### Abstract

Original language | English |
---|---|

Title of host publication | IMA International Conference on Mathematics of Surfaces |

Publisher | Springer Verlag |

Pages | 106-123 |

Volume | XIII |

Publication status | Published - 7 Sep 2009 |

### Fingerprint

### Keywords

- Subdivision Surface

### Fields of Expertise

- Information, Communication & Computing

### Cite this

*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. .

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*IMA International Conference on Mathematics of Surfaces.*vol. XIII, Springer Verlag, pp. 106-123.

}

TY - GEN

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

Y1 - 2009/9/7

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.

KW - Subdivision Surface

M3 - Conference contribution

VL - XIII

SP - 106

EP - 123

BT - IMA International Conference on Mathematics of Surfaces

PB - Springer Verlag

ER -