https://github.com/looooo/noorbs

some tests with de boor algorithm and other geometry stuff
https://github.com/looooo/noorbs

cpp11 nurbs python

Last synced: 3 months ago
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some tests with de boor algorithm and other geometry stuff

• Host: GitHub
• URL: https://github.com/looooo/noorbs
• Owner: looooo
• License: gpl-3.0
• Created: 2016-11-11T22:16:57.000Z (about 8 years ago)
• Default Branch: master
• Last Pushed: 2024-07-26T21:52:18.000Z (5 months ago)
• Last Synced: 2024-10-09T10:47:48.775Z (3 months ago)
• Topics: cpp11, nurbs, python
• Language: Jupyter Notebook
• Size: 262 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# 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:  

```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

- ...