = sin(radians[2]), c2 = cos(radians[2]); |
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545 | |
---|
546 | if (k == i) |
---|
547 | { |
---|
548 | k = 3 - i - j; |
---|
549 | |
---|
550 | ret[i][i] = c1; |
---|
551 | ret[j][i] = s1 * s2; |
---|
552 | ret[i][j] = s0 * s1; |
---|
553 | ret[j][j] = c0 * c2 - s0 * c1 * s2; |
---|
554 | ret[k][k] = - s0 * s2 + c0 * c1 * c2; |
---|
555 | |
---|
556 | if ((2 + i - j) % 3) |
---|
557 | { |
---|
558 | ret[k][i] = s1 * c2; |
---|
559 | ret[k][j] = - c0 * s2 - s0 * c1 * c2; |
---|
560 | ret[i][k] = - c0 * s1; |
---|
561 | ret[j][k] = s0 * c2 + c0 * c1 * s2; |
---|
562 | } |
---|
563 | else |
---|
564 | { |
---|
565 | ret[k][i] = - s1 * c2; |
---|
566 | ret[k][j] = c0 * s2 + s0 * c1 * c2; |
---|
567 | ret[i][k] = c0 * s1; |
---|
568 | ret[j][k] = - s0 * c2 - c0 * c1 * s2; |
---|
569 | } |
---|
570 | } |
---|
571 | else |
---|
572 | { |
---|
573 | ret[i][i] = c1 * c2; |
---|
574 | ret[k][k] = c0 * c1; |
---|
575 | |
---|
576 | if ((2 + i - j) % 3) |
---|
577 | { |
---|
578 | ret[j][i] = - c1 * s2; |
---|
579 | ret[k][i] = s1; |
---|
580 | |
---|
581 | ret[i][j] = c0 * s2 + s0 * s1 * c2; |
---|
582 | ret[j][j] = c0 * c2 - s0 * s1 * s2; |
---|
583 | ret[k][j] = - s0 * c1; |
---|
584 | |
---|
585 | ret[i][k] = s0 * s2 - c0 * s1 * c2; |
---|
586 | ret[j][k] = s0 * c2 + c0 * s1 * s2; |
---|
587 | } |
---|
588 | else |
---|
589 | { |
---|
590 | ret[j][i] = c1 * s2; |
---|
591 | ret[k][i] = - s1; |
---|
592 | |
---|
593 | ret[i][j] = - c0 * s2 + s0 * s1 * c2; |
---|
594 | ret[j][j] = c0 * c2 + s0 * s1 * s2; |
---|
595 | ret[k][j] = s0 * c1; |
---|
596 | |
---|
597 | ret[i][k] = s0 * s2 + c0 * s1 * c2; |
---|
598 | ret[j][k] = - s0 * c2 + c0 * s1 * s2; |
---|
599 | } |
---|
600 | } |
---|
601 | |
---|
602 | return ret; |
---|
603 | } |
---|
604 | |
---|
605 | static inline quat quat_fromeuler_generic(vec3 const &v, int i, int j, int k) |
---|
606 | { |
---|
607 | vec3 half_angles = (M_PI / 360.0f) * v; |
---|
608 | float s0 = sin(half_angles[0]), c0 = cos(half_angles[0]); |
---|
609 | float s1 = sin(half_angles[1]), c1 = cos(half_angles[1]); |
---|
610 | float s2 = sin(half_angles[2]), c2 = cos(half_angles[2]); |
---|
611 | |
---|
612 | quat ret; |
---|
613 | |
---|
614 | if (k == i) |
---|
615 | { |
---|
616 | k = 3 - i - j; |
---|
617 | |
---|
618 | ret[0] = c1 * (c0 * c2 - s0 * s2); |
---|
619 | ret[1 + i] = c1 * (c0 * s2 + s0 * c2); |
---|
620 | ret[1 + j] = s1 * (c0 * c2 + s0 * s2); |
---|
621 | ret[1 + k] = ((2 + i - j) % 3) ? s1 * (s0 * c2 - c0 * s2) |
---|
622 | : s1 * (c0 * s2 - s0 * c2); |
---|
623 | } |
---|
624 | else |
---|
625 | { |
---|
