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What is FRep?

The Function Representation (or FRep) defines a geometric object by a single real continuous function of point coordinates as

F(X) >= 0

It combines many different models like

  • algebraic surfaces
  • skeleton based “implicit” surfaces
  • set-theoretic solids or CSG (Constructive Solid Geometry)
  • sweeps
  • volumetric objects
  • parametric models
  • procedural models

Main features of FRep:

  • Defining the function evaluation procedure traversing the constructive tree structure
  • Leaves of the constructive tree are primitives with known types of defining functions
  • Nodes of the tree contain operations and relations
  • Extensibility of primitives, operations, and relations

The main goal of this project is to develop a rich system of geometric operations and relations. Our approach is based on the R-functions - C^k continuous definitions of set-theoretic operations.

FRep can also be used to model point-wise object's properties such as material, density, color. This is supported by the constructive hypervolume model.

We apply theoretic results in different areas:

  • computer-aided design
  • rapid prototyping and digital fabrication
  • computer animation
  • physically based simulation
  • artificial life
  • computer art

Frequently asked question: Why not just "implicit" surfaces?


  • A. Pasko and V. Adzhiev, “Function-based shape modeling: mathematical framework and specialized language”, Automated Deduction in Geometry, Lecture Notes in Artificial Intelligence 2930, Ed. F. Winkler, Springer-Verlag, Berlin Heidelberg, 2004, pp. 132-160.
    Electronic version: PDF (847K)
  • Pasko A., Adzhiev V., Sourin A., Savchenko V. “Function representation in geometric modeling: concepts, implementation and applications”, The Visual Computer, vol.11, No.8, 1995, pp.429-446.
    Electronic version (scanned): PDF (7 Mb)
  • Pasko A., Adzhiev V., Schmitt B., Schlick C., “Constructive hypervolume modeling”, Graphical Models, special issue on Volume Modeling, vol. 63, No. 6, November 2001, pp. 413-442.
    Electronic version: PDF (1.69 Mb)

This FRep Home Page represents the results of joint work by an international group of researchers (see the authors of publications).

frep/what.txt · Last modified: 2020/12/31 10:49 (external edit)