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Spline research

This repo contains protoype research code for a new spline. It is based on my earlier Spiro work and builds on my PhD thesis but has significant advantages.

First, the new spline is robust. That means that a small change to an input point yields a proportionally small change in the generated spline. By contrast, Spiro was prone to large flips, as a loop would change direction. Even worse, Spiro would sometimes fail to converge (often producing incorrect results resembline particle accelerator tracks). This lack of robustness was a major reason Spiro didn’t catch on more widely.

Second, it uses explicit tangents as a unifying and simple user experience refinement to control a wide range of behaviors. These explicit tangents replace Spiro’s “one-way constraints,” which were powerful but confusing from a user-experience perspective. With explicit tangents, the designer make smooth straight-to-curved transitions, control the curvature when a curve is terminated at a corner, control the exact locations of extrema (especially important for font design), and signal a transition from low curvature to high curvature regions. The new control is intuitive and will be familiar to designers experienced in Bézier drawing.

The new spline should be useful in font design (my original motivation), vector illustration in general, CAD, and other applications such as maps and representation of path centerlines for autonomous vehicles.

Try the online demo.

Read more about the spline in research paper 1.


The code in this repository is licensed under the terms of the Apache-2 or MIT license, at your choice.

The ideas in this repository are free for all to implement. Previously there were patents and a provisional patent application, but those are hereby passed into the public domain.


Contributions are welcome.

Raph Levien


A repository for research code, papers, interactive visualizers, etc., for spline research



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