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annotate utils/src/math.rs @ 790:d005f5927447

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utils: Use const_for to make more const fn
author Link Mauve <linkmauve@linkmauve.fr>
date Sat, 17 Jan 2026 14:12:08 +0100
parents b5bca9274335
children a29122662cde
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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 pub struct Mat4 {
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7 inner: [[f32; 4]; 4]
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8 }
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9
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10 impl Mat4 {
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11 /// Create a new matrix from a set of 16 f32.
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12 pub const fn new(inner: [[f32; 4]; 4]) -> Mat4 {
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13 Mat4 {
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14 inner
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15 }
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16 }
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17
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18 const fn zero() -> Mat4 {
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19 Mat4 {
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20 inner: [[0.; 4]; 4]
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21 }
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22 }
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23
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24 const fn identity() -> Mat4 {
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25 Mat4 {
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26 inner: [[1., 0., 0., 0.],
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27 [0., 1., 0., 0.],
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28 [0., 0., 1., 0.],
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29 [0., 0., 0., 1.]]
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30 }
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31 }
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32
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33 /// Immutably borrow the array of f32 inside this matrix.
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34 pub const fn borrow_inner(&self) -> &[[f32; 4]; 4] {
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35 &self.inner
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36 }
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37
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38 /// Scale the matrix in 2D.
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39 pub const fn scale2d(&mut self, x: f32, y: f32) {
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40 const_for!(i in 0..4 => {
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41 self.inner[0][i] *= x;
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42 self.inner[1][i] *= y;
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43 });
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44 }
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45
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46 /// Flip the matrix.
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47 pub const fn flip(&mut self) {
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48 const_for!(i in 0..4 => {
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49 self.inner[0][i] = -self.inner[0][i];
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50 });
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51 }
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52
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53 /// Rotate the matrix around its x angle (in radians).
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54 pub fn rotate_x(&mut self, angle: f32) {
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55 let mut lines: [f32; 8] = [0.; 8];
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56 let cos_a = angle.cos();
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57 let sin_a = angle.sin();
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58 const_for!(i in 0..4 => {
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59 lines[ i] = self.inner[0][i];
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60 lines[4 + i] = self.inner[1][i];
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61 });
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62 const_for!(i in 0..4 => {
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63 self.inner[1][i] = cos_a * lines[i] - sin_a * lines[4+i];
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64 self.inner[2][i] = sin_a * lines[i] + cos_a * lines[4+i];
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65 });
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66 }
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67
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68 /// Rotate the matrix around its y angle (in radians).
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69 pub fn rotate_y(&mut self, angle: f32) {
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70 let mut lines: [f32; 8] = [0.; 8];
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71 let cos_a = angle.cos();
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72 let sin_a = angle.sin();
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73 const_for!(i in 0..4 => {
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74 lines[ i] = self.inner[0][i];
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75 lines[4 + i] = self.inner[2][i];
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76 });
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77 const_for!(i in 0..4 => {
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78 self.inner[0][i] = cos_a * lines[i] + sin_a * lines[4+i];
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79 self.inner[2][i] = -sin_a * lines[i] + cos_a * lines[4+i];
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80 });
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81 }
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82
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83 /// Rotate the matrix around its z angle (in radians).
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84 pub fn rotate_z(&mut self, angle: f32) {
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85 let mut lines: [f32; 8] = [0.; 8];
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86 let cos_a = angle.cos();
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87 let sin_a = angle.sin();
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88 const_for!(i in 0..4 => {
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89 lines[ i] = self.inner[0][i];
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90 lines[4 + i] = self.inner[1][i];
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91 });
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92 const_for!(i in 0..4 => {
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93 self.inner[0][i] = cos_a * lines[i] - sin_a * lines[4+i];
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94 self.inner[1][i] = sin_a * lines[i] + cos_a * lines[4+i];
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95 });
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96 }
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97
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98 /// Translate the matrix by a 3D offset.
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99 pub const fn translate(&mut self, offset: [f32; 3]) {
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100 let mut item: [f32; 3] = [0.; 3];
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101 const_for!(i in 0..3 => {
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102 item[i] = self.inner[3][i] * offset[i];
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103 });
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104 const_for!(i in 0..3 => {
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105 const_for!(j in 0..4 => {
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106 self.inner[i][j] += item[i];
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107 });
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108 });
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109 }
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110
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111 /// Translate the matrix by a 2D offset.
