Having Trouble With A Python Bezier Surface Plot- Keeps Returning An Empty Plot

I'm trying to plot a Bezier surface in matplotlib. I have my functions for x,y, and z (I didnt type them out, I had sympy automatically generate them) but whenever I run my code,

Solution 1:

Here's a couple of examples to plot bezier curves with matplotlib:

EXAMPLE1

From stackoverflow

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()

EXAMPLE2

From matplotlib tutorial

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()

If you ask me... my favourite way to think about parametric curves is using their matrix form, like showed in this website

EDIT:

If you want to extend it to the 3d case, here's a working example:

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()