Using Oshima splines to produce accurate numerical results and high quality graphical output
This work provides a practical tool for educators and researchers to create precise mathematical handouts and figures, but it is an incremental application of existing spline methods.
The paper demonstrates the use of Oshima splines via the KeTCindy package to produce accurate numerical computations (derivatives, integrals) and high-quality graphical output (silhouettes, wireframe surfaces) for educational and research materials. It shows how to integrate with Maxima for accuracy checks and C compilers for speed.
We illustrate the use of Oshima splines in producing high-quality \LaTeX\ output 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.