CISE Submissions

Item: REP-2007-422

Item:REP-2007-422

Title:Fast and stable evaluation of box-splines via the Bézier form

Minho Kim
University of Florida
(352) 392-1226
Jörg Peters, Professor
University of Florida
(352) 392-1226

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 fac- tor and derive a hash table for efficiently accessing the Bézier pieces. The preprocessing, the resulting evaluation algorithm and use in a widely avail- able 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.

Supporting File:here

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