
What is it aboutKeywords: 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 T^{2}. The oriented projective plane T^{2} is an extension of the Euclidean plane E^{2} 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. T^{2} can be viewed by means of two very insightful models. By representing each point with signed homogeneous coordinates [w,x,y] of R^{3}_{*}, one naturally arrives at the planar model of T^{2} which consists of two copies of E^{2}, representing the two ranges of T^{2} (w>0 and w<0), and a circle S^{1}, representing the points at infinity (w=0). An equally natural visualization of T^{2} is the spherical model which consists of the surface of the sphere S^{2} 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. References
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