×

Diagrammatic tools for generating biorthogonal multiresolutions. (English) Zbl 1097.65028

Summary: Elsewhere we have introduced a construction to produce biorthogonal multiresolutions from given subdivisions. This construction is formulated in matrix terms, which is appropriate for curves and tensor-product surfaces. For mesh surfaces of non-tensor connectivity, however, matrix notation is inconvenient. This work presents the construction for regular meshes using diagrams (stencils, masks) and interactions between diagrams to replace matrices and matrix multiplication. Regular triangular meshes with butterfly subdivision and a variant of Loop subdivision due to N. Litke, A. Levin and P. Schröder [Comput. Aided Geom. Des. 18, No. 5, 463–481 (2001; Zbl 0970.68185)] are used as examples.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D10 Numerical smoothing, curve fitting

Citations:

Zbl 0970.68185
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/S0377-0427(00)00370-8 · Zbl 0964.65007 · doi:10.1016/S0377-0427(00)00370-8
[2] DOI: 10.1145/78956.78958 · Zbl 0726.68076 · doi:10.1145/78956.78958
[3] DOI: 10.1016/S0167-8396(01)00042-5 · Zbl 0970.68185 · doi:10.1016/S0167-8396(01)00042-5
[4] Strang G., Wavelets and Filter Banks (1996)
[5] DOI: 10.1137/S0036141095289051 · Zbl 0911.42016 · doi:10.1137/S0036141095289051
[6] Samavati F., Synthesis and Analysis in Biometrics (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.