oxihuman-mesh 0.2.1

Mesh processing, topology, and geometry algorithms for OxiHuman
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
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235

// Copyright (C) 2026 COOLJAPAN OU (Team KitaSan)
// SPDX-License-Identifier: Apache-2.0
#![allow(dead_code)]

//! Dual Laplacian (cotangent-weighted) smoothing for triangle meshes.

/// Config for dual Laplacian smoothing.
#[allow(dead_code)]
pub struct DualLaplacianConfig {
    pub iterations: usize,
    pub lambda: f32,
}

impl Default for DualLaplacianConfig {
    fn default() -> Self {
        Self {
            iterations: 5,
            lambda: 0.5,
        }
    }
}

fn sub3(a: [f32; 3], b: [f32; 3]) -> [f32; 3] {
    [a[0] - b[0], a[1] - b[1], a[2] - b[2]]
}

fn dot3(a: [f32; 3], b: [f32; 3]) -> f32 {
    a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
}

fn length3(v: [f32; 3]) -> f32 {
    (v[0] * v[0] + v[1] * v[1] + v[2] * v[2]).sqrt()
}

/// Cotangent of angle at vertex opposite to edge (v_a, v_b) in triangle (v_a, v_shared, v_b).
#[allow(dead_code)]
pub fn cotangent_weight(v_shared: [f32; 3], v_a: [f32; 3], v_b: [f32; 3]) -> f32 {
    let ea = sub3(v_a, v_shared);
    let eb = sub3(v_b, v_shared);
    let cos_a = dot3(ea, eb);
    let cross = [
        ea[1] * eb[2] - ea[2] * eb[1],
        ea[2] * eb[0] - ea[0] * eb[2],
        ea[0] * eb[1] - ea[1] * eb[0],
    ];
    let sin_a = length3(cross);
    if sin_a.abs() < 1e-9 {
        0.0
    } else {
        cos_a / sin_a
    }
}

/// Perform dual Laplacian smoothing using cotangent weights.
#[allow(dead_code)]
pub fn dual_laplacian_smooth(
    positions: &mut [[f32; 3]],
    indices: &[u32],
    config: &DualLaplacianConfig,
) {
    let n = positions.len();
    for _ in 0..config.iterations {
        let mut weight_sum = vec![0.0_f32; n];
        let mut delta = vec![[0.0_f32; 3]; n];
        let n_tri = indices.len() / 3;
        for t in 0..n_tri {
            let i0 = indices[t * 3] as usize;
            let i1 = indices[t * 3 + 1] as usize;
            let i2 = indices[t * 3 + 2] as usize;
            let p0 = positions[i0];
            let p1 = positions[i1];
            let p2 = positions[i2];
            let w0 = cotangent_weight(p0, p1, p2).max(0.0);
            let w1 = cotangent_weight(p1, p0, p2).max(0.0);
            let w2 = cotangent_weight(p2, p0, p1).max(0.0);
            for k in 0..3 {
                delta[i0][k] += (w1 + w2) * (p1[k] + p2[k] - 2.0 * p0[k]);
                delta[i1][k] += (w0 + w2) * (p0[k] + p2[k] - 2.0 * p1[k]);
                delta[i2][k] += (w0 + w1) * (p0[k] + p1[k] - 2.0 * p2[k]);
            }
            weight_sum[i0] += w1 + w2;
            weight_sum[i1] += w0 + w2;
            weight_sum[i2] += w0 + w1;
        }
        for i in 0..n {
            let w = weight_sum[i];
            if w > 1e-9 {
                for k in 0..3 {
                    positions[i][k] += config.lambda * delta[i][k] / w;
                }
            }
        }
    }
}

/// Compute the cotangent Laplacian operator value at a vertex.
#[allow(dead_code)]
pub fn laplacian_at_vertex(vertex_idx: usize, positions: &[[f32; 3]], indices: &[u32]) -> [f32; 3] {
    let p = positions[vertex_idx];
    let mut delta = [0.0_f32; 3];
    let mut w_total = 0.0_f32;
    let n_tri = indices.len() / 3;
    for t in 0..n_tri {
        let i0 = indices[t * 3] as usize;
        let i1 = indices[t * 3 + 1] as usize;
        let i2 = indices[t * 3 + 2] as usize;
        let verts = [i0, i1, i2];
        let pos = [positions[i0], positions[i1], positions[i2]];
        for (local, &vi) in verts.iter().enumerate() {
            if vi != vertex_idx {
                continue;
            }
            let j = (local + 1) % 3;
            let k = (local + 2) % 3;
            let w = cotangent_weight(p, pos[j], pos[k]).max(0.0);
            w_total += w;
            for d in 0..3 {
                delta[d] += w * (pos[j][d] + pos[k][d] - 2.0 * p[d]);
            }
        }
    }
    if w_total > 1e-9 {
        [delta[0] / w_total, delta[1] / w_total, delta[2] / w_total]
    } else {
        [0.0; 3]
    }
}

