trimesh_gaussian_curvature

compas.datastructures.trimesh_gaussian_curvature(mesh)

Compute the gaussian curvature at the vertices of a triangle mesh using the angular deficit.

Parameters:

meshcompas.datastructures.Mesh

The triangle mesh data structure.

Returns:

list[float]

Per vertex curvature values.

Warning

This function will not check if the provided mesh is actually a triangle mesh. It will just treat it as such…

Notes

The angular deficit at a vertex is defined as the difference between a full circle angle ($2\pi$) and the sum of the angles in the adjacent trianlges.

$$k_G(v_i)=2\pi -\sum _{j\in N(i)}{\theta }_{ij}$$

where $N(i)$ are the triangles incident on vertex $i$ and ${\theta }_{ij}$ is the angle at vertex $i$ in triangle $j$.