What is FRep?

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

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?

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)

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).