draco-oxide 0.1.0-alpha.5

draco-oxide is a rust rewrite of Google's draco mesh compression library.
Documentation 
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use faer::{traits::pulp::num_complex::ComplexFloat, Mat};

#[allow(unused)]
pub(crate) fn weak_eq_by_laplacian(x: &[[usize; 3]], y: &[[usize; 3]]) -> Option<bool> {
    // Check if the two meshes have the same number of faces
    if x.len() != y.len() {
        return Some(false);
    }

    // Check if the two meshes have the same number of vertices
    let n_vertices = x.iter().flatten().max().unwrap() + 1;
    if n_vertices != y.iter().flatten().max().unwrap() + 1 {
        return Some(false);
    }

    // Check if the two meshes have no unconnected vertices
    let mut x_v_set = vec![false; n_vertices];
    for v in x.iter().flatten() {
        x_v_set[*v] = true;
    }
    if x_v_set.iter().any(|&v| !v) {
        return None;
    }

    let mut y_v_set = vec![false; n_vertices];
    for v in y.iter().flatten() {
        y_v_set[*v] = true;
    }
    if y_v_set.iter().any(|&v| !v) {
        return None;
    }

    // laplacian matrix
    let l1_x = compute_l1(x);
    let n_edges = l1_x.nrows();
    // compute the eigenvalues and eigenvectors of the laplacian matrix
    let l1_x_eigen = l1_x.clone().eigen().unwrap();
    let mut l1_x_eigen = (0..n_edges)
        .map(|i| l1_x_eigen.S()[i].re())
        .collect::<Vec<_>>();
    l1_x_eigen.sort_by(|a, b| a.partial_cmp(b).unwrap());

    // laplacian matrix
    let l1_y = compute_l1(y);
    // compute the eigenvalues and eigenvectors of the laplacian matrix
    let l1_y_eigen = l1_y.eigen().unwrap();
    let mut l1_y_eigen = (0..n_edges)
        .map(|i| l1_y_eigen.S()[i].re())
        .collect::<Vec<_>>();
    l1_y_eigen.sort_by(|a, b| a.partial_cmp(b).unwrap());

    let err = l1_x_eigen
        .iter()
        .zip(l1_y_eigen.iter())
        .map(|(a, b)| (a - b).abs())
        .sum::<f64>();
    Some(err < 1e-6)
}

fn compute_l1(x: &[[usize; 3]]) -> Mat<f64> {
    let mut x = x.to_vec();
    x.iter_mut().for_each(|face| face.sort());
    x.sort();

    // compute edges
    let edges = {
        let mut edges = x
            .iter()
            .flat_map(|face| [[face[0], face[1]], [face[1], face[2]], [face[2], face[0]]])
            .collect::<Vec<_>>();
        edges.iter_mut().for_each(|e| {
            e.sort();
        });
        edges.sort();
        edges.dedup();
        edges
    };

    let mut l1_up = Mat::<f64>::zeros(edges.len(), edges.len());
    for face in x.iter() {
        let mut face = *face;
        face.sort();
        let e1 = edges.binary_search(&[face[0], face[1]]).unwrap();
        let e2 = edges.binary_search(&[face[1], face[2]]).unwrap();
        let e3 = edges.binary_search(&[face[0], face[2]]).unwrap();

        l1_up[(e1, e1)] += 1.0;
        l1_up[(e2, e2)] += 1.0;
        l1_up[(e3, e3)] += 1.0;

        l1_up[(e1, e2)] += 1.0;
        l1_up[(e2, e1)] += 1.0;

        l1_up[(e2, e3)] -= 1.0;
        l1_up[(e3, e2)] -= 1.0;

        l1_up[(e3, e1)] -= 1.0;
        l1_up[(e1, e3)] -= 1.0;
    }

    let mut l1_down = Mat::<f64>::zeros(edges.len(), edges.len());
    for i in 0..edges.len() {
        l1_down[(i, i)] += 2.0;
        for j in i + 1..edges.len() {
            let e1 = edges[i];
            let e2 = edges[j];
            if let Some(&v) = e1.iter().find(|v| e2.contains(v)) {
                if (e1[0] == v && e2[0] == v) || (e1[1] == v && e2[1] == v) {
                    // if v has the same sign with both edges...
                    l1_down[(i, j)] += 1.0;
                    l1_down[(j, i)] += 1.0;
                } else {
                    l1_down[(i, j)] -= 1.0;
                    l1_down[(j, i)] -= 1.0;
                }
            } else {
                continue;
            }
        }
    }

    l1_down + l1_up
}

#[cfg(test)]
mod tests {
    use super::*;
    use faer::mat;
    use faer::traits::pulp::num_complex::Complex64;

