A New Approach to the Construction of Subdivision Algorithms: The MATLAB Software Package

This software package creates subdivision matrices for generalized quadratic and cubic B-spline subdivision. The algorithms produce subdivision matrices for subdivision surfaces as well as subdivision volumes. The subdivision matrices define refinement rules for arbitrary combinatorial structures. Irregular points and edges are supported in all cases.

All generated subdivision matrices have a valid eigenstructure: they have a subdominant eigenvalue of 1/2 with multiplicity two (for subdivision surfaces) and multiplicity three (for subdivision volumes). Moreover the central part of the structure forms a convex polytope (or in the cubic case, a set of cubes whose outer faces form a central polytope).

The software package also includes a number of additional functions, such as plotting the evaluated B-spline elements or uniformly refining structures of any size.

Identifier
Source https://tudatalib.ulb.tu-darmstadt.de/handle/tudatalib/4676
Related Identifier IsCitedBy https://doi.org/10.26083/tuprints-00030194
Related Identifier IsCitedBy https://doi.org/10.26083/tuprints-00030195
Related Identifier Cites https://doi.org/10.26083/tuprints-00030194
Related Identifier Cites https://doi.org/10.26083/tuprints-00030195
Metadata Access https://tudatalib.ulb.tu-darmstadt.de/server/oai/openairedata?verb=GetRecord&metadataPrefix=oai_datacite&identifier=oai:tudatalib.ulb.tu-darmstadt.de:tudatalib/4676
Provenance
Creator Dietz, Alexander ORCID logo
Publisher Technische Universität Darmstadt
Contributor Technische Universität Darmstadt
Publication Year 2025
Rights Creative Commons Attribution 4.0 International; info:eu-repo/semantics/openAccess; https://creativecommons.org/licenses/by/4.0
OpenAccess true
Contact https://tudatalib.ulb.tu-darmstadt.de/docs/en/kontakt/
Representation
Language English
Resource Type Software
Format application/pdf; application/zip
Size 713.88 KB; 4.99 MB
Discipline Design; Fine Arts, Music, Theatre and Media Studies; Humanities; Mathematics; Natural Sciences