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Amenta's Directory of Computational Geometry Software http://www.geom.uiuc.edu/software/cglist/
Lot of categories and links.
CGAL - Computational Geometry Algorithms Library http://www.cgal.org/
A collaborative effort to develop a robust, easy to use, and efficient C++ software library of geometric data structures and algorithms.
CM2 Mesh Tools http://www.computing-objects.com/en/meshtools.html
Professional C++ mesh generators. Includes product information and news releases.
Computational Geometry Code http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html
Jeff Erickson's links to freely available implementations of geometric algorithms and software.
Delaunay Triangulation Code http://www-sop.inria.fr/prisme/logiciel/del-tree.html
J-D. Boissonnat et al.'s code for Delaunay meshing in 2 and 3 dimensions in C++.
Edgebreaker 3D Compression for Triangle Meshes http://www.gvu.gatech.edu/~jarek/edgebreaker/eb/
Source code, explanations, file formats, and examples of the Edgebreaker compression and decompression techniques.
Fast Industrial-Strength Triangulation http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html
By Martin Held. Copes with polygons with holes and degeneracies/self-intersections; based on repeatedly clipping ears. Source code on request.
Fast Robust Predicates for Computational Geometry http://www.cs.cmu.edu/~quake/robust.html
C code for orientation and incircle tests using adaptive-precision floating-point arithmetic
FastGEO Computational Geometry Library http://www.partow.net/projects/fastgeo/index.html
FastGEO, A computational geometry library written in the object pascal language.
Gmsh http://www.geuz.org/gmsh/
Gmsh is a three-dimensional finite element mesh generator, primarily Delaunay, with built-in pre- and post-processing facilities. Gmsh is freely available for Windows and most UNIX platforms.
GTS - The GNU Triangulated Surface Library http://gts.sourceforge.net/
Open-source library for manipulating 3D triangular surface meshes. Delaunay triangulations, robust geometric predicates, robust boolean set operations on surfaces, surface refinement and coarsening, level-of-detail, k-d trees, volume and curvature, strips generation.
JeoEdit http://cgm.cs.mcgill.ca/~godfried/jeoedit/
Two Java applets for editing polygons and point sets for input to computational geometry software.
Knotenpunkt http://www.knotenpunkt.com/home_E.htm
Produces commercial software that creates a surface model out of a pointcloud or polymesh [Balingen, Germany].
Polyhedral FAQ http://www.ifor.math.ethz.ch/~fukuda/polyfaq/polyfaq.html
Frequently Asked Questions in Polyhedral Computation.
Polymake http://www.math.tu-berlin.de/polymake/
A tool for the algorithmic treatment of polytopes and polyhedra.
Qhull http://www.qhull.org/
Computes convex hulls, Delaunay triangulations, Voronoi diagrams, half-space intersections about a point, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. It runs in 2-d, 3-d, 4-d, and higher dimensions.
QMG project http://www.cs.cornell.edu/Info/People/vavasis/qmg-home.html
Mesh generation in 2D and 3D on Unix and NT, and related software by Steven Vavasis.
Smallest Enclosing Ball of Points http://www.inf.ethz.ch/personal/gaertner/miniball.html
Fast and robust C++ code available under GNU license. Handles arbitrary dimensions, and has high numerical stability.
Stony Brook Algorithm Repository - Section on Computational Geometry http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml
Summary of major CG problems and implementations of their solutions
Surface Evolver http://www.susqu.edu/facstaff/b/brakke/evolver/
Free interactive program for modelling liquid surfaces shaped by various forces and constraints, e.g., minimal surfaces (bubbles). Applies gradient descent to minimize energy. Available for most platforms.
Surface Reconstruction Algorithms Page http://www.compgeom.com/www.sites.html
Links to Surface Reconstruction software, papers, people.
Triangle http://www.cs.cmu.edu/~quake/triangle.html
Jonathan Richard Shewchuk's Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.

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