Title: Speeding up the computation of uniform bicubic spline surfaces
Authors: Kačala, Viliam
Miňo, Lukáš
Citation: WSCG 2017: full papers proceedings: 25th International Conference in Central Europe on Computer Graphics, Visualization and Computer Visionin co-operation with EUROGRAPHICS Association, p. 73-80.
Issue Date: 2017
Publisher: Václav Skala - UNION Agency
Document type: konferenční příspěvek
URI: wscg.zcu.cz/WSCG2017/!!_CSRN-2701.pdf
ISBN: 978-80-86943-44-2
ISSN: 2464–4617 (print)
2464–4625 (CD-ROM)
Keywords: splotová interpolace;bikupický spline;Hermitův spline;biquartický polynom;jednotná mřížka;tridiagonální systémy;zrychlení
Keywords in different language: spline interpolation;bicubic spline;hermite spline;biquartic polynomial;uniform grid;tridiagonal systems;speedup
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.
Rights: © Václav Skala - UNION Agency
Appears in Collections:WSCG 2017: Full Papers Proceedings

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