Goldman, Ronald2018-12-032018-12-032007Song, Ning. "Mu -bases and their applications in geometric modeling." (2007) Diss., Rice University. <a href="https://hdl.handle.net/1911/103668">https://hdl.handle.net/1911/103668</a>.https://hdl.handle.net/1911/103668This 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.88 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Computer scienceApplied sciencesMu-bases Planar curvesUnivariate polynomialsThesis304817983THESIS COMP.SCI. 2008 SONG