Computer-aided geometric design

Computer-aided geometric design

Computer-aided geometric design (CAGD), also known as geometric modeling, is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumes. [Farin, G.: A History of Curves and Surfaces in CAGD, [http://books.google.com/books?id=0SV5G8fgxLoC&printsec=frontcover&dq=Computer+Aided+GEOMETRIC+DESIGN&source=gbs_summary_s&cad=0 Handbook of Computer Aided Geometric Design] ]

Computera-aided geometric design (CAGD) studies especially the construction and manipulation of curves and surfaces given by a set of points using polynomial, rational, piecewise polynomial, or piecewise rational methods. This branch is closely related to several other branches, such as geometric modeling (for example, Non-Uniform Rational B-Spline (NURBS) objects represent the fundamental structures of modern computer systems used in the aircraft and car industry, such as CATIA V5) or data fitting (interpolation, approximation of a set of points). [ [http://library.wolfram.com/infocenter/Conferences/5812/ Computer Aided Geometric Design in Mathematica] ]

Fields of application

Architectural freeform design

Frank Gehry | Zaha Hadid | Herzog & de Meuron | ...

Cecil Balmond |
[http://www.smartgeometry.org/ Smart Geometry] | [http://www.smartgeometry2007.com/agenda.asp Architecture in a Parametric Age]

Geometric problems originating in architecture can lead to interesting research and results in geometry processing, computer-aided geometric design, and discrete differential geometry. [H. Pottmann, S. Brell-Cokcan and J. Wallner: [http://www.geometrie.tuwien.ac.at/ig/sn/2007/pbw_surfaces_07/pbw_surfaces_07.html Discrete surfaces for architectural design] ]

References

Journals

* [http://www.elsevier.com/wps/find/journaldescription.cws_home/505604/description#description Computer Aided Geometric Design]

See also

* CAD/CAM/CAE
* Solid modeling
* Computational topology
* Digital geometry
* Computational Geometry Algorithms Library (CGAL)
* Space partitioning
*

* geometric modelling
* parametric curves
* parametric surfaces
* Architectural geometry

External links

* [http://www.geometrie.tuwien.ac.at/ig/ Geometric Modeling and Industrial Geometry ]
* [http://k3dsurf.sourceforge.net/ K3DSurf — A program to visualize and manipulate Mathematical models in three, four, five and six dimensions. K3DSurf supports Parametric equations and Isosurfaces]
* [http://www.javaview.de/ JavaView — a 3D geometry viewer and a mathematical visualization software.]
* [http://demonstrations.wolfram.com/topic.html?topic=3D+Graphics&limit=100 Related Wolfram Demonstration Projects]


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