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?

Surveys

  • 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: 2012/04/17 08:33 by ap
Copyright (c) 1996-2013 by the contributing authors. This material may not be published, modified or otherwise redistributed in whole or part without prior approval.
If you have questions and comments about particular research topics, contact the respective authors directly.
Project hosted by the Digital Materialization Group
HyperFun CGPL HyperFun on SourceForge Creative Commons License Valid CSS Driven by DokuWiki