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annotate src/util/math.rs @ 662:107bb5ca5cc8

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Implement Enemy::update(), which now renders the first fairy from stage 1 perfectly!
author Emmanuel Gil Peyrot <linkmauve@linkmauve.fr>
date Sun, 11 Aug 2019 18:14:01 +0200
parents 01849ffd0180
children
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1 //! Various helpers to deal with vectors and matrices.
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2
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3 /// A 4×4 f32 matrix type.
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4 pub struct Mat4 {
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5 inner: [[f32; 4]; 4]
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6 }
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7
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8 impl Mat4 {
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9 /// Create a new matrix from a set of 16 f32.
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10 pub fn new(inner: [[f32; 4]; 4]) -> Mat4 {
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11 Mat4 {
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12 inner
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13 }
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14 }
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15
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16 fn zero() -> Mat4 {
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17 Mat4 {
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18 inner: [[0.; 4]; 4]
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19 }
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20 }
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21
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22 fn identity() -> Mat4 {
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23 Mat4 {
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24 inner: [[1., 0., 0., 0.],
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25 [0., 1., 0., 0.],
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26 [0., 0., 1., 0.],
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27 [0., 0., 0., 1.]]
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28 }
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29 }
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30
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31 /// Immutably borrow the array of f32 inside this matrix.
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32 pub fn borrow_inner(&self) -> &[[f32; 4]; 4] {
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33 &self.inner
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34 }
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35
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36 /// Scale the matrix in 2D.
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37 pub fn scale2d(&mut self, x: f32, y: f32) {
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38 for i in 0..4 {
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39 self.inner[0][i] *= x;
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40 self.inner[1][i] *= y;
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41 }
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42 }
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43
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44 /// Flip the matrix.
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45 pub fn flip(&mut self) {
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46 for i in 0..4 {
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47 self.inner[0][i] = -self.inner[0][i];
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48 }
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49 }
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50
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51 /// Rotate the matrix around its x angle (in radians).
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52 pub fn rotate_x(&mut self, angle: f32) {
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53 let mut lines: [f32; 8] = [0.; 8];
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54 let cos_a = angle.cos();
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55 let sin_a = angle.sin();
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56 for i in 0..4 {
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57 lines[ i] = self.inner[0][i];
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58 lines[4 + i] = self.inner[1][i];
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59 }
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60 for i in 0..4 {
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61 self.inner[1][i] = cos_a * lines[i] - sin_a * lines[4+i];
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62 self.inner[2][i] = sin_a * lines[i] + cos_a * lines[4+i];
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63 }
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64 }
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65
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66 /// Rotate the matrix around its y angle (in radians).
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67 pub fn rotate_y(&mut self, angle: f32) {
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68 let mut lines: [f32; 8] = [0.; 8];
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69 let cos_a = angle.cos();
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70 let sin_a = angle.sin();
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71 for i in 0..4 {
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72 lines[ i] = self.inner[0][i];
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73 lines[4 + i] = self.inner[2][i];
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74 }
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75 for i in 0..4 {
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76 self.inner[0][i] = cos_a * lines[i] + sin_a * lines[4+i];
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77 self.inner[2][i] = -sin_a * lines[i] + cos_a * lines[4+i];
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78 }
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79 }
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80
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81 /// Rotate the matrix around its z angle (in radians).
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82 pub fn rotate_z(&mut self, angle: f32) {
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83 let mut lines: [f32; 8] = [0.; 8];
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84 let cos_a = angle.cos();
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85 let sin_a = angle.sin();
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86 for i in 0..4 {
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87 lines[ i] = self.inner[0][i];
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88 lines[4 + i] = self.inner[1][i];
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89 }
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90 for i in 0..4 {
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91 self.inner[0][i] = cos_a * lines[i] - sin_a * lines[4+i];
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92 self.inner[1][i] = sin_a * lines[i] + cos_a * lines[4+i];
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93 }
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94 }
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95
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96 /// Translate the matrix by a 3D offset.
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97 pub fn translate(&mut self, offset: [f32; 3]) {
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98 let mut item: [f32; 3] = [0.; 3];
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99 for i in 0..3 {
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100 item[i] = self.inner[3][i] * offset[i];
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101 }
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102 for i in 0..3 {
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103 for j in 0..4 {
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104 self.inner[i][j] += item[i];
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105 }
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106 }
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107 }
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108
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109 /// Translate the matrix by a 2D offset.
