Deriving Box-Spline Subdivision Schemes

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

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


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
Publication statusPublished - 7 Sept 2009


  • Subdivision Surface

Fields of Expertise

  • Information, Communication & Computing

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