What is FRep?

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

<m>F(X) >= 0</m>

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 - <m>C^k</m> 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)

• FRep in the SIGGRAPH'96 Course on Implicit Surfaces

• Modeling shapes using real functions, Open Systems, No.5 (19), 1996, pp.14-18 (in Russian).

• 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).