| Fast and stable evaluation of box-splines via the Bézier (2007) | |||||||||||||
Abstract | |||||||||||||
| To repeatedly evaluate linear combinations of box-splines in a fast and stable way, in particular along knot planes, we convert to and tabulate the box-spline as piecewise polynomials in Bézier form. We show that the Bézier coefficients can be stored as integers and a rational scale factor and derive a hash table for efficiently accessing the Bézier pieces. The preprocessing, the resulting evaluation algorithm and use in a widely available ray-tracing package are illustrated for splines based on two trivariate box-splines, the 7-direction box-spline on the Cartesian lattice and the 6-direction box-spline on the FCC lattice. 1 | |||||||||||||
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