Projecting a Curve in 3D Space

Question

I am plotting a curve in a 3D space using three vectors X, Y and Z.

How can I draw the projections of the curve onto the planes XOY, XOZ, YOZ?

import matplotlib.pylab as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
fig = plt.figure()
ax = Axes3D(fig)
X = [4, 2, 7, 4]
Y = [7, 4, 9, 6]
Z = [9, 6, 10, 3]
ax.plot(X, Y, Z, 'b-', linewidth=4, label='parametric curve')
plt.show()

Answer 1

Since you are simply plotting points in 3D space (meaning that even though you call it parametric, your curve is not parametric), you get the "projection" by just setting the respective dimension to zero.

For example, to plot on th XoY plane, you'd neglect the Z component and use

zeros = [0,0,0,0]
plt.plot(X,Y,zeros)

In total this would look like

import matplotlib.pylab as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
fig = plt.figure()
ax = Axes3D(fig)
X = [4, 2, 7, 4]
Y = [7, 4, 9, 6]
Z = [9, 6, 10, 3]
ax.plot(X, Y, Z, 'b-', linewidth=4, label='curve')

null = [0]*len(Z)
ax.plot(null, Y, Z)
ax.plot(X,null, Z)
ax.plot(X, Y, null)

plt.show()