1use std::f64::consts::PI;
2use std::ops::Mul;
3
4/// The projection matrix which is used to project the 3D space to the 2D display panel
5#[derive(Clone, Debug, Copy)]
6pub struct ProjectionMatrix([[f64; 4]; 4]);
7
8impl AsRef<[[f64; 4]; 4]> for ProjectionMatrix {
9 fn as_ref(&self) -> &[[f64; 4]; 4] {
10 &self.0
11 }
12}
13
14impl AsMut<[[f64; 4]; 4]> for ProjectionMatrix {
15 fn as_mut(&mut self) -> &mut [[f64; 4]; 4] {
16 &mut self.0
17 }
18}
19
20impl From<[[f64; 4]; 4]> for ProjectionMatrix {
21 fn from(data: [[f64; 4]; 4]) -> Self {
22 ProjectionMatrix(data)
23 }
24}
25
26impl Default for ProjectionMatrix {
27 fn default() -> Self {
28 ProjectionMatrix::rotate(PI, 0.0, 0.0)
29 }
30}
31
32impl Mul<ProjectionMatrix> for ProjectionMatrix {
33 type Output = ProjectionMatrix;
34 fn mul(self, other: ProjectionMatrix) -> ProjectionMatrix {
35 let mut ret = ProjectionMatrix::zero();
36 for r in 0..4 {
37 for c in 0..4 {
38 for k in 0..4 {
39 ret.0[r][c] += other.0[r][k] * self.0[k][c];
40 }
41 }
42 }
43 ret.normalize();
44 ret
45 }
46}
47
48impl Mul<(i32, i32, i32)> for ProjectionMatrix {
49 type Output = (i32, i32);
50 fn mul(self, (x, y, z): (i32, i32, i32)) -> (i32, i32) {
51 let (x, y, z) = (x as f64, y as f64, z as f64);
52 let m = self.0;
53 (
54 (x * m[0][0] + y * m[0][1] + z * m[0][2] + m[0][3]) as i32,
55 (x * m[1][0] + y * m[1][1] + z * m[1][2] + m[1][3]) as i32,
56 )
57 }
58}
59
60impl Mul<(f64, f64, f64)> for ProjectionMatrix {
61 type Output = (i32, i32);
62 fn mul(self, (x, y, z): (f64, f64, f64)) -> (i32, i32) {
63 let m = self.0;
64 (
65 (x * m[0][0] + y * m[0][1] + z * m[0][2] + m[0][3]) as i32,
66 (x * m[1][0] + y * m[1][1] + z * m[1][2] + m[1][3]) as i32,
67 )
68 }
69}
70
71impl ProjectionMatrix {
72 /// Returns the identity matrix
73 pub fn one() -> Self {
74 ProjectionMatrix([
75 [1.0, 0.0, 0.0, 0.0],
76 [0.0, 1.0, 0.0, 0.0],
77 [0.0, 0.0, 1.0, 0.0],
78 [0.0, 0.0, 0.0, 1.0],
79 ])
80 }
81 /// Returns the zero maxtrix
82 pub fn zero() -> Self {
83 ProjectionMatrix([[0.0; 4]; 4])
84 }
85 /// Returns the matrix which shift the coordinate
86 pub fn shift(x: f64, y: f64, z: f64) -> Self {
87 ProjectionMatrix([
88 [1.0, 0.0, 0.0, x],
89 [0.0, 1.0, 0.0, y],
90 [0.0, 0.0, 1.0, z],
91 [0.0, 0.0, 0.0, 1.0],
92 ])
93 }
94 /// Returns the matrix which rotates the coordinate
95 #[allow(clippy::many_single_char_names)]
96 pub fn rotate(x: f64, y: f64, z: f64) -> Self {
97 let (c, b, a) = (x, y, z);
98 ProjectionMatrix([
99 [
100 a.cos() * b.cos(),
101 a.cos() * b.sin() * c.sin() - a.sin() * c.cos(),
102 a.cos() * b.sin() * c.cos() + a.sin() * c.sin(),
103 0.0,
104 ],
105 [
106 a.sin() * b.cos(),
107 a.sin() * b.sin() * c.sin() + a.cos() * c.cos(),
108 a.sin() * b.sin() * c.cos() - a.cos() * c.sin(),
