Legendre curve plotting demo

In this notebook we show the spectral nature of Legendre curves. The parameters we learn are a kind of a frequency domain, defining the spectrum of the curves. They oscilate more close to the origin, and less farther away from the origin.

import matplotlib.pyplot as plt
import torch
import torch.nn.functional as f

import torchcurves.functional as tcf

Define parameters

degree = 10
n_coefficients = 1 + degree

Define coefficients of various curves

num_curves = 3
dim = 2

t = torch.linspace(-1, 1, n_coefficients)

freq = torch.pi * n_coefficients
first_coef = torch.stack([torch.sin(freq * t), torch.cos(freq * t)], dim=1)
second_coef = torch.stack([torch.sin(freq * t) / f.softplus(t), torch.cos(freq * t) / f.softplus(t)], dim=1)
third_coef = torch.stack([torch.exp(t) / (1 + 5 * (1 + t)), torch.sin(freq * t) / (1 + 10 * (1 + t))], dim=1)
coefs = torch.stack([first_coef, second_coef, third_coef], dim=1)
coefs.shape

torch.Size([6, 3, 2])

Sample and draw the Legendre curves with 100 sample points from -1 to 1

sample_points = torch.torch.linspace(-1, 1, 1000)
curve_args = sample_points.reshape(-1, 1).expand(-1, 3)

curve_points = tcf.legendre_curves(curve_args, coefs)
curve_points.shape

torch.Size([1000, 3, 2])

first_curve, second_curve, third_curve = curve_points.unbind(dim=1)

plt.plot(*first_curve.unbind(dim=1), label='Curve')
plt.legend()
plt.show()

plt.plot(*second_curve.unbind(dim=1), label='Curve')
plt.legend()
plt.show()

plt.plot(*third_curve.unbind(dim=1), label='Curve')
plt.legend()
plt.show()