noorbs

This is a little library (c++ and python-bindings) to compute 1D, 2D, 3D non uniform rational bsplines. Computing derivatives analytically can be used to solve pde's.

Dependencies

To build the library cmake, eigen, pybind11 are necessary. Numpy is essential to use the library from python.

Usage in python:

import numpy as np
import nurbs

# setup the basic input for the basis
u_degreee = 2
v_degree = 3

u_knots = nurbs.create_knots_vector(u_min=0, u_max=1, degree=u_degreee, num_poles=4)
v_knots = nurbs.create_knots_vector(u_min=0, u_max=1, degree=v_degree, num_poles=4)

weights = np.ones([16])

# create the nurbs-object
a = nurbs.NurbsBase2D(u_knots, v_knots, weights, u_degreee, v_degree)

# precompute the derivatives (setup functions)
a.computeFirstDerivatives()

# specify points where we want to evaluate the nurbs-surface
u = np.linspace(u_knots[0], u_knots[-1], 21)
v = np.linspace(v_knots[0], v_knots[-1], 21)
uv = np.array([[i, j] for i in u for j in v])

# compute influence-matrix and derivatives at given points
mat = a.getInfluenceMatrix(uv)
dv = a.getDvMatrix(uv)
du = a.getDuMatrix(uv)

# now we can easily compute the interpolation-data by matrix-products
data = uv.T[0] ** 2 + uv.T[1] ** 2
poles = np.linalg.lstsq(mat.toarray(), data)[0]  # approximation of data
int_data = mat @ poles
int_data_du = du @ poles
int_data_dv = dv @ poles

Still there are many things missing like:

• higher derivatives (theoretically possible)
• faster computation of influence and derivatives
• ...