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 language | English |
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Title of host publication | IMA International Conference on Mathematics of Surfaces |
Publisher | Springer Verlag |
Pages | 106-123 |
Volume | XIII |
Publication status | Published - 7 Sept 2009 |
Keywords
- Subdivision Surface
Fields of Expertise
- Information, Communication & Computing