626 | vec4 v1(c0 * c1 * c2, s0 * c1 * c2, c0 * s1 * c2, c0 * c1 * s2); |
---|
627 | vec4 v2(s0 * s1 * s2, -c0 * s1 * s2, s0 * c1 * s2, -s0 * s1 * c2); |
---|
628 | |
---|
629 | if ((2 + i - j) % 3) |
---|
630 | v1 -= v2; |
---|
631 | else |
---|
632 | v1 += v2; |
---|
633 | |
---|
634 | ret[0] = v1[0]; |
---|
635 | ret[1 + i] = v1[1]; |
---|
636 | ret[1 + j] = v1[2]; |
---|
637 | ret[1 + k] = v1[3]; |
---|
638 | } |
---|
639 | |
---|
640 | return ret; |
---|
641 | } |
---|
642 | |
---|
643 | #define DEFINE_FROMEULER_GENERIC(name, i, j, k) \ |
---|
644 | template<> quat quat::fromeuler_##name(vec3 const &v) \ |
---|
645 | { \ |
---|
646 | return quat_fromeuler_generic(v, i, j, k); \ |
---|
647 | } \ |
---|
648 | \ |
---|
649 | template<> quat quat::fromeuler_##name(float phi, float theta, float psi) \ |
---|
650 | { \ |
---|
651 | return quat::fromeuler_##name(vec3(phi, theta, psi)); \ |
---|
652 | } \ |
---|
653 | \ |
---|
654 | template<> mat3 mat3::fromeuler_##name(vec3 const &v) \ |
---|
655 | { \ |
---|
656 | return mat3_fromeuler_generic(v, i, j, k); \ |
---|
657 | } \ |
---|
658 | \ |
---|
659 | template<> mat3 mat3::fromeuler_##name(float phi, float theta, float psi) \ |
---|
660 | { \ |
---|
661 | return mat3::fromeuler_##name(vec3(phi, theta, psi)); \ |
---|
662 | } \ |
---|
663 | \ |
---|
664 | template<> mat4 mat4::fromeuler_##name(vec3 const &v) \ |
---|
665 | { \ |
---|
666 | return mat4(mat3_fromeuler_generic(v, i, j, k), 1.f); \ |
---|
667 | } \ |
---|
668 | \ |
---|
669 | template<> mat4 mat4::fromeuler_##name(float phi, float theta, float psi) \ |
---|
670 | { \ |
---|
671 | return mat4::fromeuler_##name(vec3(phi, theta, psi)); \ |
---|
672 | } |
---|
673 | |
---|
674 | DEFINE_FROMEULER_GENERIC(xyx, 0, 1, 0) |
---|
675 | DEFINE_FROMEULER_GENERIC(xzx, 0, 2, 0) |
---|
676 | DEFINE_FROMEULER_GENERIC(yxy, 1, 0, 1) |
---|
677 | DEFINE_FROMEULER_GENERIC(yzy, 1, 2, 1) |
---|
678 | DEFINE_FROMEULER_GENERIC(zxz, 2, 0, 2) |
---|
679 | DEFINE_FROMEULER_GENERIC(zyz, 2, 1, 2) |
---|
680 | |
---|
681 | DEFINE_FROMEULER_GENERIC(xyz, 0, 1, 2) |
---|
682 | DEFINE_FROMEULER_GENERIC(xzy, 0, 2, 1) |
---|
683 | DEFINE_FROMEULER_GENERIC(yxz, 1, 0, 2) |
---|
684 | DEFINE_FROMEULER_GENERIC(yzx, 1, 2, 0) |
---|
685 | DEFINE_FROMEULER_GENERIC(zxy, 2, 0, 1) |
---|
686 | DEFINE_FROMEULER_GENERIC(zyx, 2, 1, 0) |
---|
687 | |
---|
688 | #undef DEFINE_FROMEULER_GENERIC |
---|
689 | |
---|
690 | template<> mat4 mat4::lookat(vec3 eye, vec3 center, vec3 up) |
---|
691 | { |
---|
692 | vec3 v3 = normalize(eye - center); |
---|
693 | vec3 v2 = normalize(up); |
---|
694 | vec3 v1 = normalize(cross(v2, v3)); |
---|
695 | v2 = cross(v3, v1); |
---|
696 | |
---|
697 | mat4 orient(1.0f); |
