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Computational Geometry is the area of computer science that studies efficient algorithms for geometric problems. The problems studied come from applications in graphics, CAD, robotics, GIS, and other areas of geometric computation, but are studied from a theoretical point of view. Algorithms are formally analyzed and proven correct. Otfried Cheong is one of the authors of the standard textbook on computational geometry.
Discrete geometry is an area of mathematics that studies combinatorial properties of geometric objects. Going back to Kepler and Gauss, the field owes much to the work of Paul Erdös.