Tracer un plan basé sur un vecteur normal et un point dans Matlab ou matplotlib

Pour Matlab:

point = [1,2,3];
normal = [1,1,2];

%# a plane is a*x+b*y+c*z+d=0
%# [a,b,c] is the normal. Thus, we have to calculate
%# d and we're set
d = -point*normal'; %'# dot product for less typing

%# create x,y
[xx,yy]=ndgrid(1:10,1:10);

%# calculate corresponding z
z = (-normal(1)*xx - normal(2)*yy - d)/normal(3);

%# plot the surface
figure
surf(xx,yy,z)

Remarque: cette solution ne fonctionne que tant que la normale(3) n'est pas 0. Si le plan est parallèle à l'axe z, vous pouvez faire pivoter les dimensions de garder la même approche:

z = (-normal(3)*xx - normal(1)*yy - d)/normal(2); %% assuming normal(3)==0 and normal(2)~=0

%% plot the surface
figure
surf(xx,yy,z)

%% label the axis to avoid confusion
xlabel('z')
ylabel('x')
zlabel('y')

Pour copier-dérouleurs de vouloir un dégradé sur la surface:

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import numpy as np
import matplotlib.pyplot as plt

point = np.array([1, 2, 3])
normal = np.array([1, 1, 2])

# a plane is a*x+b*y+c*z+d=0
# [a,b,c] is the normal. Thus, we have to calculate
# d and we're set
d = -point.dot(normal)

# create x,y
xx, yy = np.meshgrid(range(10), range(10))

# calculate corresponding z
z = (-normal[0] * xx - normal[1] * yy - d) * 1. / normal[2]

# plot the surface
plt3d = plt.figure().gca(projection='3d')

Gx, Gy = np.gradient(xx * yy)  # gradients with respect to x and y
G = (Gx ** 2 + Gy ** 2) ** .5  # gradient magnitude
N = G / G.max()  # normalize 0..1

plt3d.plot_surface(xx, yy, z, rstride=1, cstride=1,
                   facecolors=cm.jet(N),
                   linewidth=0, antialiased=False, shade=False
)
plt.show()

Un nettoyant exemple Python qui fonctionne également pour la délicate $z,y,z$ 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()