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introduction.rst

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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 or conda
  • Docker images are available
  • geomdl-shapes module for generating common spline and analytic geometries
  • geomdl-cli module for using the library from the command line

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.

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