{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/41356"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/41356","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Intersection of B-spline surfaces by elimination method","abstract":"Parametric surface representations such as the B-spline and Bezier geometries are widely used among the aerospace, automobile, and shipbuilding industries. These surfaces have proven to be very advantageous for defining and combining primitive geometries to form complex models. However, the task of finding the intersection curve between two surfaces has remained a difficult one. Presently, most of the research done in this area has resulted in various subdivision techniques. These subdivision techniques are based on approximations of the surface using planar polygons. This thesis presents an analytical approach to the intersection problem. The approach taken is to approximate the B-spline surface using subsets such as the ruled surface. Once the B-spline surface has been simplified, elimination techniques which solve for the surface variables can be used to analytically determine the intersection curve between two B-spline surfaces.","abstract_html":"Parametric surface representations such as the B-spline and Bezier geometries are widely used among the aerospace, automobile, and shipbuilding industries. These surfaces have proven to be very advantageous for defining and combining primitive geometries to form complex models. However, the task of finding the intersection curve between two surfaces has remained a difficult one. Presently, most of the research done in this area has resulted in various subdivision techniques. These subdivision techniques are based on approximations of the surface using planar polygons. This thesis presents an analytical approach to the intersection problem. The approach taken is to approximate the B-spline surface using subsets such as the ruled surface. Once the B-spline surface has been simplified, elimination techniques which solve for the surface variables can be used to analytically determine the intersection curve between two B-spline surfaces.","abstract_has_math":false,"creators":["Wong, Chee Kiang"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-22T22:19:16Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-03032009-040559"],"render_values":[{"text":"etd-03032009-040559","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/41356","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Wong, Chee Kiang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:30:34Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:30:34Z","2009-03-03"]},{"key":"dc:date.issued","label":"Date","values":["1990"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-03032009-040559"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/41356"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Parametric surface representations such as the B-spline and Bezier geometries are widely used among the aerospace, automobile, and shipbuilding industries. 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