libigl是一个很方便的几何网格处理库

可以计算出Gaussian Curvature、Principle Curvature等基础信息。 

python 基础代码如下：

from scipy.sparse.linalg import spsolve
import igl
import os
import numpy as np
import igl
import scipy as sp
from meshplot import plot, subplot, interact
import meshplot
meshplot.jupyter()
meshplot.offline()

v, f = igl.read_triangle_mesh("data/******.obj")

l = igl.cotmatrix(v, f)

n = igl.per_vertex_normals(v, f)*0.5+0.5
c = np.linalg.norm(n, axis=1)

vs = [v]
cs = [c]
for i in range(10):
    m = igl.massmatrix(v, f, igl.MASSMATRIX_TYPE_BARYCENTRIC)
    s = (m - 0.001 * l)
    b = m.dot(v)
    v = spsolve(s, m.dot(v))
    n = igl.per_vertex_normals(v, f)*0.5+0.5
    c = np.linalg.norm(n, axis=1)
    vs.append(v)
    cs.append(c)

# plot(v, f)
# plot(vs[0], f, c, shading={"wireframe": False}, s=[1, 4, 0])
p = subplot(vs[0], f, c, shading={"wireframe": False}, s=[1, 4, 0])
subplot(vs[3], f, c, shading={"wireframe": False}, s=[1, 4, 1], data=p)
subplot(vs[6], f, c, shading={"wireframe": False}, s=[1, 4, 2], data=p)
subplot(vs[9], f, c, shading={"wireframe": False}, s=[1, 4, 3], data=p)
p.save("subplot.html")
# @interact(level=(0, 9))
# def mcf(level=0):
#     p.update_object(vertices=vs[level], colors=cs[level])
k = igl.gaussian_curvature(v, f)
p = plot(v, f, k, return_plot=True)
p.save("gaussian_curvature.html")

m = igl.massmatrix(v, f, igl.MASSMATRIX_TYPE_VORONOI)
minv = sp.sparse.diags(1 / m.diagonal())
kn = minv.dot(k)
p = plot(v, f, kn, return_plot=True)
p.save("igl.massmatrix2222.html")

l = igl.cotmatrix(v, f)
m = igl.massmatrix(v, f, igl.MASSMATRIX_TYPE_VORONOI)
minv = sp.sparse.diags(1 / m.diagonal())
hn = -minv.dot(l.dot(v))
h = np.linalg.norm(hn, axis=1)
p = plot(v, f, h, return_plot=True)
p.save("igl.massmatrix.html")

v1, v2, k1, k2 = igl.principal_curvature(v, f)
h2 = 0.5 * (k1 + k2)
p = plot(v, f, h2, shading={"wireframe": False}, return_plot=True)
p.save("principal_curvature.html")

avg = igl.avg_edge_length(v, f) / 2.0
p.add_lines(v + v1 * avg, v - v1 * avg, shading={"line_color": "red"})
p.add_lines(v + v2 * avg, v - v2 * avg, shading={"line_color": "green"})
p.save("principal_curvature_line.html")

## Select a vertex from which the distances should be calculated
vs = np.array([0])
##All vertices are the targets
vt = np.arange(v.shape[0])
d = igl.exact_geodesic(v, f, vs, vt)#, fs, ft)
strip_size = 0.02
##The function should be 1 on each integer coordinate
c = np.abs(np.sin((d / strip_size * np.pi)))
p = plot(v, f, c, shading={"wireframe": False}, return_plot=True)
p.save("exact_geodesic.html")

import pdb
pdb.set_trace()