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://sam.zoy.org/projects/COPYING.WTFPL 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 <cmath> /* for M_PI */ |
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29 | #include <cstdlib> /* free() */ |
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30 | #include <cstring> /* strdup() */ |
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31 | |
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32 | #include "core.h" |
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33 | |
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34 | using namespace std; |
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35 | |
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36 | namespace lol |
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37 | { |
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38 | |
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39 | static inline float det2(float a, float b, |
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40 | float c, float d) |
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41 | { |
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42 | return a * d - b * c; |
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43 | } |
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44 | |
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45 | static inline float det3(float a, float b, float c, |
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46 | float d, float e, float f, |
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47 | float g, float h, float i) |
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48 | { |
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49 | return a * (e * i - h * f) |
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50 | + b * (f * g - i * d) |
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51 | + c * (d * h - g * e); |
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52 | } |
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53 | |
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54 | static inline float cofact(mat2 const &mat, int i, int j) |
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55 | { |
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56 | return mat[(i + 1) & 1][(j + 1) & 1] * (((i + j) & 1) ? -1.0f : 1.0f); |
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57 | } |
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58 | |
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59 | static inline float cofact(mat3 const &mat, int i, int j) |
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60 | { |
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61 | return det2(mat[(i + 1) % 3][(j + 1) % 3], |
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62 | mat[(i + 2) % 3][(j + 1) % 3], |
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63 | mat[(i + 1) % 3][(j + 2) % 3], |
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64 | mat[(i + 2) % 3][(j + 2) % 3]); |
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65 | } |
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66 | |
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67 | static inline float cofact(mat4 const &mat, int i, int j) |
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68 | { |
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69 | return det3(mat[(i + 1) & 3][(j + 1) & 3], |
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70 | mat[(i + 2) & 3][(j + 1) & 3], |
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71 | mat[(i + 3) & 3][(j + 1) & 3], |
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72 | mat[(i + 1) & 3][(j + 2) & 3], |
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73 | mat[(i + 2) & 3][(j + 2) & 3], |
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74 | mat[(i + 3) & 3][(j + 2) & 3], |
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75 | mat[(i + 1) & 3][(j + 3) & 3], |
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76 | mat[(i + 2) & 3][(j + 3) & 3], |
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77 | mat[(i + 3) & 3][(j + 3) & 3]) * (((i + j) & 1) ? -1.0f : 1.0f); |
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78 | } |
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79 | |
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80 | template<> float determinant(mat2 const &mat) |
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81 | { |
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82 | return mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]; |
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83 | } |
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84 | |
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85 | template<> mat2 transpose(mat2 const &mat) |
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86 | { |
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87 | mat2 ret; |
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88 | for (int j = 0; j < 2; j++) |
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89 | for (int i = 0; i < 2; i++) |
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90 | ret[j][i] = mat[i][j]; |
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91 | return ret; |
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92 | } |
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93 | |
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94 | template<> mat2 inverse(mat2 const &mat) |
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95 | { |
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96 | mat2 ret; |
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97 | float d = determinant(mat); |
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98 | if (d) |
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99 | { |
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100 | d = 1.0f / d; |
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101 | for (int j = 0; j < 2; j++) |
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102 | for (int i = 0; i < 2; i++) |
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103 | ret[j][i] = cofact(mat, i, j) * d; |
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104 | } |
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105 | return ret; |
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106 | } |
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107 | |
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108 | template<> float determinant(mat3 const &mat) |
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109 | { |
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110 | return det3(mat[0][0], mat[0][1], mat[0][2], |
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111 | mat[1][0], mat[1][1], mat[1][2], |
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112 | mat[2][0], mat[2][1], mat[2][2]); |
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113 | } |
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114 | |
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115 | template<> mat3 transpose(mat3 const &mat) |
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116 | { |
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117 | mat3 ret; |
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118 | for (int j = 0; j < 3; j++) |
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119 | for (int i = 0; i < 3; i++) |
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120 | ret[j][i] = mat[i][j]; |
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121 | return ret; |
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122 | } |
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123 | |
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124 | template<> mat3 inverse(mat3 const &mat) |
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125 | { |
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126 | mat3 ret; |
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127 | float d = determinant(mat); |
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128 | if (d) |
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129 | { |
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130 | d = 1.0f / d; |
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131 | for (int j = 0; j < 3; j++) |
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132 | for (int i = 0; i < 3; i++) |
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133 | ret[j][i] = cofact(mat, i, j) * d; |
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134 | } |
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135 | return ret; |
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136 | } |
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137 | |
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138 | template<> float determinant(mat4 const &mat) |
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139 | { |
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140 | float ret = 0; |