/// Laplacian energy (sum of squared Laplacian vectors).
#[allow(dead_code)]
pub fn laplacian_energy_dual(positions: &[[f32; 3]], indices: &[u32]) -> f32 {
    let mut energy = 0.0_f32;
    for i in 0..positions.len() {
        let lap = laplacian_at_vertex(i, positions, indices);
        energy += lap[0] * lap[0] + lap[1] * lap[1] + lap[2] * lap[2];
    }
    energy
}

#[cfg(test)]
mod tests {
    use super::*;

    fn flat_grid_mesh() -> (Vec<[f32; 3]>, Vec<u32>) {
        let positions = vec![
            [0.0, 0.0, 0.0],
            [1.0, 0.0, 0.0],
            [2.0, 0.0, 0.0],
            [0.0, 1.0, 0.0],
            [1.0, 1.0, 0.0],
            [2.0, 1.0, 0.0],
        ];
        let indices: Vec<u32> = vec![0, 1, 4, 0, 4, 3, 1, 2, 5, 1, 5, 4];
        (positions, indices)
    }

    #[test]
    fn smooth_does_not_panic() {
        let (mut pos, idx) = flat_grid_mesh();
        let config = DualLaplacianConfig::default();
        dual_laplacian_smooth(&mut pos, &idx, &config);
        assert_eq!(pos.len(), 6);
    }

    #[test]
    fn smooth_zero_iterations_unchanged() {
        let (mut pos, idx) = flat_grid_mesh();
        let orig = pos.clone();
        let config = DualLaplacianConfig {
            iterations: 0,
            lambda: 0.5,
        };
        dual_laplacian_smooth(&mut pos, &idx, &config);
        for (a, b) in pos.iter().zip(orig.iter()) {
            for k in 0..3 {
                assert!((a[k] - b[k]).abs() < 1e-6);
            }
        }
    }

    #[test]
    fn cotangent_weight_right_angle() {
        let v_shared = [0.0, 0.0, 0.0];
        let v_a = [1.0, 0.0, 0.0];
        let v_b = [0.0, 1.0, 0.0];
        let w = cotangent_weight(v_shared, v_a, v_b);
        assert!(w.abs() < 1e-5, "cot(90) should be ~0, got {w}");
    }

    #[test]
    fn laplacian_at_interior_vertex() {
        let (pos, idx) = flat_grid_mesh();
        let lap = laplacian_at_vertex(4, &pos, &idx);
        assert!(lap[0].abs() < 5.0 && lap[1].abs() < 5.0);
    }

    #[test]
    fn laplacian_energy_nonneg() {
        let (pos, idx) = flat_grid_mesh();
        let e = laplacian_energy_dual(&pos, &idx);
        assert!(e >= 0.0);
    }

    #[test]
    fn default_config_reasonable() {
        let c = DualLaplacianConfig::default();
        assert!(c.iterations > 0);
        assert!((0.0..=1.0).contains(&c.lambda));
    }

    #[test]
    fn smooth_preserves_vertex_count() {
        let (mut pos, idx) = flat_grid_mesh();
        let n = pos.len();
        let config = DualLaplacianConfig::default();
        dual_laplacian_smooth(&mut pos, &idx, &config);
        assert_eq!(pos.len(), n);
    }

    #[test]
    fn laplacian_flat_mesh_near_zero() {
        let (pos, idx) = flat_grid_mesh();
        let lap = laplacian_at_vertex(4, &pos, &idx);
        assert!(lap[2].abs() < 1e-5, "Z laplacian on flat mesh should be ~0");
    }

    #[test]
    fn cotangent_weight_acute_positive() {
        let v_shared = [0.0, 0.0, 0.0];
        let v_a = [1.0, 0.1, 0.0];
        let v_b = [0.1, 1.0, 0.0];
        let w = cotangent_weight(v_shared, v_a, v_b);
        assert!(w >= 0.0);
    }
}