Deriving Box-Spline Subdivision Schemes

Neil A. Dodgson, Ursula Augsdörfer, Thomas J. Cashman, Malcolm A. Sabin

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

We describe and demonstrate an arrow notation for deriving box-spline subdivision schemes. We compare it with the z-transform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We demonstrate the properties that can be derived easily using the arrow method: mask, stencils, continuity in regular regions, safe extrusion directions. We derive all of the symmetric quadrilateral binary box-spline subdivision schemes with up to eight arrows and all of the symmetric triangular binary box-spline subdivision schemes with up to six arrows. We explain how the arrow notation can be extended to handle ternary schemes.
Original languageEnglish
Title of host publicationIMA International Conference on Mathematics of Surfaces
PublisherSpringer Verlag
Pages106-123
VolumeXIII
Publication statusPublished - 7 Sep 2009

Fingerprint

subdivisions
splines
boxes
coding
masks
convolution integrals
continuity
matrices

Keywords

  • Subdivision Surface

Fields of Expertise

  • Information, Communication & Computing

Cite this

Dodgson, N. A., Augsdörfer, U., Cashman, T. J., & Sabin, M. A. (2009). Deriving Box-Spline Subdivision Schemes. In IMA International Conference on Mathematics of Surfaces (Vol. XIII, pp. 106-123). Springer Verlag.

Deriving Box-Spline Subdivision Schemes. / Dodgson, Neil A. ; Augsdörfer, Ursula; Cashman, Thomas J. ; Sabin, Malcolm A. .

IMA International Conference on Mathematics of Surfaces. Vol. XIII Springer Verlag, 2009. p. 106-123.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Dodgson, NA, Augsdörfer, U, Cashman, TJ & Sabin, MA 2009, Deriving Box-Spline Subdivision Schemes. in IMA International Conference on Mathematics of Surfaces. vol. XIII, Springer Verlag, pp. 106-123.
Dodgson NA, Augsdörfer U, Cashman TJ, Sabin MA. Deriving Box-Spline Subdivision Schemes. In IMA International Conference on Mathematics of Surfaces. Vol. XIII. Springer Verlag. 2009. p. 106-123
Dodgson, Neil A. ; Augsdörfer, Ursula ; Cashman, Thomas J. ; Sabin, Malcolm A. . / Deriving Box-Spline Subdivision Schemes. IMA International Conference on Mathematics of Surfaces. Vol. XIII Springer Verlag, 2009. pp. 106-123
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