Splinter is a spline library with proven and tested curve and spline algorithms.

There are a lot of resources out there that provide information on quadratic and cubic curves, but many of them contain information that either:

• is simply incorrect
• is correct but not proven
• is correct and proven but inefficient

The goal of splinter is to provide not only a set of robust and efficient algorithms, but to also provide proofs along the way.

Splinter provides functions and proofs for:

• optimal approximations of higher-order curves by lower-order curves, with error margins
• a closed-form solution for the length of a quadratic curve
• an exact calculation of the nearest point on a quadratic curve
• a robust iterative algorithm to parameterize a quadratic curve by length

When possible, splinter will provide optimal algorithms for both quadratic and cubic curves. However, when such algorithms are not available it is typically best to choose error margins, subdivide, and approximate the cubic with quadratics.

Proofs are located in markdown files, split up by category. Look in cubic_curves.md and quadratic_curves.md. You'll want a markdown viewer that supports rendering LaTeX math.

Licensed under the MIT license.