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Compute cotangent weights correctly for integer mesh vertices #40

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8 changes: 8 additions & 0 deletions src/potpourri3d/mesh.py
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Original file line number Diff line number Diff line change
Expand Up @@ -184,6 +184,11 @@ def cotan_laplacian(V, F, denom_eps=0.):
validate_mesh(V, F, force_triangular=True)
nV = V.shape[0]

integer_coordinates = np.issubdtype(V.dtype, np.integer)
if integer_coordinates:
# Keep coordinate differences exact, including unsigned and wide integers.
V = V.astype(np.int64 if V.dtype.itemsize < 8 else object)

mat_i = []
mat_j = []
mat_data = []
Expand All @@ -195,6 +200,9 @@ def cotan_laplacian(V, F, denom_eps=0.):
inds_k = F[:,(i+2)%3]
vec_ki = V[inds_i,:] - V[inds_k,:]
vec_kj = V[inds_j,:] - V[inds_k,:]
if integer_coordinates:
vec_ki = vec_ki.astype(float)
vec_kj = vec_kj.astype(float)
dots = np.sum(vec_ki * vec_kj, axis=1)
cross_mags = np.linalg.norm(np.cross(vec_ki, vec_kj), axis=1)
cotans = 0.5 * dots / (cross_mags + denom_eps)
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38 changes: 38 additions & 0 deletions test/potpourri3d_test.py
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Expand Up @@ -153,6 +153,44 @@ def test_mesh_vector_heat(self):
self.assertEqual(logmap.shape[0], V.shape[0])
self.assertEqual(logmap.shape[1], 2)

def test_integer_cotan_laplacian(self):
cases = [(np.int8, 10), (np.uint8, 10),
(np.int16, 100), (np.uint16, 100),
(np.int32, 100000), (np.uint32, 100000),
(np.int64, 100000), (np.uint64, 100000),
(np.float32, 100), (np.float64, 100)]
# Integrated linear basis gradients on a right triangle of sides 3 and 4.
expected = np.array([[25. / 24., -2. / 3., -3. / 8.],
[-2. / 3., 2. / 3., 0.],
[-3. / 8., 0., 3. / 8.]])
for dtype, scale in cases:
V = np.array([[0, 0, 0], [3 * scale, 0, 0],
[0, 4 * scale, 0]], dtype=dtype)
original = V.copy()
for winding in [[0, 1, 2], [0, 2, 1]]:
F = np.array([winding])
for eps in [0., 1.]:
with self.subTest(dtype=dtype, winding=winding, eps=eps):
L = pp3d.cotan_laplacian(V, F, denom_eps=eps)
factor = 12. * scale * scale / (12. * scale * scale + eps)
np.testing.assert_allclose(L.toarray(), expected * factor,
rtol=1e-6, atol=1e-8)
np.testing.assert_array_equal(V, original)

def test_integer_cotan_laplacian_large_offset(self):
expected = np.array([[25. / 24., -2. / 3., -3. / 8.],
[-2. / 3., 2. / 3., 0.],
[-3. / 8., 0., 3. / 8.]])
for dtype in [np.int64, np.uint64]:
V = np.array([[0, 0, 0], [3, 0, 0], [0, 4, 0]], dtype=dtype)
V += 2**60
original = V.copy()
for winding in [[0, 1, 2], [0, 2, 1]]:
with self.subTest(dtype=dtype, winding=winding):
L = pp3d.cotan_laplacian(V, np.array([winding]))
np.testing.assert_allclose(L.toarray(), expected)
np.testing.assert_array_equal(V, original)

def test_mesh_cotan_laplace(self):

V, F = pp3d.read_mesh(os.path.join(asset_path, "bunny_small.ply"))
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