除了CGAL python绑定之外,python中的3维中是否存在“alpha形状”函数?
或者,有没有办法将下面的例子扩展到3D?
2D示例:draw a smooth polygon around data points in a scatter plot, in matplotlib
我目前正在使用此ConvexHull示例计算音量,但就我的目的而言,由于“凸”约束,音量会膨胀。
谢谢,
答案 0 :(得分:2)
我写了一些代码来查找alpha形状的表面。我希望这会有所帮助。
from scipy.spatial import Delaunay
import numpy as np
from collections import defaultdict
def alpha_shape_3D(pos, alpha):
"""
Compute the alpha shape (concave hull) of a set of 3D points.
Parameters:
pos - np.array of shape (n,3) points.
alpha - alpha value.
return
outer surface vertex indices, edge indices, and triangle indices
"""
tetra = Delaunay(pos)
# Find radius of the circumsphere.
# By definition, radius of the sphere fitting inside the tetrahedral needs
# to be smaller than alpha value
# http://mathworld.wolfram.com/Circumsphere.html
tetrapos = np.take(pos,tetra.vertices,axis=0)
normsq = np.sum(tetrapos**2,axis=2)[:,:,None]
ones = np.ones((tetrapos.shape[0],tetrapos.shape[1],1))
a = np.linalg.det(np.concatenate((tetrapos,ones),axis=2))
Dx = np.linalg.det(np.concatenate((normsq,tetrapos[:,:,[1,2]],ones),axis=2))
Dy = -np.linalg.det(np.concatenate((normsq,tetrapos[:,:,[0,2]],ones),axis=2))
Dz = np.linalg.det(np.concatenate((normsq,tetrapos[:,:,[0,1]],ones),axis=2))
c = np.linalg.det(np.concatenate((normsq,tetrapos),axis=2))
r = np.sqrt(Dx**2+Dy**2+Dz**2-4*a*c)/(2*np.abs(a))
# Find tetrahedrals
tetras = tetra.vertices[r<alpha,:]
# triangles
TriComb = np.array([(0, 1, 2), (0, 1, 3), (0, 2, 3), (1, 2, 3)])
Triangles = tetras[:,TriComb].reshape(-1,3)
Triangles = np.sort(Triangles,axis=1)
# Remove triangles that occurs twice, because they are within shapes
TrianglesDict = defaultdict(int)
for tri in Triangles:TrianglesDict[tuple(tri)] += 1
Triangles=np.array([tri for tri in TrianglesDict if TrianglesDict[tri] ==1])
#edges
EdgeComb=np.array([(0, 1), (0, 2), (1, 2)])
Edges=Triangles[:,EdgeComb].reshape(-1,2)
Edges=np.sort(Edges,axis=1)
Edges=np.unique(Edges,axis=0)
Vertices = np.unique(Edges)
return Vertices,Edges,Triangles
答案 1 :(得分:0)
您正在寻找“凹面船体”。 marching cube algorithm可用于查找这种船体。您可以找到a full example here。
局限性:如果您的数据来自于体积数据集,或者您具有可以轻松转换为体积数据集(类似体素)的点云,则此方法效果很好。例如,使用scipy cKDTree之类的空间索引器,可以使用一组密集的点相对容易地完成此操作,但是如果您的云比较稀疏,您可能最终会挠头以取得好结果点。