Stephen MannResearch interests

Professor Mann's interests are in the area of modeling surfaces for use in design of cars, airplanes, etc., and for using in modeling objects for computer animation. These surfaces are formed of combinations of smaller sub-surfaces called patches. He has a long time interest in triangular shaped patches.

He is also interested in Geometric Algebra, a mathematical abstraction that provides additional primitives and operators, allowing the manipulation of arbitrary dimensional subspaces in a manner similar to a vector in a vector's space. His interest is in how to use Geometric Algebra to solve problems in computer graphics and surface modeling.

Professor Mann has also been working on surface modeling in numerical control machining (NC-machining). An NC-machine is a computer controlled machine for making moulds, etc., for car parts and body panels. In particular, he is doing research in 5-axis machining. 5-axis machines are becoming increasing popular in industry but the techniques required to take advantage of the additional flexibility of these machines are still in their infancy. Professor Mann's research efforts have focused on simulating the surfaces machined by a 5-axis milling machine, allowing the machine operator to test a tool path without having to machine a test part.

Degrees and awards

BA, BA (California, Berkeley), MS, PhD (Washington)

Industrial and sabbatical experience

In 2007, Professor Mann was a visiting research for six months at Solid Works Corporation in Concord, Massachusetts where he studied the polynomial Least. In 1999, Professor Mann was a visiting professor for six months at the University of Amsterdam, where he began his investigations of geometric algebra and how it applies to computer graphics.

Representative publications

R. Duvedi, S. Bedi, A. Batish, and S. Mann. A multipoint method for 5-axis machining of triangulated surface models, Computer-Aided Design, 52:17-26, 2014.

R. Goldman, S. Mann, X. Jia. Computing Perspective Projections in 3-Dimensions using Rotors in the Homogeneous and Conformal Models of Clifford Algebra, Advances in Applied Clifford Algebras. 24:465-491, 2014

A. Rababah and S. Mann. Linear Methods for G1, G2, and G3-Multi-Degree Reduction of Bezier Curves, Computer-Aided Design, 45:405-414.

L. Dorst, D. Fontijne, and S. Mann. Geometric Algebra for Computer Science, Morgan-Kauffman, 2007.

S. Mann. A Blossoming Development of Splines, Morgan-Claypool, 2006.

University of Waterloo
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