Motivation

NURBS-Python (geomdl) is a self-contained, object-oriented pure Python B-Spline and NURBS library with implementations of curve, surface and volume generation and evaluation algorithms. It also provides convenient and easy-to-use data structures for storing curve, surface and volume descriptions.

Some significant features of NURBS-Python (geomdl):

  • Self-contained, object-oriented, extensible and highly customizable API
  • Convenient data structures for storing curve, surface and volume descriptions
  • Surface and curve fitting with interpolation and least squares approximation
  • Knot vector and surface grid generators
  • Customizable visualization and animation options with Matplotlib, Plotly and VTK modules
  • Exporting curve, surface and volume data into various file formats, such as JSON, YAML, Libconfig, STL, OBJ and VTK
  • Support for common algorithms: tessellation, voxelization, ray intersection, etc.
  • Shapes component for generation common surfaces and curves
  • Pure Python, no external C/C++ or FORTRAN library dependencies
  • Python compatibility: 2.7.x, 3.4.x and later
  • No compilation steps are necessary, everything is implemented in pure Python
  • For higher performance, optional Compile with Cython options are also available
  • Easy to install via pip: pip install geomdl or conda: conda install -c orbingol geomdl
  • Docker images are available

NURBS-Python (geomdl) contains the following fundamental geometric algorithms:

  • Point evaluation
  • Derivative evaluation
  • Knot insertion
  • Knot removal
  • Knot vector refinement
  • Degree elevation
  • Degree reduction

References

  • Piegl, Les, and Wayne Tiller. The NURBS book. Springer Science & Business Media, 2012.
  • Berg, Mark de, et al. Computational Geometry: Algorithms and Applications. Springer-Verlag TELOS, 2008.
  • Hughes, John F., et al. Computer Graphics: Principles and Practice. Pearson Education, 2014.
  • Dunn, Fletcher, and Ian Parberry. 3D Math Primer for Graphics and Game Development. CRC Press, 2015.
  • Kreyszig, Erwin. Advanced Engineering Mathematics. John Wiley & Sons, 2010.
  • Gamma, Erich. Design Patterns: Elements of Reusable Object-Oriented Software. Pearson Education India, 1995.

Author