computational geometry algorithms library source: cgal web page
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Computational Geometry Algorithms Library
Source: CGAL web page http://www.cgal.org
Source: CGAL web page
Source: CGAL web page
* as of 2004
Source: CGAL web page
2D Convex Hull
Source: CGAL web page
2D Polygon Partitioning
Source: CGAL web page
Partitions polygons into convex pieces.
Delaunay Triangulations
Source: CGAL web page
2D Boolean Operations
Source: CGAL web page
“A Nef-polyhedron in dimension d is a point set generated from a finite number of open halfspaces by set complement and set intersection operations.” [Nef78]
dP
2D Arrangements
Source: CGAL web page
Spatial Searching
Source: CGAL web page
Geometric Optimization
Source: CGAL web page
Finds either maximum area or maximum perimeter convex k-gon whose vertices are vertices of convex hull of point set.
Geometric Optimization (continued)
Source: CGAL web page
Geometric Optimization (continued)
Source: CGAL web page
Robustness
Source: CGAL web page
CGAL Basics
• C++• Can work with LEDA• 3 Main Parts:
– Kernel• Geometric primitive objects & operations on them
– Unmodifiable– Dual object representation
» Stand-alone classes parameterized by representation class» Members of kernel class
• Basic data structures & algorithms– Parameterized by traits classes
» Define interface with primitives• Non-geometric support facilities
Source: CGAL web page
Source: CGAL web page
Source: CGAL web page
Source: CGAL web page
Source: CGAL web page
Source: CGAL web page
Source: CGAL web page
Source: CGAL web page
Programming Details
• Preface CGAL names with CGAL::
• #include CGAL/basic.h first in program– Or another CGAL header file that includes it
Source: CGAL web page
Programming Example
Source: CGAL web page
Simple Nongraphical CGAL Example
Simple Nongraphical CGAL Example