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. We introduce two new binary dual quadrilateral box-spline schemes and one new box-spline scheme. With appropriate extensions to handle extraordinary cases, these could each form the basis for a new subdivision scheme. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Dodgson, N. A., Augsdörfer, U. H., Cashman, T. J., & Sabin, M. A. (2009). Deriving box-spline subdivision schemes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5654 LNCS, pp. 106–123). https://doi.org/10.1007/978-3-642-03596-8_7
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