What is it about
Keywords: Computational Geometry, Dynamic Visualization, Oriented Projective Plane
In the Institute of Computing at UNICAMP (State University of Campinas), we have extended the Computational Geometry Algorithms Library (CGAL) to allow for the implementation of geometric algorithms on the Oriented Projective Plane T2.
The oriented projective plane T2 is an extension of the Euclidean plane E2 and comprises a number of advantages for algorithm design and implementation. It consists of an alternative geometric model that combines the elegance and efficiency of projective geometry with the consistent handling of oriented lines and planes, signed angles, segments, convex sets, and many other concepts that the classical theory doesn't support. The value of this model for practical computing is well known.
T2 can be viewed by means of two very insightful models. By representing each point with signed homogeneous coordinates [w,x,y] of R3*, one naturally arrives at the planar model of T2 which consists of two copies of E2, representing the two ranges of T2 (w>0 and w<0), and a circle S1, representing the points at infinity (w=0). An equally natural visualization of T2 is the spherical model which consists of the surface of the sphere S2 whose points (w,x,y) belong to the front range when w>0, to the back range when w<0 and to the line at infinity when w=0.
What is available
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