×

zbMATH — the first resource for mathematics

Using Oshima splines to produce accurate numerical results and high quality graphical output. (English) Zbl 1453.68225
Summary: We illustrate the use of Oshima splines in producing high-quality LATEXoutput in two cases: first, the numerical computation of derivatives and integrals, and second, the display of silhouettes and wireframe surfaces, using the macros package KeTCindy. Both cases are of particular interest for college and university teachers wanting to create handouts to be used by students, or drawing figures for a research paper. When dealing with numerical computations, KeTCindy can make a call to the CAS Maxima to check for accuracy; in the case of surface graphics, it is particularly important to be able to detect intersections of projected curves, and we show how to do it in a seamlessly manner using Oshima splines in KeTCindy. A C compiler can be called in this case to speed up computations.
MSC:
68W30 Symbolic computation and algebraic computation
65D17 Computer-aided design (modeling of curves and surfaces)
68U15 Computing methodologies for text processing; mathematical typography
97U50 Computer-assisted instruction, e-learning (aspects of mathematics education)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Takato, S.: What is and how to use KeTCindy—linkage between dynamic geometry software and collaborative use of KetCindy and free computer algebra systems and LaTeX graphics capabilities. In: Mathematical Software—ICMS 2016, LNCS 9725, pp. 371-379. Springer (2016) · Zbl 1434.68617
[2] Takato, S.; McAndrew, A.; Vallejo, J.; Kaneko, M., Collaborative use of KeTCindy and free computer algebra systems, Math. Comput. Sci., 11, 3-4, 503-514 (2017)
[3] Takato, S.; Vallejo, J., Hamiltonian dynamical systems: symbolical, numerical and graphical study, Math. Comput. Sci., 13, 1, 281-295 (2019) · Zbl 07095845
[4] Kaneko, M.; Yamashita, S.; Kitahara, K.; Maeda, Y.; Nakamura, Y.; Kortenkamp, U.; Takato, S., KETCindy—collaboration of Cinderella and KETpic, reports on CADGME 2014 conference working group, Int. J. Technol. Math. Educ., 22, 4, 179-185 (2015)
[5] Takato, S., Hamaguchi, N., Sarafian, H.: Generating data of mathematical figures for 3D printers with KETpic and educational impact of the printed models. In: ICMS 2014, LNCS, vol. 8592, pp. 629-634. Springer, Heidelberg (2014) · Zbl 1434.97018
[6] Kaneko, M., Maeda, Y., Hamaguchi, N., Nozawa, T., Takato, S.: A scheme for demonstrating and improving the effect of CAS use in mathematics education. In: Proceedings on ICCSA, pp. 62-71. IEEE (2013)
[7] Kaneko, M.; Takato, S., The effective use of LaTeX drawing in linear algebra, Electron. J. Math. Technol., 5, 2, 1-20 (2011)
[8] Kaneko, M., Takato, S.: A CAS macro package as LaTeX graphical command generator and its applications. In: Proceedings on ICCSA, pp. 72-81. IEEE (2011)
[9] Kortenkamp, U., Interoperable interactive geometry for Europe, Electron. J. Math. Technol., 5, 1, 1-14 (2011)
[10] CTAN. https://ctan.org. Accessed 5 Apr 2019
[11] Cinderella. http://www.cinderella.de/tiki-index.php. Accessed 5 Apr 2019
[12] R. https://www.r-project.org. Accessed 5 Apr 2019
[13] Maxima. http://maxima.sourceforge.net. Accessed 5 Apr 2019
[14] Oshima, T.; Dobashi, Y.; Ochiai, H., Drawing curves, mathematical progress in expressive image synthesis III, Mathematics for Industry, 95-106 (2016), Berlin: Springer, Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.