A Curious Case of Curbed Condition

This is the repository for a paper I wrote and posted on the arXiv.

This repository is laid out in a manner described in Good Enough Practices in Scientific Computing.

Abstract

In computer aided geometric design a polynomial is usually represented in Bernstein form. The de Casteljau algorithm is the most well-known algorithm for evaluating a polynomial in this form. Evaluation via the de Casteljau algorithm has relative forward error proportional to the condition number of evaluation. However, for a particular family of polynomials, a curious phenomenon occurs: the observed error is much smaller than the expected error bound. We examine this family and prove a much stronger error bound than the one that applies to the general case. Then we provide a few examples to demonstrate the difference in rounding.

Installation

The code used to build the manuscript is written in Python. To run the code, Python 3.6 should be installed, along with nox-automation:

python -m pip install --upgrade nox-automation

Once installed, the various build jobs can be listed.

$ nox --list-sessions
Available sessions:
* build_tex
* make_images
* update_requirements

To run nox -s build_tex (i.e. to build the PDF), pdflatex is required.