frep:what

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 - 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)

- 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).

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

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