trimesh_gaussian_curvature

compas.datastructures.trimesh_gaussian_curvature(mesh)[source]

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

Parameters

mesh (compas.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 $j$.