Deriving Box-Spline Subdivision Schemes

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

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

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.
Originalspracheenglisch
TitelIMA International Conference on Mathematics of Surfaces
Herausgeber (Verlag)Springer Verlag
Seiten106-123
BandXIII
PublikationsstatusVeröffentlicht - 7 Sep 2009

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subdivisions
splines
boxes
coding
masks
convolution integrals
continuity
matrices

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    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 (Band XIII, S. 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. Band XIII Springer Verlag, 2009. S. 106-123.

    Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

    Dodgson, NA, Augsdörfer, U, Cashman, TJ & Sabin, MA 2009, Deriving Box-Spline Subdivision Schemes. in IMA International Conference on Mathematics of Surfaces. Bd. XIII, Springer Verlag, S. 106-123.
    Dodgson NA, Augsdörfer U, Cashman TJ, Sabin MA. Deriving Box-Spline Subdivision Schemes. in IMA International Conference on Mathematics of Surfaces. Band XIII. Springer Verlag. 2009. S. 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. Band XIII Springer Verlag, 2009. S. 106-123
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    title = "Deriving Box-Spline Subdivision Schemes",
    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.",
    keywords = "Subdivision Surface",
    author = "Dodgson, {Neil A.} and Ursula Augsd{\"o}rfer and Cashman, {Thomas J.} and Sabin, {Malcolm A.}",
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    T1 - Deriving Box-Spline Subdivision Schemes

    AU - Dodgson, Neil A.

    AU - Augsdörfer, Ursula

    AU - Cashman, Thomas J.

    AU - Sabin, Malcolm A.

    PY - 2009/9/7

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    N2 - 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.

    AB - 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.

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    SP - 106

    EP - 123

    BT - IMA International Conference on Mathematics of Surfaces

    PB - Springer Verlag

    ER -