# Using Oshima splines to produce accurate numerical results and high quality graphical output

## TL;DR

This paper demonstrates how Oshima splines can be used within KeTCindy to produce precise numerical derivatives, integrals, and high-quality graphical figures, enhancing educational and research documentation.

## Contribution

It introduces the application of Oshima splines in KeTCindy for accurate numerical computations and high-quality graphics, integrating CAS and C compiler calls for improved performance.

## Key findings

- Oshima splines enable accurate numerical derivatives and integrals.
- KeTCindy can detect intersections in surface graphics using Oshima splines.
- The approach improves the quality of educational and research figures.

## Abstract

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.