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annotate utils/src/math.rs @ 791:a29122662cde

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utils: Simplify translate_2d and align Mat4 to 16 bytes This lowers the amount of instructions from 61 to 32 on PowerPC with AltiVec, and from 25 to 14 on amd64 with AVX2.
author Link Mauve <linkmauve@linkmauve.fr>
date Sat, 17 Jan 2026 14:19:58 +0100
parents d005f5927447
children
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1 //! Various helpers to deal with vectors and matrices.
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2
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3 use const_for::const_for;
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4
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5 /// A 4×4 f32 matrix type.
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6 #[repr(align(16))]
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7 pub struct Mat4 {
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8 inner: [[f32; 4]; 4]
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9 }
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10
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11 impl Mat4 {
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12 /// Create a new matrix from a set of 16 f32.
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13 pub const fn new(inner: [[f32; 4]; 4]) -> Mat4 {
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14 Mat4 {
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15 inner
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16 }
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17 }
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18
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19 const fn zero() -> Mat4 {
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20 Mat4 {
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21 inner: [[0.; 4]; 4]
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22 }
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23 }
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24
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25 const fn identity() -> Mat4 {
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26 Mat4 {
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27 inner: [[1., 0., 0., 0.],
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28 [0., 1., 0., 0.],
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29 [0., 0., 1., 0.],
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30 [0., 0., 0., 1.]]
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31 }
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32 }
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33
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34 /// Immutably borrow the array of f32 inside this matrix.
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35 pub const fn borrow_inner(&self) -> &[[f32; 4]; 4] {
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36 &self.inner
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37 }
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38
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39 /// Scale the matrix in 2D.
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40 pub const fn scale2d(&mut self, x: f32, y: f32) {
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41 const_for!(i in 0..4 => {
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42 self.inner[0][i] *= x;
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43 self.inner[1][i] *= y;
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44 });
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45 }
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46
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47 /// Flip the matrix.
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48 pub const fn flip(&mut self) {
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49 const_for!(i in 0..4 => {
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50 self.inner[0][i] = -self.inner[0][i];
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51 });
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52 }
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53
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54 /// Rotate the matrix around its x angle (in radians).
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55 pub fn rotate_x(&mut self, angle: f32) {
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56 let mut lines: [f32; 8] = [0.; 8];
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57 let cos_a = angle.cos();
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58 let sin_a = angle.sin();
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59 const_for!(i in 0..4 => {
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60 lines[ i] = self.inner[0][i];
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61 lines[4 + i] = self.inner[1][i];
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62 });
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63 const_for!(i in 0..4 => {
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64 self.inner[1][i] = cos_a * lines[i] - sin_a * lines[4+i];
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65 self.inner[2][i] = sin_a * lines[i] + cos_a * lines[4+i];
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66 });
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67 }
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68
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69 /// Rotate the matrix around its y angle (in radians).
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70 pub fn rotate_y(&mut self, angle: f32) {
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71 let mut lines: [f32; 8] = [0.; 8];
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72 let cos_a = angle.cos();
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73 let sin_a = angle.sin();
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74 const_for!(i in 0..4 => {
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75 lines[ i] = self.inner[0][i];
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76 lines[4 + i] = self.inner[2][i];
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77 });
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78 const_for!(i in 0..4 => {
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79 self.inner[0][i] = cos_a * lines[i] + sin_a * lines[4+i];
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80 self.inner[2][i] = -sin_a * lines[i] + cos_a * lines[4+i];
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81 });
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82 }
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83
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84 /// Rotate the matrix around its z angle (in radians).
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85 pub fn rotate_z(&mut self, angle: f32) {
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86 let mut lines: [f32; 8] = [0.; 8];
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87 let cos_a = angle.cos();
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88 let sin_a = angle.sin();
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89 const_for!(i in 0..4 => {
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90 lines[ i] = self.inner[0][i];
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91 lines[4 + i] = self.inner[1][i];
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92 });
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93 const_for!(i in 0..4 => {
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94 self.inner[0][i] = cos_a * lines[i] - sin_a * lines[4+i];
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95 self.inner[1][i] = sin_a * lines[i] + cos_a * lines[4+i];
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96 });
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97 }
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98
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99 /// Translate the matrix by a 3D offset.
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100 pub const fn translate(&mut self, offset: [f32; 3]) {
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101 let mut item: [f32; 3] = [0.; 3];
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102 const_for!(i in 0..3 => {
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103 item[i] = self.inner[3][i] * offset[i];
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104 });
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105 const_for!(i in 0..3 => {
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106 const_for!(j in 0..4 => {
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107 self.inner[i][j] += item[i];
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108 });
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109 });
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110 }
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111
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112 /// Translate the matrix by a 2D offset.
