Tutorial 4 - Bspline

DiffinyTrace uses B-splines by default for freeform lenses. They are represented as explicit functions by mapping the local physical space to the parametric domain.

import sys
import os

sys.path.insert(0, os.path.abspath(".."))

import diffinytrace as dit
from diffinytrace.basis_functions.bspline import basis_2D
import torch


U1 = torch.tensor([0., 0.2, 0.4, 0.6, 0.8, 1])
Us = [U1, U1]
ps = [3, 3]
ns = [3, 3]

side_points = 100
_x = torch.linspace(0, 1, side_points)
_y = torch.linspace(0, 1, side_points)
grid_y, grid_x = torch.meshgrid(_y, _x, indexing='ij')
points = torch.cat([grid_x.reshape(-1, 1), grid_y.reshape(-1, 1)], dim=-1)

N2D = basis_2D(points,Us, ps, ns,torch.tensor([0,1]),torch.tensor([0,1]))

xi = 0
yi = 2
dit.plotting.quantity2D.plot(
    N2D[:, yi, xi].reshape(side_points, side_points),
    "basis fun",
    [0, 1],
    [0, 1],
    xlabel="x",
    ylabel="y"
)

<Figure size 640x480 with 0 Axes>