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.
- mesh
- 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 \(j\).