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113 pub const fn translate_2d(&mut self, mut x: f32, mut y: f32) {
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114 x *= self.inner[3][0];
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115 y *= self.inner[3][1];
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116 const_for!(i in 0..4 => {
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117 self.inner[0][i] += x;
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118 self.inner[1][i] += y;
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119 });
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120 }
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121 }
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122
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123 impl std::ops::Mul<Mat4> for Mat4 {
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124 type Output = Mat4;
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125 fn mul(self, rhs: Mat4) -> Mat4 {
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126 let mut tmp = Mat4::zero();
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127 const_for!(i in 0..4 => {
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128 const_for!(j in 0..4 => {
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129 const_for!(k in 0..4 => {
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130 tmp.inner[i][j] += self.inner[i][k] * rhs.inner[k][j];
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131 });
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132 });
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133 });
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134 tmp
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135 }
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136 }
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137
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138 /// Create an orthographic projection matrix.
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139 pub const fn ortho_2d(left: f32, right: f32, bottom: f32, top: f32) -> Mat4 {
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140 let mut mat = Mat4::identity();
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141 mat.inner[0][0] = 2. / (right - left);
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142 mat.inner[1][1] = 2. / (top - bottom);
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143 mat.inner[2][2] = -1.;
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144 mat.inner[3][0] = -(right + left) / (right - left);
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145 mat.inner[3][1] = -(top + bottom) / (top - bottom);
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146 mat
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147 }
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148
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149 /// Setup a camera view matrix.
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150 pub fn setup_camera(dx: f32, dy: f32, dz: f32) -> Mat4 {
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151 // Some explanations on the magic constants:
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152 // 192. = 384. / 2. = width / 2.
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153 // 224. = 448. / 2. = height / 2.
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154 // 835.979370 = 224./math.tan(math.radians(15)) = (height/2.)/math.tan(math.radians(fov/2))
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155 // This is so that objects on the (O, x, y) plane use pixel coordinates
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156 look_at([192., 224., -835.979370 * dz], [192. + dx, 224. - dy, 0.], [0., -1., 0.])
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157 }
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158
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159 /// Creates a perspective projection matrix.
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160 pub fn perspective(fov_y: f32, aspect: f32, z_near: f32, z_far: f32) -> Mat4 {
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161 let top = (fov_y / 2.).tan() * z_near;
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162 let bottom = -top;
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163 let left = -top * aspect;
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164 let right = top * aspect;
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165
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166 let mut mat = Mat4::identity();
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167 mat.inner[0][0] = (2. * z_near) / (right - left);
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168 mat.inner[1][1] = (2. * z_near) / (top - bottom);
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169 mat.inner[2][2] = -(z_far + z_near) / (z_far - z_near);
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170 mat.inner[2][3] = -1.;
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171 mat.inner[3][2] = -(2. * z_far * z_near) / (z_far - z_near);
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172 mat.inner[3][3] = 0.;
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173 mat
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174 }
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175
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176 type Vec3 = [f32; 3];
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177
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178 fn look_at(eye: Vec3, center: Vec3, up: Vec3) -> Mat4 {
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179 let f = normalize(sub(center, eye));
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180 let u = normalize(up);
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181 let s = normalize(cross(f, u));
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182 let u = cross(s, f);
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183
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184 Mat4::new([[s[0], u[0], -f[0], 0.],
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185 [s[1], u[1], -f[1], 0.],
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186 [s[2], u[2], -f[2], 0.],
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187 [-dot(s, eye), -dot(u, eye), dot(f, eye), 1.]])
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188 }
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189
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190 const fn sub(a: Vec3, b: Vec3) -> Vec3 {
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191 [a[0] - b[0],
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192 a[1] - b[1],
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193 a[2] - b[2]]
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194 }
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195
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196 fn normalize(vec: Vec3) -> Vec3 {
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197 let normal = 1. / (vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]).sqrt();
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198 [vec[0] * normal, vec[1] * normal, vec[2] * normal]
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199 }
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200
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201 const fn cross(a: Vec3, b: Vec3) -> Vec3 {
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202 [a[1] * b[2] - b[1] * a[2],
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203 a[2] * b[0] - b[2] * a[0],
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204 a[0] * b[1] - b[0] * a[1]]
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205 }
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206
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207 const fn dot(a: Vec3, b: Vec3) -> f32 {
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208 a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
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209 }