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| """Mesh utils.""" |
|
|
| import torch as t |
| import torch.nn.functional as F |
|
|
| def sample_points_from_mesh(mesh: t.tensor, num_sample_points: int): |
| """Samples points on a mesh, uniformly distributed over the surface area.""" |
| surface_areas = ( |
| t.norm( |
| t.linalg.cross(mesh[:, 0, :], mesh[:, 1, :]) |
| + t.linalg.cross(mesh[:, 1, :], mesh[:, 2, :]) |
| + t.linalg.cross(mesh[:, 2, :], mesh[:, 0, :]), |
| dim=-1) / 2.) |
|
|
| cdf = F.pad(t.cumsum(surface_areas, dim=-1), (1, 0)) |
| cdf = cdf / cdf[-1] |
| rv = t.rand([num_sample_points]) |
| triangle_index = t.searchsorted(cdf, rv, side="right") - 1 |
| assert ( |
| triangle_index.min() >= 0 |
| and triangle_index.max() < mesh.shape[0] |
| ) |
|
|
| sampled_tri = mesh[triangle_index, ...] |
| r1, r2 = t.unbind(t.rand([num_sample_points, 2]), dim=-1) |
| r1 = t.sqrt(r1) |
| u = 1 - r1 |
| v = (1 - r2) * r1 |
| w = r2 * r1 |
| sampled_pts = ( |
| sampled_tri[:, 0] * u[:, None] |
| + sampled_tri[:, 1] * v[:, None] |
| + sampled_tri[:, 2] * w[:, None]) |
|
|
| return sampled_pts, triangle_index |
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