computational geometry algorithms library source: cgal web page

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