trimesh_principal_curvature

compas_rhino.geometry.trimesh.trimesh_principal_curvature(M)[source]

Compute the principal 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 max curvature per vertex.

  • list[float] – The min curvature per vertex.

Notes

Description: The discrete principal curvature is computed by mean curvature, Gaussian curvature, and vertex area.

Notation Convention:
  • κ1i,κ2i - The max principal curvature and the min principal curvature at the vertex i

  • Hi - the discrete mean curvature at vertex i

  • Ki - the discrete Gaussian curvature at vertex i

  • Ai - the area of the dual cell centered at vertex i

Formula:

κ1i,κ2i=HiAi±(HiAi)2KiAi

References

1

Formula of Discrete Principal Curvature available at Keenan Crane’s lecture, 03:16-07:11, at https://youtu.be/sokeN5VxBB8

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 principal curvature >>> H = trimesh_principal_curvature(M)