    #[test]
    fn test_compute_l1() {
        let x = [[0, 1, 2], [1, 2, 3]];
        let l1 = compute_l1(&x);
        let expected =
            // l1 up
            mat![
                [ 1.0, -1.0,  1.0,  0.0,  0.0], // [0,1]
                [-1.0,  1.0, -1.0,  0.0,  0.0], // [0,2]
                [ 1.0, -1.0,  2.0, -1.0,  1.0], // [1,2]
                [ 0.0,  0.0, -1.0,  1.0, -1.0], // [1,3]
                [ 0.0,  0.0,  1.0, -1.0,  1.0], // [2,3]
            ]
            +
            mat![
                [ 2.0,  1.0, -1.0, -1.0,  0.0], // [0,1]
                [ 1.0,  2.0,  1.0,  0.0, -1.0], // [0,2]
                [-1.0,  1.0,  2.0,  1.0, -1.0], // [1,2]
                [-1.0,  0.0,  1.0,  2.0,  1.0], // [1,3]
                [ 0.0, -1.0, -1.0,  1.0,  2.0], // [2,3]
            ];
        assert_eq!(l1, expected, "l1={:?}, expected={:?}", l1, expected);
    }
    #[test]
    fn test_weak_eq_by_laplacian() {
        let x = [[0, 1, 2], [1, 2, 3]];
        let y = [[0, 1, 2], [0, 1, 3]];
        assert_eq!(weak_eq_by_laplacian(&x, &y), Some(true));

        let torus1 = vec![
            [9, 12, 13],
            [8, 9, 13],
            [8, 9, 10],
            [1, 8, 10],
            [1, 10, 11],
            [1, 2, 11],
            [2, 11, 12],
            [2, 12, 13],
            [8, 13, 14],
            [7, 8, 14],
            [1, 7, 8],
            [0, 1, 7],
            [0, 1, 2],
            [0, 2, 3],
            [2, 3, 13],
            [3, 13, 14],
            [7, 14, 15],
            [6, 7, 15],
            [0, 6, 7],
            [0, 5, 6],
            [0, 3, 5],
            [3, 4, 5],
            [3, 4, 14],
            [4, 14, 15],
            [6, 12, 15],
            [6, 9, 12],
            [5, 6, 9],
            [5, 9, 10],
            [4, 5, 10],
            [4, 10, 11],
            [4, 11, 15],
            [11, 12, 15],
        ];

        let num_vertices = torus1.iter().flat_map(|face| face).max().unwrap() + 1;
        // create permutation for the vertices
        let p = (0..num_vertices)
            .map(|i| (i * (num_vertices - 1)) % num_vertices)
            .collect::<Vec<_>>();
        let mut torus2 = torus1.clone();
        for face in torus2.iter_mut() {
            for i in 0..3 {
                face[i] = p[face[i]];
            }
        }

        assert_eq!(weak_eq_by_laplacian(&torus1, &torus2), Some(true));
    }

    #[test]
    fn test_faer() {
        let m = mat![[2.0, 1.0, 0.0], [1.0, 2.0, 1.0], [0.0, 1.0, 2.0]];

        let eigen = m.eigen().unwrap();
        let eigen = eigen.S();
        assert!(((eigen[0] - Complex64::from(2_f64 - 2_f64.sqrt())) as Complex64).abs() < 1e-6);
        assert!(((eigen[1] - Complex64::from(2_f64)) as Complex64).abs() < 1e-6);
        assert!(((eigen[2] - Complex64::from(2_f64 + 2_f64.sqrt())) as Complex64).abs() < 1e-6);
    }
}