Ning Song, Mu-bases and their applications in geometric modeling

Geometric modeling is the sub-field of computer science concerned with constructing, manipulating, and analyzing geometric models - computer models of physical, virtual or mathematical objects. In practice, many geometric models are represented by smooth algebraic functions, especially rational functions. For rational curves and surfaces, there are several common problems that are frequently encountered: computing intersections, finding implicit equations, and detecting singular points and base points. Generally, each of these problems eventually reduce to solving systems of polynomial equations.

This talk will focus on solving these common problems by mu-bases. The notion of a mu-basis is defined for an arbitrary number of polynomials in one variable. The properties of these mu-bases are derived, and a straightforward algorithm is provided to calculate a mu-basis for any collection of univariate polynomials. Systems where base points are present are also discussed. mu-bases are then applied to solve implicitization, inversion and intersection problems for rational space curves.