tang 0.2.0

Math library for physical reality — geometry, spatial algebra, tensor, training, GPU compute, and 3D gaussian splatting
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131

//! Camera model for gaussian splatting.
//!
//! Pinhole camera with intrinsics (focal length, principal point) and
//! extrinsics (view matrix). Handles 3D→2D projection and provides the
//! Jacobian needed for covariance projection.

/// Camera intrinsics.
#[derive(Debug, Clone, Copy)]
pub struct Intrinsics {
    pub fx: f32,
    pub fy: f32,
    pub cx: f32,
    pub cy: f32,
}

/// Pinhole camera with intrinsics and extrinsics.
#[derive(Debug, Clone)]
pub struct Camera {
    pub intrinsics: Intrinsics,
    /// View matrix (world → camera), 4×4 column-major.
    pub view_matrix: [f32; 16],
    /// Projection matrix, 4×4 column-major.
    pub proj_matrix: [f32; 16],
    /// Camera position in world space.
    pub position: [f32; 3],
}

impl Camera {
    /// Create a camera looking at a target from a given position.
    pub fn look_at(
        eye: [f32; 3],
        target: [f32; 3],
        up: [f32; 3],
        intrinsics: Intrinsics,
        width: u32,
        height: u32,
        near: f32,
        far: f32,
    ) -> Self {
        let view_matrix = look_at_rh(eye, target, up);
        let proj_matrix = perspective(
            intrinsics.fx, intrinsics.fy,
            intrinsics.cx, intrinsics.cy,
            width, height,
            near, far,
        );

        Self {
            intrinsics,
            view_matrix,
            proj_matrix,
            position: eye,
        }
    }

    /// Pack camera data into a uniform buffer.
    pub fn as_uniform(&self) -> CameraUniform {
        CameraUniform {
            view_matrix: self.view_matrix,
            proj_matrix: self.proj_matrix,
            camera_position: self.position,
            _pad: 0.0,
            focal: [self.intrinsics.fx, self.intrinsics.fy],
            principal: [self.intrinsics.cx, self.intrinsics.cy],
        }
    }
}

/// GPU-friendly camera data (uniform buffer layout).
#[derive(Debug, Clone, Copy, bytemuck::Pod, bytemuck::Zeroable)]
#[repr(C)]
pub struct CameraUniform {
    pub view_matrix: [f32; 16],
    pub proj_matrix: [f32; 16],
    pub camera_position: [f32; 3],
    pub _pad: f32,
    pub focal: [f32; 2],
    pub principal: [f32; 2],
}

/// Right-handed look-at view matrix (column-major).
fn look_at_rh(eye: [f32; 3], target: [f32; 3], up: [f32; 3]) -> [f32; 16] {
    let f = normalize(sub(target, eye));
    let s = normalize(cross(f, up));
    let u = cross(s, f);

    [
        s[0], u[0], -f[0], 0.0,
        s[1], u[1], -f[1], 0.0,
        s[2], u[2], -f[2], 0.0,
        -dot(s, eye), -dot(u, eye), dot(f, eye), 1.0,
    ]
}

/// Perspective projection from intrinsics (column-major).
fn perspective(
    fx: f32, fy: f32, cx: f32, cy: f32,
    width: u32, height: u32,
    near: f32, far: f32,
) -> [f32; 16] {
    let w = width as f32;
    let h = height as f32;

    [
        2.0 * fx / w, 0.0, 0.0, 0.0,
        0.0, 2.0 * fy / h, 0.0, 0.0,
        1.0 - 2.0 * cx / w, 2.0 * cy / h - 1.0, -(far + near) / (far - near), -1.0,
        0.0, 0.0, -2.0 * far * near / (far - near), 0.0,
    ]
}

fn sub(a: [f32; 3], b: [f32; 3]) -> [f32; 3] {
    [a[0] - b[0], a[1] - b[1], a[2] - b[2]]
}

fn cross(a: [f32; 3], b: [f32; 3]) -> [f32; 3] {
    [
        a[1] * b[2] - a[2] * b[1],
        a[2] * b[0] - a[0] * b[2],
        a[0] * b[1] - a[1] * b[0],
    ]
}

fn dot(a: [f32; 3], b: [f32; 3]) -> f32 {
    a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
}

fn normalize(v: [f32; 3]) -> [f32; 3] {
    let len = dot(v, v).sqrt();
    [v[0] / len, v[1] / len, v[2] / len]
}