{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/40638"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/40638","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Data reduction and knot removal for non-uniform B-spline surfaces","abstract":"B-Spline curves and surfaces are being used throughout the aircraft industry for geometric modeling. Geometric models having accurate surface representations in the non-uniform B-Spline surface format can contain very large quantities of data. The computing power required by a CAD system for visualization and analysis is directly influenced by these large amounts of data. Accordingly, a method for reducing the amount of data in a geometric model while maintaining accuracy is needed to reduce the computing power necessary to visualize and analyze a design. This thesis describes the refinement and implementation of a data reduction algorithm for non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces. The topic of determining the significance of knots in non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is addressed. Also, a method for determining the order in which knots should be removed from non-uniform cubic B-Spline curves or non-uniform bi-cubic B-Spline surfaces during data reduction is presented. Finally, an algorithm for performing data reduction by removing knots from non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is presented.","abstract_html":"B-Spline curves and surfaces are being used throughout the aircraft industry for geometric modeling. Geometric models having accurate surface representations in the non-uniform B-Spline surface format can contain very large quantities of data. The computing power required by a CAD system for visualization and analysis is directly influenced by these large amounts of data. Accordingly, a method for reducing the amount of data in a geometric model while maintaining accuracy is needed to reduce the computing power necessary to visualize and analyze a design. This thesis describes the refinement and implementation of a data reduction algorithm for non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces. The topic of determining the significance of knots in non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is addressed. Also, a method for determining the order in which knots should be removed from non-uniform cubic B-Spline curves or non-uniform bi-cubic B-Spline surfaces during data reduction is presented. Finally, an algorithm for performing data reduction by removing knots from non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is presented.","abstract_has_math":false,"creators":["Marcaly, Fred W."],"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":1991,"date_issued":"1991","date_published":"1991","updated_at":"2026-07-22T22:19:42Z","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-01172009-063148"],"render_values":[{"text":"etd-01172009-063148","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/40638","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":["Marcaly, Fred W."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:27:17Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:27:17Z","2009-01-17"]},{"key":"dc:date.issued","label":"Date","values":["1991"]},{"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-01172009-063148"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/40638"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["B-Spline curves and surfaces are being used throughout the aircraft industry for geometric modeling. 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