trimesh_principal_curvature

compas_rhino.geometry.trimesh_principal_curvature(M)

Compute the principal curvature of a triangle mesh.

Parameters:

Mtuple[sequence[[float, float, float] | compas.geometry.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:

• ${\kappa }_i^1,{\kappa }_i^2$ - 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:

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

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)