{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/81802"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/81802","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quadrilateral Remeshing and Efficient Surface Parameterization","abstract":"In the third part, we deal explicitly with the problem of surface parameterization. We present two complementary methods for automatically improving mesh parameterization, and demonstrate that they provide a desirable combination of efficiency and quality. First, we describe a new iterative method for constructing quasi-conformal parameterizations with free boundaries. We formulate the problem as fitting the coordinate gradients to two guidance vector fields of equal magnitude that are everywhere orthogonal. In only one linear step, our method efficiently generates parameterization with natural boundaries from those with convex boundaries. Next, we introduce a new non-linear optimization framework that, can rapidly reduce interior distortion under a variety of metrics. By iteratively solving linear systems, our algorithm converges to a high quality, low distortion parameterization in very few iterations.","abstract_html":"In the third part, we deal explicitly with the problem of surface parameterization. We present two complementary methods for automatically improving mesh parameterization, and demonstrate that they provide a desirable combination of efficiency and quality. First, we describe a new iterative method for constructing quasi-conformal parameterizations with free boundaries. We formulate the problem as fitting the coordinate gradients to two guidance vector fields of equal magnitude that are everywhere orthogonal. In only one linear step, our method efficiently generates parameterization with natural boundaries from those with convex boundaries. Next, we introduce a new non-linear optimization framework that, can rapidly reduce interior distortion under a variety of metrics. By iteratively solving linear systems, our algorithm converges to a high quality, low distortion parameterization in very few iterations.","abstract_has_math":false,"creators":["Dong, Shen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Michael Garland"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:20:31Z","date_published":"2015-09-25T20:20:31Z","updated_at":"2026-07-22T22:26:17Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3301127"],"render_values":[{"text":"(MiAaPQ)AAI3301127","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/81802","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Michael Garland"]},{"key":"dc:creator","label":"Author","values":["Dong, Shen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:20:31Z","10000-01-01","2007"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/81802","(MiAaPQ)AAI3301127"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In the third part, we deal explicitly with the problem of surface parameterization. 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We present two complementary methods for automatically improving mesh parameterization, and demonstrate that they provide a desirable combination of efficiency and quality. First, we describe a new iterative method for constructing quasi-conformal parameterizations with free boundaries. We formulate the problem as fitting the coordinate gradients to two guidance vector fields of equal magnitude that are everywhere orthogonal. In only one linear step, our method efficiently generates parameterization with natural boundaries from those with convex boundaries. Next, we introduce a new non-linear optimization framework that, can rapidly reduce interior distortion under a variety of metrics. By iteratively solving linear systems, our algorithm converges to a high quality, low distortion parameterization in very few iterations.","Made available in DSpace on 2015-09-25T20:20:31Z (GMT). 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