用python绘制三维立方体的二维投影

Question

我有一个立方体，我知道它的顶点的x，y，z位置，我还有一个数组将面与顶点联系起来（这些面由2个三角形组成）：

import numpy as np

x = np.array([ 0.16257299, -0.370805  , -1.09232295,  1.62570095,
              -1.62570095,  1.09232295,  0.370805  , -0.16257299])
y = np.array([-1.71022499, -0.81153202, -0.52910602, -0.36958599,
               0.369587  ,  0.52910602,  0.81153202,  1.71022499])
z = np.array([ 0.22068501, -1.48456001,  1.23566902,  0.469576  ,
              -0.469576  , -1.23566902,  1.48456001, -0.22068501])

faces = ([[3, 0, 1],[6, 7, 4],[3, 6, 2],[0, 2, 4],[1, 4, 7],[6, 3, 5],
          [1, 5, 3],[4, 2, 6],[2, 0, 3],[4, 1, 0],[7, 5, 1],[5, 7, 6]])

我设法用以下内容绘制立方体的三维可视化：

^{pr2}$

但是我想要的是绘制立方体在Y轴上的二维投影，我尝试了以下方法：

valuesOfFaces = [5,10,9,1,2,3,7,8]

import matplotlib.pyplot as plt
%matplotlib notebook
fig, ax = plt.subplots()

ax.tricontourf(x,z,valuesOfFaces,triangles = faces,zdir='y',levels=np.sort(valuesOfFaces))

但结果如下：

我想要的是能够给每一张脸涂上一个恒定的值，而且不可见的脸不会出现。matplotlib可以吗？如果是，你建议我怎么做？在

Answer 1

你很幸运我正好回答了这个问题，Plot 3D convex closed regions in matplot lib， 最近。方法可能非常相似。首先将三角形简化为立方体的面（这在链接的答案中完成），然后只需移除隐藏的面。这里的方法是沿着观察方向按质心对面进行排序，然后删除最后3个面。 最后通过去除y维来实现二维投影。在

from scipy.spatial import ConvexHull
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.collections import PolyCollection
import mpl_toolkits.mplot3d as a3
from mpl_toolkits.mplot3d import Axes3D

x = np.array([ 0.16257299, -0.370805  , -1.09232295,  1.62570095,
              -1.62570095,  1.09232295,  0.370805  , -0.16257299])
y = np.array([-1.71022499, -0.81153202, -0.52910602, -0.36958599,
               0.369587  ,  0.52910602,  0.81153202,  1.71022499])
z = np.array([ 0.22068501, -1.48456001,  1.23566902,  0.469576  ,
              -0.469576  , -1.23566902,  1.48456001, -0.22068501])

verts = np.c_[x,y,z]
hull = ConvexHull(verts)
simplices = hull.simplices

org_triangles = [verts[s] for s in simplices]

class Faces():
    def __init__(self,tri, sig_dig=12, method="convexhull"):
        self.method=method
        self.tri = np.around(np.array(tri), sig_dig)
        self.grpinx = list(range(len(tri)))
        norms = np.around([self.norm(s) for s in self.tri], sig_dig)
        _, self.inv = np.unique(norms,return_inverse=True, axis=0)

    def norm(self,sq):
        cr = np.cross(sq[2]-sq[0],sq[1]-sq[0])
        return np.abs(cr/np.linalg.norm(cr))

    def isneighbor(self, tr1,tr2):
        a = np.concatenate((tr1,tr2), axis=0)
        return len(a) == len(np.unique(a, axis=0))+2

    def order(self, v):
        if len(v) <= 3:
            return v
        v = np.unique(v, axis=0)
        n = self.norm(v[:3])
        y = np.cross(n,v[1]-v[0])
        y = y/np.linalg.norm(y)
        c = np.dot(v, np.c_[v[1]-v[0],y])
        if self.method == "convexhull":
            h = ConvexHull(c)
            return v[h.vertices]
        else:
            mean = np.mean(c,axis=0)
            d = c-mean
            s = np.arctan2(d[:,0], d[:,1])
            return v[np.argsort(s)]

    def simplify(self):
        for i, tri1 in enumerate(self.tri):
            for j,tri2 in enumerate(self.tri):
                if j > i: 
                    if self.isneighbor(tri1,tri2) and \
                       self.inv[i]==self.inv[j]:
                        self.grpinx[j] = self.grpinx[i]
        groups = []
        for i in np.unique(self.grpinx):
            u = self.tri[self.grpinx == i]
            u = np.concatenate([d for d in u])
            u = self.order(u)
            groups.append(u)
        return groups

    def order_along_axis(self,faces,axis):
        midpoints = np.array([f.mean(axis=0) for f in faces])
        s = np.dot(np.array(axis),midpoints.T)
        return np.argsort(s)

    def remove_last_n(self, faces, order, n=1):
        return np.array(faces)[order][::-1][n:][::-1]




f = Faces(org_triangles, sig_dig=4)
g = f.simplify()
order = f.order_along_axis(g, [0,1,0])
g = f.remove_last_n(g, order, 3)

# Reduce dimension, ommit y axis:
g2D = g[:,:,[0,2]]


fig = plt.figure(figsize=(8,3))
ax = fig.add_subplot(121, projection="3d")
ax2 = fig.add_subplot(122)


colors = np.random.rand(len(g),3)

pc = a3.art3d.Poly3DCollection(g,  facecolors=colors, 
                                   edgecolor="k", alpha=0.9)
ax.add_collection3d(pc)

pc2 = PolyCollection(g2D,  facecolors=colors, 
                                   edgecolor="k", alpha=0.9)
ax2.add_collection(pc2)
ax2.autoscale()
ax2.set_aspect("equal")


ax.set_xlim([-1.5,2])
ax.set_ylim([-1.5,2])
ax.set_zlim([-1.5,2])
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
plt.show()