109 0.0,
110 ],
111 [-b.sin(), b.cos() * c.sin(), b.cos() * c.cos(), 0.0],
112 [0.0, 0.0, 0.0, 1.0],
113 ])
114 }
115 /// Returns the matrix that applies a scale factor
116 pub fn scale(factor: f64) -> Self {
117 ProjectionMatrix([
118 [1.0, 0.0, 0.0, 0.0],
119 [0.0, 1.0, 0.0, 0.0],
120 [0.0, 0.0, 1.0, 0.0],
121 [0.0, 0.0, 0.0, 1.0 / factor],
122 ])
123 }
124 /// Normalize the matrix, this will make the metric unit to 1
125 pub fn normalize(&mut self) {
126 if self.0[3][3] > 1e-20 {
127 for r in 0..4 {
128 for c in 0..4 {
129 self.0[r][c] /= self.0[3][3];
130 }
131 }
132 }
133 }
134
135 /// Get the distance of the point in guest coordinate from the screen in pixels
136 pub fn projected_depth(&self, (x, y, z): (i32, i32, i32)) -> i32 {
137 let r = &self.0[2];
138 (r[0] * x as f64 + r[1] * y as f64 + r[2] * z as f64 + r[3]) as i32
139 }
140}
141
142/// The helper struct to build a projection matrix
143#[derive(Copy, Clone)]
144pub struct ProjectionMatrixBuilder {
145 /// Specifies the yaw of the 3D coordinate system
146 pub yaw: f64,
147 /// Specifies the pitch of the 3D coordinate system
148 pub pitch: f64,
149 /// Specifies the scale of the 3D coordinate system
150 pub scale: f64,
151 pivot_before: (i32, i32, i32),
152 pivot_after: (i32, i32),
153}
154
155impl Default for ProjectionMatrixBuilder {
156 fn default() -> Self {
157 Self {
158 yaw: 0.5,
159 pitch: 0.15,
160 scale: 1.0,
161 pivot_after: (0, 0),
162 pivot_before: (0, 0, 0),
163 }
164 }
165}
166
167impl ProjectionMatrixBuilder {
168 /// Creates a new, default projection matrix builder object.
169 pub fn new() -> Self {
170 Self::default()
171 }
172
173 /// Set the pivot point, which means the 3D coordinate "before" should be mapped into
174 /// the 2D coordinatet "after"
175 pub fn set_pivot(&mut self, before: (i32, i32, i32), after: (i32, i32)) -> &mut Self {
176 self.pivot_before = before;
177 self.pivot_after = after;
178 self
179 }
180
181 /// Build the matrix based on the configuration
182 pub fn into_matrix(self) -> ProjectionMatrix {
183 let mut ret = if self.pivot_before == (0, 0, 0) {
184 ProjectionMatrix::default()
185 } else {
186 let (x, y, z) = self.pivot_before;
187 ProjectionMatrix::shift(-x as f64, -y as f64, -z as f64) * ProjectionMatrix::default()
188 };
189
190 if self.yaw.abs() > 1e-20 {
191 ret = ret * ProjectionMatrix::rotate(0.0, self.yaw, 0.0);
192 }
193
194 if self.pitch.abs() > 1e-20 {
195 ret = ret * ProjectionMatrix::rotate(self.pitch, 0.0, 0.0);
196 }
197
198 if (self.scale - 1.0).abs() > 1e-20 {
199 ret = ret * ProjectionMatrix::scale(self.scale);
200 }
201
202 if self.pivot_after != (0, 0) {
203 let (x, y) = self.pivot_after;
204 ret = ret * ProjectionMatrix::shift(x as f64, y as f64, 0.0);
205 }
206
207 ret
208 }
209}
210