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141 | for (int n = 0; n < 4; n++) |
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142 | ret += mat[n][0] * cofact(mat, n, 0); |
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143 | return ret; |
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144 | } |
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145 | |
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146 | template<> mat4 transpose(mat4 const &mat) |
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147 | { |
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148 | mat4 ret; |
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149 | for (int j = 0; j < 4; j++) |
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150 | for (int i = 0; i < 4; i++) |
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151 | ret[j][i] = mat[i][j]; |
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152 | return ret; |
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153 | } |
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154 | |
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155 | template<> mat4 inverse(mat4 const &mat) |
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156 | { |
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157 | mat4 ret; |
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158 | float d = determinant(mat); |
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159 | if (d) |
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160 | { |
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161 | d = 1.0f / d; |
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162 | for (int j = 0; j < 4; j++) |
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163 | for (int i = 0; i < 4; i++) |
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164 | ret[j][i] = cofact(mat, i, j) * d; |
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165 | } |
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166 | return ret; |
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167 | } |
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168 | |
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169 | template<> void vec2::printf() const |
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170 | { |
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171 | Log::Debug("[ %6.6f %6.6f ]\n", x, y); |
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172 | } |
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173 | |
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174 | template<> void ivec2::printf() const |
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175 | { |
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176 | Log::Debug("[ %i %i ]\n", x, y); |
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177 | } |
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178 | |
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179 | template<> void cmplx::printf() const |
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180 | { |
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181 | Log::Debug("[ %6.6f %6.6f ]\n", x, y); |
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182 | } |
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183 | |
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184 | template<> void vec3::printf() const |
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185 | { |
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186 | Log::Debug("[ %6.6f %6.6f %6.6f ]\n", x, y, z); |
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187 | } |
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188 | |
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189 | template<> void ivec3::printf() const |
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190 | { |
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191 | Log::Debug("[ %i %i %i ]\n", x, y, z); |
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192 | } |
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193 | |
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194 | template<> void vec4::printf() const |
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195 | { |
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196 | Log::Debug("[ %6.6f %6.6f %6.6f %6.6f ]\n", x, y, z, w); |
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197 | } |
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198 | |
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199 | template<> void ivec4::printf() const |
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200 | { |
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201 | Log::Debug("[ %i %i %i %i ]\n", x, y, z, w); |
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202 | } |
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203 | |
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204 | template<> void quat::printf() const |
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205 | { |
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206 | Log::Debug("[ %6.6f %6.6f %6.6f %6.6f ]\n", w, x, y, z); |
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207 | } |
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208 | |
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209 | template<> void mat2::printf() const |
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210 | { |
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211 | mat2 const &p = *this; |
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212 | |
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213 | Log::Debug("[ %6.6f %6.6f\n", p[0][0], p[1][0]); |
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214 | Log::Debug(" %6.6f %6.6f ]\n", p[0][1], p[1][1]); |
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215 | } |
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216 | |
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217 | template<> void mat3::printf() const |
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218 | { |
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219 | mat3 const &p = *this; |
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220 | |
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221 | Log::Debug("[ %6.6f %6.6f %6.6f\n", p[0][0], p[1][0], p[2][0]); |
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222 | Log::Debug(" %6.6f %6.6f %6.6f\n", p[0][1], p[1][1], p[2][1]); |
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223 | Log::Debug(" %6.6f %6.6f %6.6f ]\n", p[0][2], p[1][2], p[2][2]); |
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224 | } |
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225 | |
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226 | template<> void mat4::printf() const |
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227 | { |
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228 | mat4 const &p = *this; |
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229 | |
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230 | Log::Debug("[ %6.6f %6.6f %6.6f %6.6f\n", |
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231 | p[0][0], p[1][0], p[2][0], p[3][0]); |
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232 | Log::Debug(" %6.6f %6.6f %6.6f %6.6f\n", |
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233 | p[0][1], p[1][1], p[2][1], p[3][1]); |
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234 | Log::Debug(" %6.6f %6.6f %6.6f %6.6f\n", |
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235 | p[0][2], p[1][2], p[2][2], p[3][2]); |
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236 | Log::Debug(" %6.6f %6.6f %6.6f %6.6f ]\n", |
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237 | p[0][3], p[1][3], p[2][3], p[3][3]); |
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238 | } |
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239 | |
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240 | #if !defined __ANDROID__ |
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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 | #endif |
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308 | |
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309 | template<> mat3 mat3::scale(float x, float y, float z) |
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310 | { |
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311 | mat3 ret(1.0f); |
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312 | |
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313 | ret[0][0] = x; |
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314 | ret[1][1] = y; |
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315 | ret[2][2] = z; |
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316 | |
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317 | return ret; |
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318 | } |
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319 | |
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320 | template<> mat3 mat3::scale(vec3 v) |
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321 | { |
