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

  • Support for common geometric algorithms: tessellation, voxelization, ray intersection, etc.

  • Construct surfaces and volumes, extract isosurfaces via construct module

  • Customizable visualization and animation options with Matplotlib, Plotly and VTK modules

  • Import geometry data from common CAD formats, such as 3DM and SAT.

  • Export geometry data into common CAD formats, such as 3DM, STL, OBJ and VTK

  • Support importing/exporting in JSON, YAML and libconfig formats

  • Jinja2 support for file imports

  • Pure Python, no external C/C++ or FORTRAN library dependencies

  • Python compatibility: 2.7.x, 3.4.x and later

  • For higher performance, optional Compile with Cython options are also available

  • Easy to install via pip

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

  • Leslie Piegl and Wayne Tiller. The NURBS Book. Springer Science & Business Media, 2012.

  • David F. Rogers. An Introduction to NURBS: With Historical Perspective. Academic Press, 2001.

  • Elaine Cohen et al. Geometric Modeling with Splines: An Introduction. CRC Press, 2001.

  • Mark de Berg et al. Computational Geometry: Algorithms and Applications. Springer-Verlag TELOS, 2008.

  • John F. Hughes et al. Computer Graphics: Principles and Practice. Pearson Education, 2014.

  • Fletcher Dunn and Ian Parberry. 3D Math Primer for Graphics and Game Development. CRC Press, 2015.

  • Erwin Kreyszig. Advanced Engineering Mathematics. John Wiley & Sons, 2010.

  • Erich Gamma et al. Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley, 1994.

Author