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112 pub const fn translate_2d(&mut self, x: f32, y: f32) {
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113 let offset = [x, y, 0.];
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114 self.translate(offset);
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115 }
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116 }
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117
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118 impl std::ops::Mul<Mat4> for Mat4 {
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119 type Output = Mat4;
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120 fn mul(self, rhs: Mat4) -> Mat4 {
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121 let mut tmp = Mat4::zero();
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122 const_for!(i in 0..4 => {
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123 const_for!(j in 0..4 => {
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124 const_for!(k in 0..4 => {
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125 tmp.inner[i][j] += self.inner[i][k] * rhs.inner[k][j];
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126 });
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127 });
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128 });
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129 tmp
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130 }
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131 }
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132
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133 /// Create an orthographic projection matrix.
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134 pub const fn ortho_2d(left: f32, right: f32, bottom: f32, top: f32) -> Mat4 {
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135 let mut mat = Mat4::identity();
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136 mat.inner[0][0] = 2. / (right - left);
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137 mat.inner[1][1] = 2. / (top - bottom);
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138 mat.inner[2][2] = -1.;
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139 mat.inner[3][0] = -(right + left) / (right - left);
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140 mat.inner[3][1] = -(top + bottom) / (top - bottom);
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141 mat
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142 }
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143
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144 /// Setup a camera view matrix.
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145 pub fn setup_camera(dx: f32, dy: f32, dz: f32) -> Mat4 {
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146 // Some explanations on the magic constants:
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147 // 192. = 384. / 2. = width / 2.
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148 // 224. = 448. / 2. = height / 2.
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149 // 835.979370 = 224./math.tan(math.radians(15)) = (height/2.)/math.tan(math.radians(fov/2))
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150 // This is so that objects on the (O, x, y) plane use pixel coordinates
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151 look_at([192., 224., -835.979370 * dz], [192. + dx, 224. - dy, 0.], [0., -1., 0.])
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152 }
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153
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154 /// Creates a perspective projection matrix.
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155 pub fn perspective(fov_y: f32, aspect: f32, z_near: f32, z_far: f32) -> Mat4 {
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156 let top = (fov_y / 2.).tan() * z_near;
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157 let bottom = -top;
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158 let left = -top * aspect;
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159 let right = top * aspect;
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160
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161 let mut mat = Mat4::identity();
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162 mat.inner[0][0] = (2. * z_near) / (right - left);
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163 mat.inner[1][1] = (2. * z_near) / (top - bottom);
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164 mat.inner[2][2] = -(z_far + z_near) / (z_far - z_near);
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165 mat.inner[2][3] = -1.;
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166 mat.inner[3][2] = -(2. * z_far * z_near) / (z_far - z_near);
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167 mat.inner[3][3] = 0.;
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168 mat
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169 }
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170
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171 type Vec3 = [f32; 3];
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172
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173 fn look_at(eye: Vec3, center: Vec3, up: Vec3) -> Mat4 {
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174 let f = normalize(sub(center, eye));
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175 let u = normalize(up);
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176 let s = normalize(cross(f, u));
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177 let u = cross(s, f);
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178
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179 Mat4::new([[s[0], u[0], -f[0], 0.],
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180 [s[1], u[1], -f[1], 0.],
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181 [s[2], u[2], -f[2], 0.],
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182 [-dot(s, eye), -dot(u, eye), dot(f, eye), 1.]])
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183 }
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184
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185 const fn sub(a: Vec3, b: Vec3) -> Vec3 {
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186 [a[0] - b[0],
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187 a[1] - b[1],
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188 a[2] - b[2]]
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189 }
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190
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191 fn normalize(vec: Vec3) -> Vec3 {
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192 let normal = 1. / (vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]).sqrt();
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193 [vec[0] * normal, vec[1] * normal, vec[2] * normal]
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194 }
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195
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196 const fn cross(a: Vec3, b: Vec3) -> Vec3 {
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197 [a[1] * b[2] - b[1] * a[2],
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198 a[2] * b[0] - b[2] * a[0],
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199 a[0] * b[1] - b[0] * a[1]]
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200 }
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201
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202 const fn dot(a: Vec3, b: Vec3) -> f32 {
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203 a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
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204 }