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322 | return scale(v.x, v.y, v.z); |
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323 | } |
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324 | |
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325 | template<> mat4 mat4::translate(float x, float y, float z) |
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326 | { |
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327 | mat4 ret(1.0f); |
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328 | ret[3][0] = x; |
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329 | ret[3][1] = y; |
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330 | ret[3][2] = z; |
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331 | return ret; |
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332 | } |
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333 | |
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334 | template<> mat4 mat4::translate(vec3 v) |
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335 | { |
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336 | return translate(v.x, v.y, v.z); |
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337 | } |
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338 | |
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339 | template<> mat2 mat2::rotate(float angle) |
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340 | { |
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341 | angle *= (M_PI / 180.0f); |
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342 | |
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343 | float st = std::sin(angle); |
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344 | float ct = std::cos(angle); |
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345 | |
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346 | mat2 ret; |
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347 | |
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348 | ret[0][0] = ct; |
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349 | ret[0][1] = st; |
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350 | |
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351 | ret[1][0] = -st; |
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352 | ret[1][1] = ct; |
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353 | |
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354 | return ret; |
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355 | } |
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356 | |
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357 | template<> mat3 mat3::rotate(float angle, float x, float y, float z) |
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358 | { |
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359 | angle *= (M_PI / 180.0f); |
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360 | |
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361 | float st = std::sin(angle); |
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362 | float ct = std::cos(angle); |
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363 | |
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364 | float len = sqrtf(x * x + y * y + z * z); |
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365 | float invlen = len ? 1.0f / len : 0.0f; |
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366 | x *= invlen; |
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367 | y *= invlen; |
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368 | z *= invlen; |
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369 | |
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370 | float mtx = (1.0f - ct) * x; |
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371 | float mty = (1.0f - ct) * y; |
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372 | float mtz = (1.0f - ct) * z; |
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373 | |
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374 | mat3 ret; |
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375 | |
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376 | ret[0][0] = x * mtx + ct; |
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377 | ret[0][1] = x * mty + st * z; |
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378 | ret[0][2] = x * mtz - st * y; |
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379 | |
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380 | ret[1][0] = y * mtx - st * z; |
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381 | ret[1][1] = y * mty + ct; |
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382 | ret[1][2] = y * mtz + st * x; |
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383 | |
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384 | ret[2][0] = z * mtx + st * y; |
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385 | ret[2][1] = z * mty - st * x; |
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386 | ret[2][2] = z * mtz + ct; |
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387 | |
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388 | return ret; |
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389 | } |
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390 | |
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391 | template<> mat3 mat3::rotate(float angle, vec3 v) |
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392 | { |
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393 | return rotate(angle, v.x, v.y, v.z); |
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394 | } |
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395 | |
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396 | template<> mat3 mat3::rotate(quat q) |
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397 | { |
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398 | float n = norm(q); |
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399 | |
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400 | if (!n) |
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401 | return mat3(1.0f); |
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402 | |
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403 | mat3 ret; |
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404 | float s = 2.0f / n; |
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405 | |
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406 | ret[0][0] = 1.0f - s * (q.y * q.y + q.z * q.z); |
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407 | ret[0][1] = s * (q.x * q.y - q.z * q.w); |
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408 | ret[0][2] = s * (q.x * q.z + q.y * q.w); |
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409 | |
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410 | ret[1][0] = s * (q.x * q.y + q.z * q.w); |
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411 | ret[1][1] = 1.0f - s * (q.z * q.z + q.x * q.x); |
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412 | ret[1][2] = s * (q.y * q.z - q.x * q.w); |
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413 | |
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414 | ret[2][0] = s * (q.x * q.z - q.y * q.w); |
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415 | ret[2][1] = s * (q.y * q.z + q.x * q.w); |
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416 | ret[2][2] = 1.0f - s * (q.x * q.x + q.y * q.y); |
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417 | |
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418 | return ret; |
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419 | } |
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420 | |
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421 | template<> quat::Quat(mat4 const &m) |
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422 | { |
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423 | /* See http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/christian.htm for a version with no branches */ |
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424 | float t = m[0][0] + m[1][1] + m[2][2]; |
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425 | if (t > 0) |
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426 | { |
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427 | w = 0.5f * sqrtf(1.0f + t); |
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428 | float s = 0.25f / w; |
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429 | x = s * (m[2][1] - m[1][2]); |
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430 | y = s * (m[0][2] - m[2][0]); |
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431 | z = s * (m[1][0] - m[0][1]); |
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432 | } |
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433 | else if (m[0][0] > m[1][1] && m[0][0] > m[2][2]) |
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434 | { |
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435 | x = 0.5f * sqrtf(1.0f + m[0][0] - m[1][1] - m[2][2]); |
