trimesh_mean_curvature
- compas_rhino.geometry.trimesh.trimesh_mean_curvature(M)[source]
Compute the discrete mean curvature of a triangle mesh.
- Parameters
M (tuple[sequence[[float, float, float] |
Point
], sequence[[int, int, int]]]) – A mesh represented by a list of vertices and a list of faces.- Returns
list[float] – The discrete mean curvature per vertex.
Notes
Description: The discrete mean curvature is computed by edge length and its dihedral angle.
- Notation Convention:
\(H_{i}\) - discrete mean curvature at vertex i
\(E\) - all the edges connected to vertex i
\(j\) - a vertex connected to vertex i
\(l_{ij}\) - the length of edge ij
\(\phi_{ij}\) - the dihedral angle of edge ij
Formula:
\[H_{i} = \frac{1}{4}\sum_{ij\in E}l_{ij}\phi_{ij}\]References
- 1
Formula of Discrete Mean Curvature available at Keenan Crane’s lecture, 03:16-07:11, at https://youtu.be/sokeN5VxBB8
- 2
Formula of dihedral angle available at Keenan Crane’s lecture, 04:20-05:43, at https://youtu.be/NlU1m-OfumE
Examples
Make a mesh from scratch >>> from compas.geometry import Sphere >>> sphere = Sphere([1, 1, 1], 1) >>> sphere = Mesh.from_shape(sphere, u=30, v=30) >>> sphere.quads_to_triangles() >>> M = sphere.to_vertices_and_faces()
Compute the discrete mean curvature >>> H = trimesh_mean_curvature(M)