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110 pub fn translate_2d(&mut self, x: f32, y: f32) {
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111 let offset = [x, y, 0.];
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112 self.translate(offset);
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113 }
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114 }
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115
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116 impl std::ops::Mul<Mat4> for Mat4 {
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117 type Output = Mat4;
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118 fn mul(self, rhs: Mat4) -> Mat4 {
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119 let mut tmp = Mat4::zero();
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120 for i in 0..4 {
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121 for j in 0..4 {
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122 for k in 0..4 {
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123 tmp.inner[i][j] += self.inner[i][k] * rhs.inner[k][j];
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124 }
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125 }
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126 }
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127 tmp
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128 }
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129 }
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130
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131 /// Create an orthographic projection matrix.
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132 pub fn ortho_2d(left: f32, right: f32, bottom: f32, top: f32) -> Mat4 {
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133 let mut mat = Mat4::identity();
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134 mat.inner[0][0] = 2. / (right - left);
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135 mat.inner[1][1] = 2. / (top - bottom);
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136 mat.inner[2][2] = -1.;
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137 mat.inner[3][0] = -(right + left) / (right - left);
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138 mat.inner[3][1] = -(top + bottom) / (top - bottom);
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139 mat
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140 }
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141
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142 /// Setup a camera view matrix.
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143 pub fn setup_camera(dx: f32, dy: f32, dz: f32) -> Mat4 {
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144 // Some explanations on the magic constants:
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145 // 192. = 384. / 2. = width / 2.
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146 // 224. = 448. / 2. = height / 2.
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147 // 835.979370 = 224./math.tan(math.radians(15)) = (height/2.)/math.tan(math.radians(fov/2))
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148 // This is so that objects on the (O, x, y) plane use pixel coordinates
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149 look_at([192., 224., -835.979370 * dz], [192. + dx, 224. - dy, 0.], [0., -1., 0.])
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150 }
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151
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152 /// Creates a perspective projection matrix.
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153 pub fn perspective(fov_y: f32, aspect: f32, z_near: f32, z_far: f32) -> Mat4 {
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154 let top = (fov_y / 2.).tan() * z_near;
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155 let bottom = -top;
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156 let left = -top * aspect;
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157 let right = top * aspect;
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158
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159 let mut mat = Mat4::identity();
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160 mat.inner[0][0] = (2. * z_near) / (right - left);
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161 mat.inner[1][1] = (2. * z_near) / (top - bottom);
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162 mat.inner[2][2] = -(z_far + z_near) / (z_far - z_near);
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163 mat.inner[2][3] = -1.;
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164 mat.inner[3][2] = -(2. * z_far * z_near) / (z_far - z_near);
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165 mat.inner[3][3] = 0.;
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166 mat
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167 }
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168
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169 type Vec3 = [f32; 3];
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170
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171 fn look_at(eye: Vec3, center: Vec3, up: Vec3) -> Mat4 {
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172 let f = normalize(sub(center, eye));
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173 let u = normalize(up);
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174 let s = normalize(cross(f, u));
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175 let u = cross(s, f);
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176
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177 Mat4::new([[s[0], u[0], -f[0], 0.],
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178 [s[1], u[1], -f[1], 0.],
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179 [s[2], u[2], -f[2], 0.],
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180 [-dot(s, eye), -dot(u, eye), dot(f, eye), 1.]])
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181 }
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182
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183 fn sub(a: Vec3, b: Vec3) -> Vec3 {
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184 [a[0] - b[0],
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185 a[1] - b[1],
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186 a[2] - b[2]]
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187 }
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188
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189 fn normalize(vec: Vec3) -> Vec3 {
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190 let normal = 1. / (vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]).sqrt();
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191 [vec[0] * normal, vec[1] * normal, vec[2] * normal]
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192 }
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193
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194 fn cross(a: Vec3, b: Vec3) -> Vec3 {
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195 [a[1] * b[2] - b[1] * a[2],
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196 a[2] * b[0] - b[2] * a[0],
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197 a[0] * b[1] - b[0] * a[1]]
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198 }
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199
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200 fn dot(a: Vec3, b: Vec3) -> f32 {
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201 a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
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202 }