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Zooming algorithms for accurate plotting of functions of two real variables. (English) Zbl 1386.65090
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 499-515 (2017).
Summary: The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the implemented algorithms, yielding continuous approximations of the given function by interpolation. This masks often discontinuities of the given function and its curvature at small scales. It can also provide strange plots, rather inaccurate. In recent years, point based geometry associated with grid approximation has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different visualisation techniques used for 2D plots of a real function and propose two new zooming algorithms for accurate visualisation near discontinuities. First we show the limitations of the classical zooming procedure used in current software, then a mathematical analysis of the zooming process leads to two different treatment of the images. A first algorithm stores representations of the function at different scales, which enables different plots, depending of the screen scale. The second algorithm uses a unique high level grid with quadratic representation. The two algorithms are illustrated and a comparison is performed.
For the entire collection see [Zbl 1379.13001].

MSC:
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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