{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22264"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22264","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Numerical variational methods in differential geometry and applications to computer graphics","abstract":"In Chapter 1, we define discrete objects like $\\delta$-tangents, $\\delta$-normals and $\\delta$-curvatures which are analogues of smooth objects in differential geometry. These are incorporated into numerical methods for computer simulation of geometric objects. Some methods to generate geodesic curves on surfaces are discussed.","abstract_html":"In Chapter 1, we define discrete objects like <span class=\"etd-inline-math\">&delta;</span>-tangents, <span class=\"etd-inline-math\">&delta;</span>-normals and <span class=\"etd-inline-math\">&delta;</span>-curvatures which are analogues of smooth objects in differential geometry. These are incorporated into numerical methods for computer simulation of geometric objects. Some methods to generate geodesic curves on surfaces are discussed.","abstract_has_math":true,"creators":["Keum, Byoung Joon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Francis, George K."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:34:20Z","date_published":"2011-05-07T13:34:20Z","updated_at":"2026-07-22T22:25:19Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1989 Keum, Byoung Joon"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010915","(UMI)AAI9010915"],"render_values":[{"text":"AAI9010915","href":null,"code":true},{"text":"(UMI)AAI9010915","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22264","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Francis, George K."]},{"key":"dc:creator","label":"Author","values":["Keum, Byoung Joon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:34:20Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Keum, Byoung Joon"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010915","(UMI)AAI9010915","http://hdl.handle.net/2142/22264"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In Chapter 1, we define discrete objects like $\\delta$-tangents, $\\delta$-normals and $\\delta$-curvatures which are analogues of smooth objects in differential geometry. These are incorporated into numerical methods for computer simulation of geometric objects. Some methods to generate geodesic curves on surfaces are discussed.","In Chapter 2, we develop several methods to generate approximate models of minimal surfaces, using the tools developed in Chapter 1. Models generated using average methods show quick convergence but some deviations from the actual solution. Normal variation methods require heavier computations, but show less deviation from the actual solution.","In Chapter 3, Rubel's Quasi-solution methods are discussed and as applications, methods are developed to find out explicit solutions of partial differential equations defining minimal surfaces and surfaces with restrictions on the man curvature.","In Chapter 4, Transversal Scalar Curvature is defined and some relations between scalar curvatures in tangential, transversal and ambient spaces are discussed.","The listing of a computer program which demonstrates the methods of Chapter 2 is include in the Appendix.","Made available in DSpace on 2011-05-07T13:34:20Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010915.pdf: 3109540 bytes, checksum: 070d15e1a8aadd78a7f146ad41444619 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:56:26Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Numerical variational methods in differential geometry and applications to computer graphics"]}]}],"canonical_facts":{"dc:contributor":["Francis, George K."],"dc:creator":["Keum, Byoung Joon"],"dc:date":["2011-05-07T13:34:20Z","10000-01-01","1989"],"dc:description":["In Chapter 1, we define discrete objects like $\\delta$-tangents, $\\delta$-normals and $\\delta$-curvatures which are analogues of smooth objects in differential geometry. These are incorporated into numerical methods for computer simulation of geometric objects. Some methods to generate geodesic curves on surfaces are discussed.","In Chapter 2, we develop several methods to generate approximate models of minimal surfaces, using the tools developed in Chapter 1. Models generated using average methods show quick convergence but some deviations from the actual solution. Normal variation methods require heavier computations, but show less deviation from the actual solution.","In Chapter 3, Rubel's Quasi-solution methods are discussed and as applications, methods are developed to find out explicit solutions of partial differential equations defining minimal surfaces and surfaces with restrictions on the man curvature.","In Chapter 4, Transversal Scalar Curvature is defined and some relations between scalar curvatures in tangential, transversal and ambient spaces are discussed.","The listing of a computer program which demonstrates the methods of Chapter 2 is include in the Appendix.","Made available in DSpace on 2011-05-07T13:34:20Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010915.pdf: 3109540 bytes, checksum: 070d15e1a8aadd78a7f146ad41444619 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:56:26Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9010915","(UMI)AAI9010915","http://hdl.handle.net/2142/22264"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Keum, Byoung Joon"],"dc:subject":["Mathematics"],"dc:title":["Numerical variational methods in differential geometry and applications to computer graphics"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:19Z"}