将定义 3D 表面的 x、y、z 坐标插入到任意平面

Question

Suppose I have a set of x,y,z co-ordinates defining the surface of a 3D structure:

points = [[x0,y0,z0],
          [x1,y1,z1],
          [xn,yn,zn]]

How do you recommend that I obtain a list of 2D points defining the perimeter of the structure for a given slice?

For example, I might want the x,z points of my structure at y = 1.5, but assume no points are actually defined on that plane, so I need to linearly interpolate.

I feel like scipy.interpolate.griddata holds the answer, but I can't seem to get my head around how to apply it in this case. Any help would be greatly appreciated.

Answer 1

You can achieve this with scipy.ndimage.map_coordinates :

from scipy.ndimage import map_coordinates
import numpy as np
arr = np.arange(25, dtype=float).reshape((5, 5))
arr
Out[39]: 
array([[ 0.,  1.,  2.,  3.,  4.],
       [ 5.,  6.,  7.,  8.,  9.],
       [10., 11., 12., 13., 14.],
       [15., 16., 17., 18., 19.],
       [20., 21., 22., 23., 24.]])

map_coordinates(arr, (np.arange(5), [1.5]*5))
Out[40]: array([ 1.55357143,  6.55357143, 11.55357143, 16.55357143, 21.55357143])

This requires passing coordinates explicitly, I'm not sure how to leverage numpy indexing with map_coordinates to get an entire column, but this is at least a solution.