Transfinte Interpolation

We can perform transfinite interpolation to interpolate a structured grid onto a closed contour. Let us first load the desired data and modules as well as specify the ids of contours we wish to interpolate transfinitely.

import numpy as np
import pymethods as pma
from pymethods.algorithms.transfinite_interpolation import Transfinite2d
import pathlib as pt

cwd = pt.Path(__file__).parent

dataset_folder = cwd/'../../Datasets/artery_structure '
data_file = dataset_folder/'00000.npz'
data = np.load(data_file)
oct_pts = data["points"]
contour_id = 0

all_ids = [0, 50, 100, 150, 200]

now for each contour specified let us transfinitely interpolate the region bounded. We do so by using our Transfinite2d class.

for contour_id in all_ids:
   oct_contour = pma.arrays.Contour(
      oct_pts[:,:, contour_id]
   )

   transfinite_interpolator = Transfinite2d(
      oct_contour
   )

during the transfinite interpolation process the contour is divided into 4 approximately equal length segments. The segments are paired. For each pair U, V let us divide the segments into a fixed number of points and plot the results,

# within the for loop
n_U = 15
n_V = 15

grid = transfinite_interpolator.pts_mesh_uniform(n_U, n_V)

x_pts = pma.arrays.Curve(grid[:,0,:])
y_pts = pma.arrays.Curve(grid[:,:,0])

x_pts.plot3d('r-')
y_pts.plot3d('b-')

x_pts = pma.arrays.Curve(grid[:,-1,:])
y_pts = pma.arrays.Curve(grid[:,:,-1])

x_pts.plot3d('r-')
y_pts.plot3d('b-')

# plot the horizontal lines
for i in range(grid.shape[1]):
   pma.arrays.Curve(grid[:,i,:]).plot3d(color='green')
for i in range(grid.shape[-1]):
   pma.arrays.Curve(grid[:,:,i]).plot3d(color='green')
interpolated = transfinite_interpolator.pts_mesh_column_uniform(15,15)

interpolated.scatter3d(color='orange', alpha=0.5)

pma.pyplot.equal_aspect_3d()
pma.pyplot.axis('off')
pma.pyplot.show()