Title: Mu-bases and their applications in geometric modeling
Abstract:This thesis defines the notion of a μ-basis for an arbitrary number of polynomials in one variable. The properties of these μ-bases are derived, and a straightforward algorithm is provided to calculat...This thesis defines the notion of a μ-basis for an arbitrary number of polynomials in one variable. The properties of these μ-bases are derived, and a straightforward algorithm is provided to calculate a μ-basis for any collection of univariate polynomials. Systems where base points are present are also discussed. μ-bases are then applied to solve implicitization, inversion and intersection problems for rational space curves.
Next, a natural one to one correspondence is derived between the singular points of rational planar curves and the axial moving lines that follow these curves. This correspondence is applied together with μ-bases to compute and to analyze all the singular points of low degree rational planar curves.Read More
Publication Year: 2007
Publication Date: 2007-01-01
Language: en
Type: dissertation
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