Speeding up the computation of uniform bicubic spline surfaces

Abstract

Approximation of surfaces plays a key role in a wide variety of computer science fields such as graphics or CAD applications. Recently a new algorithm for evaluation of interpolating spline surfaces with C2 continuity over uniform grids was proposed based on a special approximation property between biquartic and bicubic polynomials. The algorithm breaks down the classical de Boor’s computational task to reduced tasks and simple remainder ones. The paper improves the reduced part’s implementation, proposes an asymptotic equation to compute the theoretical speedup of the whole algorithm and provides results of computational experiments. Both de Boor’s and our reduced tasks involves tridiagonal linear systems. First of all, a memory-saving optimization is proposed for the solution of such equation systems. After setting the computational time complexity of arithmetic operations and clarifying the influence of modern microprocessors design on the algorithm’s remainder tasks, a new expression is suggested for assessing theoretical speedup of the whole algorithm. Validity of the equation is then confirmed by measured speedup on various microprocessors.