Question

我试图在matplotlib中绘制贝塞尔曲面。我有x，y和z的函数（我没有输出它们，我有同事自动生成它们）但是每当我运行我的代码时，我只是得到一个空白的情节。顺便说一句，px，py和pz指的是控制点矩阵。谁能告诉我我做错了什么以及我需要纠正什么？或者可能建议使用python绘制贝塞尔曲面的另一种方法？

fig = plt.figure()
ax = fig.gca(projection='3d')

u = np.linspace(0, 1, 10) 
v = np.linspace(0, 1, 10)

x = px[0][0]*u**3*v**3 + px[0][1]*3*u**3*v**2*(-v + 1) + px[0][2]*3*u**3*v*   (-v + 1)**2 + px[0][3]*u**3*(-v + 1)**3 + \
px[1][0]*3*u**2*v**3*(-u + 1) + px[1][1]*9*u**2*v**2*(-u + 1)*(-v + 1) + px[1][2]*9*u**2*v*(-u + 1)*(-v + 1)**2 + \
px[1][3]*3*u**2*(-u + 1)*(-v + 1)**3 + px[2][0]*3*u*v**3*(-u + 1)**2 + px[2][1]*9*u*v**2*(-u + 1)**2*(-v + 1) + \
px[2][2]*9*u*v*(-u + 1)**2*(-v + 1)**2 + px[2][3]*3*u*(-u + 1)**2*(-v + 1)**3 + px[3][0]*v**3*(-u + 1)**3 + \
px[3][1]*3*v**2*(-u + 1)**3*(-v + 1) + px[3][2]*3*v*(-u + 1)**3*(-v + 1)**2 + px[3][3]*(-u + 1)**3*(-v + 1)**3

y = py[0][0]*u**3*v**3 + py[0][1]*3*u**3*v**2*(-v + 1) + py[0][2]*3*u**3*v*(-v + 1)**2 + py[0][3]*u**3*(-v + 1)**3 +\
py[1][0]*3*u**2*v**3*(-u + 1) + py[1][1]*9*u**2*v**2*(-u + 1)*(-v + 1) + py[1][2]*9*u**2*v*(-u + 1)*(-v + 1)**2 + \
py[1][3]*3*u**2*(-u + 1)*(-v + 1)**3 + py[2][0]*3*u*v**3*(-u + 1)**2 + py[2][1]*9*u*v**2*(-u + 1)**2*(-v + 1) + \
py[2][2]*9*u*v*(-u + 1)**2*(-v + 1)**2 + py[2][3]*3*u*(-u + 1)**2*(-v + 1)**3 + py[3][0]*v**3*(-u + 1)**3 + \
py[3][1]*3*v**2*(-u + 1)**3*(-v + 1) + py[3][2]*3*v*(-u + 1)**3*(-v + 1)**2 + py[3][3]*(-u + 1)**3*(-v + 1)**3

z = pz[0][0]*u**3*v**3 + pz[0][1]*3*u**3*v**2*(-v + 1) + pz[0][2]*3*u**3*v*(-v + 1)**2 + pz[0][3]*u**3*(-v + 1)**3 + \
pz[1][0]*3*u**2*v**3*(-u + 1) + pz[1][1]*9*u**2*v**2*(-u + 1)*(-v + 1) + pz[1][2]*9*u**2*v*(-u + 1)*(-v + 1)**2 +\
pz[1][3]*3*u**2*(-u + 1)*(-v + 1)**3 + pz[2][0]*3*u*v**3*(-u + 1)**2 + pz[2][1]*9*u*v**2*(-u + 1)**2*(-v + 1) + \
pz[2][2]*9*u*v*(-u + 1)**2*(-v + 1)**2 + pz[2][3]*3*u*(-u + 1)**2*(-v + 1)**3 + pz[3][0]*v**3*(-u + 1)**3 + \
pz[3][1]*3*v**2*(-u + 1)**3*(-v + 1) + pz[3][2]*3*v*(-u + 1)**3*(-v + 1)**2 + pz[3][3]*(-u + 1)**3*(-v + 1)**3

ax.plot_surface(x, y, z, rstride=4, cstride=4, color='b')

plt.show()

