| Fast and stable evaluation of box-splines via the BB-form (2008) | |||||||||||||||
Abstract | |||||||||||||||
| To repeatedly evaluate linear combinations of box-splines in a fast and stable way, in particular along knot planes, the box-spline is converted to and tabulated as piecewise polynomial in BB-form (Bernstein-Bézierform). We show that the BB-coefficients can be derived and stored as integers plus a rational scale factor and derive a hash table for efficiently accessing the polynomial pieces. This pre-processing, the resulting evaluation algorithm and use in a widely-used ray-tracing package are illustrated for splines based on two trivariate box-splines: the 7-directional box-spline on the Cartesian lattice and the 6-directional box-spline on the Face-Centered Cubic lattice. 1 | |||||||||||||||
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