基于Python实现绘制一个足球

import numpy as np
from itertools import product
G = (np.sqrt(5)-1)/2
def getVertex():
    pt2 =  [(a,b) for a,b in product([1,-1], [G, -G])]
    pts =  [(a,b,0) for a,b in pt2]
    pts += [(0,a,b) for a,b in pt2]
    pts += [(b,0,a) for a,b in pt2]
    return np.array(pts)

def getDisMat(pts):
    N = len(pts)
    dMat = np.ones([N,N])*np.inf
    for i in range(N):
        for j in range(i):
            dMat[i,j] = np.linalg.norm([pts[i]-pts[j]])
    return dMat

pts = getVertex()
dMat = getDisMat(pts)
# 由于存在舍入误差，所以得到的边的数值可能不唯一
ix, jx = np.where((dMat-np.min(dMat))<0.01)
# 获取正二十面体的边
edges = [pts[[i,j]] for i,j in zip(ix, jx)]
def isFace(e1, e2, e3):
    pts = np.vstack([e1, e2, e3])
    pts = np.unique(pts, axis=0)
    return len(pts)==3

from itertools import combinations
# 获取正二十面体的面
faces = [es for es in combinations(edges, 3) 
    if isFace(*es)]

# 将角度转弧度后再求余弦
cos = lambda th : np.cos(np.deg2rad(th))
sin = lambda th : np.sin(np.deg2rad(th))

# 即 Rx(th) => Matrix
Rx = lambda th : np.array([
    [1, 0,       0],
    [0, cos(th), -sin(th)],
    [0, sin(th), cos(th)]])
Ry = lambda th : np.array([
    [cos(th),  0, sin(th)],
    [0      ,  1, 0],
    [-sin(th), 0, cos(th)]
])
Rz = lambda th : np.array([
    [cos(th) , sin(th), 0],
    [-sin(th), cos(th), 0],
    [0       , 0,       1]])

def getHexEdges(face):
    pts = []
    for st,ed in face:
        pts.append((2*st+ed)/3)
        pts.append((st+2*ed)/3)
    return np.vstack(pts)

ax = plt.subplot(projection='3d')
for f in faces:
    pt = getHexEdges(f)
    pt = Rx(1)@Ry(1)@pt.T
    ax.plot_trisurf(*pt, color="white")

def getPtEdges(pts, edges):
    N = len(pts)
    pEdge = [[] for pt in pts]
    for i,e in product(range(N),edges):
        if (pts[i] == e[0]).all(): 
            pt = (2*pts[i]+e[1])/3
        elif (pts[i] == e[1]).all(): 
            pt = (2*pts[i]+e[0])/3
        else:
            continue
        pEdge[i].append(pt)
    return np.array(pEdge)

pEdge = getPtEdges(pts, edges)

ax = plt.subplot(projection='3d')
for f in faces:
    pt = getHexEdges(f)
    pt = Rx(1)@Ry(1)@pt.T
    ax.plot_trisurf(*pt, color="white")

for pt in pEdge:
    pt = Rx(1)@Ry(1)@pt.T
    ax.plot_trisurf(*pt, color="black")

plt.show()