DCEL: A Polyhedral Database and Programming Environment

In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonstrate its use in several applications.

[1]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[2]  Micha Sharir,et al.  Filling gaps in the boundary of a polyhedron , 1995, Comput. Aided Geom. Des..

[3]  Kurt Mehlhorn,et al.  LEDA: a platform for combinatorial and geometric computing , 1997, CACM.

[4]  Charles M. Eastman,et al.  Geometric Modeling Using the Euler Operators , 1979 .

[5]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[6]  Tamara Munzner,et al.  Geomview: a system for geometric visualization , 1995, SCG '95.

[7]  Erik Brisson,et al.  Representing geometric structures in d dimensions: topology and order , 1989, SCG '89.

[8]  Geert-Jan Giezeman,et al.  The CGAL Kernel: A Basis for Geometric Computation , 1996, WACG.

[9]  Bruce G. Baumgart.  A polyhedron representation for computer vision , 1975, AFIPS '75.

[10]  Micha Sharir,et al.  Piecewise-Linear Interpolation between Polygonal Slices , 1996, Comput. Vis. Image Underst..

[11]  Peter Schorn.  Implementing the XYZ GeoBench: A Programming Environment for Geometric Algorithms , 1991, Workshop on Computational Geometry.

[12]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[13]  Leonidas J. Guibas,et al.  BOXTREE: A Hierarchical Representation for Surfaces in 3D , 1996, Comput. Graph. Forum.

[14]  Bernard Chazelle,et al.  A Functional Approach to Data Structures and Its Use in Multidimensional Searching , 1988, SIAM J. Comput..

[15]  G. Klincsek.  Minimal Triangulations of Polygonal Domains , 1980 .

[16]  David P. Dobkin,et al.  Visualization of Geometric Algorithms , 1995, IEEE Trans. Vis. Comput. Graph..

[17]  Pedro Jussieu de Rezende,et al.  GeoLab: An Environment for Development of Algorithms in Computational Geometry , 1993, CCCG.

[18]  D. T. Lee,et al.  Geosheet: A Distributed Visualization Tool for Geometric Algorithms , 1998, Int. J. Comput. Geom. Appl..

[19]  R. Fateman,et al.  A System for Doing Mathematics by Computer. , 1992 .

[20]  David Eppstein,et al.  On triangulating three-dimensional polygons , 1998, Comput. Geom..

[21]  Kurt Mehlhorn,et al.  Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry , 2012, EATCS Monographs on Theoretical Computer Science.

[22]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[23]  David P. Dobkin,et al.  Primitives for the manipulation of three-dimensional subdivisions , 1987, SCG '87.

[24]  Kurt Mehlhorn,et al.  LEDA - A Library of Efficient Data Types and Algorithms , 1990, GI Jahrestagung.