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

mesh (compas.oatastructures.Mesh) – The triangle mesh data structure.

Returns

list of 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 \(j\).