---|
698 | orient[0][0] = v1.x; |
---|
699 | orient[0][1] = v2.x; |
---|
700 | orient[0][2] = v3.x; |
---|
701 | orient[1][0] = v1.y; |
---|
702 | orient[1][1] = v2.y; |
---|
703 | orient[1][2] = v3.y; |
---|
704 | orient[2][0] = v1.z; |
---|
705 | orient[2][1] = v2.z; |
---|
706 | orient[2][2] = v3.z; |
---|
707 | |
---|
708 | return orient * mat4::translate(-eye); |
---|
709 | } |
---|
710 | |
---|
711 | template<> mat4 mat4::ortho(float left, float right, float bottom, |
---|
712 | float top, float near, float far) |
---|
713 | { |
---|
714 | float invrl = (right != left) ? 1.0f / (right - left) : 0.0f; |
---|
715 | float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f; |
---|
716 | float invfn = (far != near) ? 1.0f / (far - near) : 0.0f; |
---|
717 | |
---|
718 | mat4 ret(0.0f); |
---|
719 | ret[0][0] = 2.0f * invrl; |
---|
720 | ret[1][1] = 2.0f * invtb; |
---|
721 | ret[2][2] = -2.0f * invfn; |
---|
722 | ret[3][0] = - (right + left) * invrl; |
---|
723 | ret[3][1] = - (top + bottom) * invtb; |
---|
724 | ret[3][2] = - (far + near) * invfn; |
---|
725 | ret[3][3] = 1.0f; |
---|
726 | return ret; |
---|
727 | } |
---|
728 | |
---|
729 | template<> mat4 mat4::ortho(float width, float height, |
---|
730 | float near, float far) |
---|
731 | { |
---|
732 | return mat4::ortho(-0.5f * width, 0.5f * width, |
---|
733 | -0.5f * height, 0.5f * height, near, far); |
---|
734 | } |
---|
735 | |
---|
736 | template<> mat4 mat4::frustum(float left, float right, float bottom, |
---|
737 | float top, float near, float far) |
---|
738 | { |
---|
739 | float invrl = (right != left) ? 1.0f / (right - left) : 0.0f; |
---|
740 | float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f; |
---|
741 | float invfn = (far != near) ? 1.0f / (far - near) : 0.0f; |
---|
742 | |
---|
743 | mat4 ret(0.0f); |
---|
744 | ret[0][0] = 2.0f * near * invrl; |
---|
745 | ret[1][1] = 2.0f * near * invtb; |
---|
746 | ret[2][0] = (right + left) * invrl; |
---|
747 | ret[2][1] = (top + bottom) * invtb; |
---|
748 | ret[2][2] = - (far + near) * invfn; |
---|
749 | ret[2][3] = -1.0f; |
---|
750 | ret[3][2] = -2.0f * far * near * invfn; |
---|
751 | return ret; |
---|
752 | } |
---|
753 | |
---|
754 | template<> mat4 mat4::perspective(float fov_y, float width, |
---|
755 | float height, float near, float far) |
---|
756 | { |
---|
757 | fov_y *= (M_PI / 180.0f); |
---|
758 | |
---|
759 | float t2 = tanf(fov_y * 0.5f); |
---|
760 | float t1 = t2 * width / height; |
---|
761 | |
---|
762 | return frustum(-near * t1, near * t1, -near * t2, near * t2, near, far); |
---|
763 | } |
---|
764 | |
---|
765 | } /* namespace lol */ |
---|
766 | |
---|