trimesh_principal_curvature

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

Compute the principal curvature of a triangle mesh. :Parameters: M ((list, list)) – A mesh represented by a list of vertices and a list of faces.

Returns

Curvature ((k1, k2)) – k1_list, the max curvature per vertex. k2_list, 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:

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

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)

References

1

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