What is F-rep?

The function representation (or F-rep) 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 F-rep:

• Defining 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 - Ck continuous definitions of set-theoretic operations.

We apply theoretic results in different areas:

• reconstruction from points and contours
• computer-aided design and rapid prototyping
• computer animation
• physically based simulation
• artificial life
• computer art

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)

• F-rep 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: PDF (116K) (text only)

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

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