trimesh_principal_curvature

compas_rhino.geometry.trimesh.trimesh_principal_curvature(M)

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:

• \(\kappa^1_i, \kappa^2_i\) - The max principal curvature and the min principal curvature at the vertex i

• \(H_i\) - the discrete mean curvature at vertex i

• \(K_i\) - the discrete Gaussian curvature at vertex i

• \(A_i\) - the area of the dual cell centered at vertex i

Formula:

\[\kappa^1_i, \kappa^2_i = \frac{H_i}{A_i}\pm\sqrt{\left( \,\frac{H_i}{A_i}\right)\,^2-\frac{K_i}{A_i}}\]

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)