Mu -bases and their applications in geometric modeling

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dc.contributor.advisorGoldman, Ronalden_US
dc.creatorSong, Ningen_US
dc.date.accessioned2018-12-03T18:32:25Zen_US
dc.date.available2018-12-03T18:32:25Zen_US
dc.date.issued2007en_US
dc.description.abstractThis 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.en_US
dc.format.extent88 ppen_US
dc.identifier.callnoTHESIS COMP.SCI. 2008 SONGen_US
dc.identifier.citationSong, 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>.en_US
dc.identifier.digital304817983en_US
dc.identifier.urihttps://hdl.handle.net/1911/103668en_US
dc.language.isoengen_US
dc.rightsCopyright 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.en_US
dc.subjectComputer scienceen_US
dc.subjectApplied sciencesen_US
dc.subjectMu-bases Planar curvesen_US
dc.subjectUnivariate polynomialsen_US
dc.titleMu -bases and their applications in geometric modelingen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputer Scienceen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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