{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1312"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1312","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"T-spline Merging","abstract":"Geometric models, such as for use in CAD/CAM or animation, are often constructed in a piece-wise fashion. Historically, these models have been made of NURBS surfaces. For various reasons it is problematic and often times mathematically impossible to combine several NURBS models into one continuous surface. The recent invention of a surface type called T-splines has made the combining of NURBS surfaces into a single continuous surface possible, but much of the mathematics has yet to be explored. This thesis explores the mathematics and algorithms necessary to merge multiple NURBS, T-spline, or T-NURCC surfaces into a single continuous surface. This thesis addresses two main problems. The first problem is merging surfaces with different parameterizations. In order to merge surfaces with different parameterizations, it is often necessary to modify the parameter values of the surface, which can change the shape of the surface. This change can be alleviated through shape control methods. The second problem is merging surfaces that meet at extraordinary points, or points with a valence other than four. Results show that the merging algorithm is able to successfully convert models composed of multiple NURBS, T-spline, or T-NURCCS surfaces into models composed of a single T-spline or T-NURCC surface. The resulting models are gap-free and contain little distortion in the parameterization.","abstract_html":"Geometric models, such as for use in CAD/CAM or animation, are often constructed in a piece-wise fashion. Historically, these models have been made of NURBS surfaces. For various reasons it is problematic and often times mathematically impossible to combine several NURBS models into one continuous surface. The recent invention of a surface type called T-splines has made the combining of NURBS surfaces into a single continuous surface possible, but much of the mathematics has yet to be explored. This thesis explores the mathematics and algorithms necessary to merge multiple NURBS, T-spline, or T-NURCC surfaces into a single continuous surface. This thesis addresses two main problems. The first problem is merging surfaces with different parameterizations. In order to merge surfaces with different parameterizations, it is often necessary to modify the parameter values of the surface, which can change the shape of the surface. This change can be alleviated through shape control methods. The second problem is merging surfaces that meet at extraordinary points, or points with a valence other than four. Results show that the merging algorithm is able to successfully convert models composed of multiple NURBS, T-spline, or T-NURCCS surfaces into models composed of a single T-spline or T-NURCC surface. The resulting models are gap-free and contain little distortion in the parameterization.","abstract_has_math":false,"creators":["Ipson, Heather"],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:27:34Z","subjects":["merging","T-spline","NURBS","reparameterization","Computer Sciences"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/313","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Ipson, Heather"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2005-04-19T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["merging","T-spline","NURBS","reparameterization","Computer Sciences"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/313","https://scholarsarchive.byu.edu/context/etd/article/1312/viewcontent/ETD_CISOPTR_333.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Computer Science"]},{"key":"dc:description.abstract","label":"Abstract","values":["Geometric models, such as for use in CAD/CAM or animation, are often constructed in a piece-wise fashion. Historically, these models have been made of NURBS surfaces. For various reasons it is problematic and often times mathematically impossible to combine several NURBS models into one continuous surface. The recent invention of a surface type called T-splines has made the combining of NURBS surfaces into a single continuous surface possible, but much of the mathematics has yet to be explored. This thesis explores the mathematics and algorithms necessary to merge multiple NURBS, T-spline, or T-NURCC surfaces into a single continuous surface. This thesis addresses two main problems. The first problem is merging surfaces with different parameterizations. In order to merge surfaces with different parameterizations, it is often necessary to modify the parameter values of the surface, which can change the shape of the surface. This change can be alleviated through shape control methods. The second problem is merging surfaces that meet at extraordinary points, or points with a valence other than four. Results show that the merging algorithm is able to successfully convert models composed of multiple NURBS, T-spline, or T-NURCCS surfaces into models composed of a single T-spline or T-NURCC surface. The resulting models are gap-free and contain little distortion in the parameterization."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["T-spline Merging"]}]}],"canonical_facts":{"dc:creator":["Ipson, Heather"],"dc:date":["2005-04-19T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Computer Science"],"dc:description.abstract":["Geometric models, such as for use in CAD/CAM or animation, are often constructed in a piece-wise fashion. Historically, these models have been made of NURBS surfaces. For various reasons it is problematic and often times mathematically impossible to combine several NURBS models into one continuous surface. The recent invention of a surface type called T-splines has made the combining of NURBS surfaces into a single continuous surface possible, but much of the mathematics has yet to be explored. This thesis explores the mathematics and algorithms necessary to merge multiple NURBS, T-spline, or T-NURCC surfaces into a single continuous surface. This thesis addresses two main problems. The first problem is merging surfaces with different parameterizations. In order to merge surfaces with different parameterizations, it is often necessary to modify the parameter values of the surface, which can change the shape of the surface. This change can be alleviated through shape control methods. The second problem is merging surfaces that meet at extraordinary points, or points with a valence other than four. Results show that the merging algorithm is able to successfully convert models composed of multiple NURBS, T-spline, or T-NURCCS surfaces into models composed of a single T-spline or T-NURCC surface. The resulting models are gap-free and contain little distortion in the parameterization."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/313","https://scholarsarchive.byu.edu/context/etd/article/1312/viewcontent/ETD_CISOPTR_333.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["merging","T-spline","NURBS","reparameterization","Computer Sciences"],"dc:title":["T-spline Merging"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:27:34Z"}