Plot a plane based on a normal vector and a point in Matlab or matplotlib
Solution 1:
For all the copy/pasters out there, here is similar code for Python using matplotlib:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
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')
plt3d.plot_surface(xx, yy, z)
plt.show()
Solution 2:
For 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)
Note: this solution only works as long as normal(3) is not 0. If the plane is parallel to the z-axis, you can rotate the dimensions to keep the same approach:
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')
Solution 3:
For copy-pasters wanting a gradient on the 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()