Plot a plane based on a normal vector and a point in Matlab or matplotlib

Question

How would one go plotting a plane in matlab or matplotlib from a normal vector and a point?

Answer 1

A cleaner Python example that also works for tricky $z,y,z$ situations,

from mpl_toolkits.mplot3d import axes3d
from matplotlib.patches import Circle, PathPatch
import matplotlib.pyplot as plt
from matplotlib.transforms import Affine2D
from mpl_toolkits.mplot3d import art3d
import numpy as np

def plot_vector(fig, orig, v, color='blue'):
   ax = fig.gca(projection='3d')
   orig = np.array(orig); v=np.array(v)
   ax.quiver(orig[0], orig[1], orig[2], v[0], v[1], v[2],color=color)
   ax.set_xlim(0,10);ax.set_ylim(0,10);ax.set_zlim(0,10)
   ax = fig.gca(projection='3d')  
   return fig

def rotation_matrix(d):
    sin_angle = np.linalg.norm(d)
    if sin_angle == 0:return np.identity(3)
    d /= sin_angle
    eye = np.eye(3)
    ddt = np.outer(d, d)
    skew = np.array([[    0,  d[2],  -d[1]],
                  [-d[2],     0,  d[0]],
                  [d[1], -d[0],    0]], dtype=np.float64)

    M = ddt + np.sqrt(1 - sin_angle**2) * (eye - ddt) + sin_angle * skew
    return M

def pathpatch_2d_to_3d(pathpatch, z, normal):
    if type(normal) is str: #Translate strings to normal vectors
        index = "xyz".index(normal)
        normal = np.roll((1.0,0,0), index)

    normal /= np.linalg.norm(normal) #Make sure the vector is normalised
    path = pathpatch.get_path() #Get the path and the associated transform
    trans = pathpatch.get_patch_transform()

    path = trans.transform_path(path) #Apply the transform

    pathpatch.__class__ = art3d.PathPatch3D #Change the class
    pathpatch._code3d = path.codes #Copy the codes
    pathpatch._facecolor3d = pathpatch.get_facecolor #Get the face color    

    verts = path.vertices #Get the vertices in 2D

    d = np.cross(normal, (0, 0, 1)) #Obtain the rotation vector    
    M = rotation_matrix(d) #Get the rotation matrix

    pathpatch._segment3d = np.array([np.dot(M, (x, y, 0)) + (0, 0, z) for x, y in verts])

def pathpatch_translate(pathpatch, delta):
    pathpatch._segment3d += delta

def plot_plane(ax, point, normal, size=10, color='y'):    
    p = Circle((0, 0), size, facecolor = color, alpha = .2)
    ax.add_patch(p)
    pathpatch_2d_to_3d(p, z=0, normal=normal)
    pathpatch_translate(p, (point[0], point[1], point[2]))


o = np.array([5,5,5])
v = np.array([3,3,3])
n = [0.5, 0.5, 0.5]

from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.gca(projection='3d')  
plot_plane(ax, o, n, size=3)    
ax.set_xlim(0,10);ax.set_ylim(0,10);ax.set_zlim(0,10)
plt.show()