School of Computing Research Colloquia

Certified Geometric Computing

Amit Chattopadhyay

Certified geometric computation (CGC), a newly emerging branch of computing science, is a computation paradigm where the main goal is not only numerical accuracy, but above all the geometric and topological correctness of the output. More precisely, in certified geometric computation, the challenge is to develop algorithms for computing topologically correct and geometrically close approximations of geometric shapes.

This talk will introduce two problems from computational geometry: (1) computing implicit surfaces and (2) computing Morse-Smale complexes. It will be shown how CGC algorithms give topologically correct results, where ordinary algorithms fail.