Multi-scale space-variant FRep cellular structures

Oleg Fryazinov, Turlif Vilbrandt, Alexander Pasko

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations.

Original languageEnglish
Pages (from-to)26-34
Number of pages9
JournalCAD Computer Aided Design
Issue number1
Publication statusPublished - Jan 2013
Externally publishedYes


  • Direct fabrication
  • Direct rendering
  • FRep
  • Microstructures
  • Procedural modeling


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