dc.contributor.advisor Gortler, Stephen dc.contributor.author Palmer, David R. dc.date.accessioned 2019-04-05T16:24:13Z dash.embargo.terms 2017-03-01 dc.date.created 2016-03 dc.date.issued 2017-02-07 dc.date.submitted 2016 dc.identifier.citation Palmer, David R. 2016. Toward Computing Extremal Quasiconformal Maps via Discrete Harmonic Measured Foliations. Bachelor's thesis, Harvard College. dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:39011779 * dc.description.abstract Conformal maps, which preserve angles, are widely used in computer graphics for applications such as parameterization. However, conformal maps are usually unavailable between multiply-connected domains or when extra constraints are imposed. Extremal quasiconformal maps naturally generalize conformal maps and are available under a larger class of constraints. Teichmüller’s theorem guarantees the existence of such maps and describes them in terms of holomorphic quadratic differentials. This enables computation of extremal maps by first computing holomorphic quadratic differentials on the domain and range. In this thesis, we take the first step toward that project. We define a new type of object—a discrete measured foliation—and prove some results analogous to those for smooth measured foliations. In particular, measured foliations form topological equivalence classes called Whitehead classes, and each Whitehead class contains a unique "harmonic" representative corresponding to a holomorphic quadratic differential. Finally, we develop an algorithm for evolving any discrete foliation to the harmonic representative in its Whitehead class. dc.format.mimetype application/pdf dc.language.iso en dash.license LAA dc.subject Computer Science dc.subject Mathematics dc.title Toward Computing Extremal Quasiconformal Maps via Discrete Harmonic Measured Foliations dc.type Thesis or Dissertation dash.depositing.author Palmer, David R. dash.embargo.until 2017-03-01 dc.date.available 2019-04-05T16:24:13Z thesis.degree.date 2016 thesis.degree.discipline Computer Science thesis.degree.discipline Computer Science thesis.degree.grantor Harvard College thesis.degree.level Undergraduate thesis.degree.name AB dc.type.material text thesis.degree.department Computer Science dash.identifier.vireo http://etds.lib.harvard.edu/college/admin/view/111 dash.author.email dpalmer93@gmail.com
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