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436 | float s = 0.25f / x; |
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437 | y = s * (m[1][0] + m[0][1]); |
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438 | z = s * (m[0][2] + m[2][0]); |
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439 | w = s * (m[2][1] - m[1][2]); |
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440 | } |
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441 | else if (m[1][1] > m[2][2]) |
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442 | { |
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443 | y = 0.5f * sqrtf(1.0f - m[0][0] + m[1][1] - m[2][2]); |
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444 | float s = 0.25f / y; |
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445 | x = s * (m[1][0] + m[0][1]); |
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446 | z = s * (m[2][1] + m[1][2]); |
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447 | w = s * (m[0][2] - m[2][0]); |
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448 | } |
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449 | else |
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450 | { |
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451 | z = 0.5f * sqrtf(1.0f - m[0][0] - m[1][1] + m[2][2]); |
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452 | float s = 0.25f / z; |
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453 | x = s * (m[0][2] + m[2][0]); |
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454 | y = s * (m[2][1] + m[1][2]); |
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455 | w = s * (m[1][0] - m[0][1]); |
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456 | } |
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457 | } |
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458 | |
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459 | template<> quat quat::rotate(float angle, vec3 const &v) |
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460 | { |
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461 | angle *= (M_PI / 360.0f); |
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462 | |
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463 | vec3 tmp = normalize(v) * std::sin(angle); |
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464 | |
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465 | return quat(tmp.x, tmp.y, tmp.z, std::cos(angle)); |
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466 | } |
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467 | |
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468 | template<> quat quat::rotate(float angle, float x, float y, float z) |
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469 | { |
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470 | return quat::rotate(angle, vec3(x, y, z)); |
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471 | } |
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472 | |
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473 | template<> mat4 mat4::lookat(vec3 eye, vec3 center, vec3 up) |
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474 | { |
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475 | vec3 v3 = normalize(eye - center); |
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476 | vec3 v2 = normalize(up); |
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477 | vec3 v1 = normalize(cross(v2, v3)); |
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478 | v2 = cross(v3, v1); |
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479 | |
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480 | mat4 orient(1.0f); |
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481 | orient[0][0] = v1.x; |
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482 | orient[0][1] = v2.x; |
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483 | orient[0][2] = v3.x; |
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484 | orient[1][0] = v1.y; |
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485 | orient[1][1] = v2.y; |
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486 | orient[1][2] = v3.y; |
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487 | orient[2][0] = v1.z; |
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488 | orient[2][1] = v2.z; |
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489 | orient[2][2] = v3.z; |
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490 | |
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491 | return orient * mat4::translate(-eye); |
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492 | } |
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493 | |
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494 | template<> mat4 mat4::ortho(float left, float right, float bottom, |
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495 | float top, float near, float far) |
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496 | { |
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497 | float invrl = (right != left) ? 1.0f / (right - left) : 0.0f; |
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498 | float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f; |
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499 | float invfn = (far != near) ? 1.0f / (far - near) : 0.0f; |
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500 | |
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501 | mat4 ret(0.0f); |
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502 | ret[0][0] = 2.0f * invrl; |
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503 | ret[1][1] = 2.0f * invtb; |
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504 | ret[2][2] = -2.0f * invfn; |
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505 | ret[3][0] = - (right + left) * invrl; |
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506 | ret[3][1] = - (top + bottom) * invtb; |
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507 | ret[3][2] = - (far + near) * invfn; |
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508 | ret[3][3] = 1.0f; |
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509 | return ret; |
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510 | } |
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511 | |
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512 | template<> mat4 mat4::frustum(float left, float right, float bottom, |
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513 | float top, float near, float far) |
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514 | { |
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515 | float invrl = (right != left) ? 1.0f / (right - left) : 0.0f; |
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516 | float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f; |
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517 | float invfn = (far != near) ? 1.0f / (far - near) : 0.0f; |
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518 | |
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519 | mat4 ret(0.0f); |
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520 | ret[0][0] = 2.0f * near * invrl; |
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521 | ret[1][1] = 2.0f * near * invtb; |
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522 | ret[2][0] = (right + left) * invrl; |
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523 | ret[2][1] = (top + bottom) * invtb; |
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524 | ret[2][2] = - (far + near) * invfn; |
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525 | ret[2][3] = -1.0f; |
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526 | ret[3][2] = -2.0f * far * near * invfn; |
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527 | return ret; |
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528 | } |
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529 | |
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530 | template<> mat4 mat4::perspective(float fov_y, float width, |
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531 | float height, float near, float far) |
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532 | { |
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533 | fov_y *= (M_PI / 180.0f); |
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534 | |
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535 | float t2 = tanf(fov_y * 0.5f); |
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536 | float t1 = t2 * width / height; |
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537 | |
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538 | return frustum(-near * t1, near * t1, -near * t2, near * t2, near, far); |
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539 | } |
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540 | |
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541 | } /* namespace lol */ |
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542 | |
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