Answer 1

以下是使用matplotlib绘制贝塞尔曲线的几个例子：

<强> EXAMPLE1

来自emulator

import numpy as np
from scipy.misc import comb
from matplotlib import pyplot as plt


def bernstein_poly(i, n, t):
    return comb(n, i) * (t**(n - i)) * (1 - t)**i


def bezier_curve(points, nTimes=1000):
    nPoints = len(points)
    xPoints = np.array([p[0] for p in points])
    yPoints = np.array([p[1] for p in points])

    t = np.linspace(0.0, 1.0, nTimes)

    polynomial_array = np.array(
        [bernstein_poly(i, nPoints - 1, t) for i in range(0, nPoints)])

    xvals = np.dot(xPoints, polynomial_array)
    yvals = np.dot(yPoints, polynomial_array)

    return xvals, yvals


if __name__ == "__main__":
    nPoints = 4
    points = np.random.rand(nPoints, 2) * 200
    xpoints = [p[0] for p in points]
    ypoints = [p[1] for p in points]

    xvals, yvals = bezier_curve(points, nTimes=1000)
    plt.plot(xvals, yvals)
    plt.plot(xpoints, ypoints, "ro")
    for nr in range(len(points)):
        plt.text(points[nr][0], points[nr][1], nr)

    plt.show()

<强> EXAMPLE2

来自stackoverflow

import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches

verts = [
    (0., 0.),  # P0
    (0.2, 1.), # P1
    (1., 0.8), # P2
    (0.8, 0.), # P3
    ]

codes = [Path.MOVETO,
         Path.CURVE4,
         Path.CURVE4,
         Path.CURVE4,
         ]

path = Path(verts, codes)

fig = plt.figure()
ax = fig.add_subplot(111)
patch = patches.PathPatch(path, facecolor='none', lw=2)
ax.add_patch(patch)

xs, ys = zip(*verts)
ax.plot(xs, ys, 'x--', lw=2, color='black', ms=10)

ax.text(-0.05, -0.05, 'P0')
ax.text(0.15, 1.05, 'P1')
ax.text(1.05, 0.85, 'P2')
ax.text(0.85, -0.05, 'P3')

ax.set_xlim(-0.1, 1.1)
ax.set_ylim(-0.1, 1.1)
plt.show()

如果你问我...我最喜欢考虑参数曲线的方法就是使用它们的矩阵形式，如matplotlib tutorial

中所示

修改

如果你想将它扩展到3d案例，这是一个有效的例子：

import matplotlib as mpl import numpy as np from scipy.misc import comb from matplotlib import pyplot as plt from mpl_toolkits.mplot3d import Axes3D def bernstein_poly(i, n, t): return comb(n, i) * (t**(n - i)) * (1 - t)**i def bezier_curve(points, nTimes=1000): nPoints = len(points) xPoints = np.array([p[0] for p in points]) yPoints = np.array([p[1] for p in points]) zPoints = np.array([p[2] for p in points]) t = np.linspace(0.0, 1.0, nTimes) polynomial_array = np.array( [bernstein_poly(i, nPoints - 1, t) for i in range(0, nPoints)]) xvals = np.dot(xPoints, polynomial_array) yvals = np.dot(yPoints, polynomial_array) zvals = np.dot(zPoints, polynomial_array) return xvals, yvals, zvals if __name__ == "__main__": nPoints = 4 points = np.random.rand(nPoints, 3) * 200 xpoints = [p[0] for p in points] ypoints = [p[1] for p in points] zpoints = [p[2] for p in points] xvals, yvals, zvals = bezier_curve(points, nTimes=1000) fig = plt.figure() ax = fig.gca(projection='3d') ax.plot(xvals, yvals, zvals, label='bezier') ax.plot(xpoints, ypoints, zpoints, "ro") for nr in range(len(points)): ax.text(points[nr][0], points[nr][1], points[nr][2], nr) plt.show()

遇到python bezier曲面图时出现问题 - 不断返回空图

1 个答案: