raphlinus/spline-research

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

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.

License

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

Contributions are welcome.

— Raph Levien

spline-research's Issues

Question about splitting splines

I wasn't sure whether this would be the most appropriate way to get in contact, but I'm wondering if you ever looked into splitting splines as part of your research?

At $JOB we develop a CAD system and a common task is to break an entity into two at a particular point. For example, say the first half generates the desired shape perfectly, but you don't need the rest. This is easy enough to implement for regular shapes like lines and arcs, and even ellipse segments, but I wasn't sure how it'd be implemented for a B-Spline or Bezier Curve.

Have you come across anything in the literature around this sort of operation?

Closed all-smooth shapes not smooth

The following closed shape with three smooth point and no tangents doesn't appear smooth at the first point:

{"subpaths":[{"closed":true,"pts":[{"x":223.86,"y":168.2,"c":1},{"x":483.06,"y":64.2,"c":1},{"x":491.86,"y":273,"c":1}]}]}

Whereas setting explicit tangents on one point makes all points properly smooth.

{"subpaths":[{"closed":true,"pts":[{"x":223.86,"y":168.2,"c":1},{"x":483.06,"y":64.2,"c":1},{"x":491.86,"y":273,"c":1,"t":2.393}]}]}

Use more TypeScript?

Just for better code organization...

Explore ways to achieve kinkless interpolation/OFV production

To provide correct interpolation (preventing kinks) we need some sort of C continuity at smooth knots, even if we specified the tangent direction.

Add CurveToLine and LineToCurve types

README correctly indicates that Spiro's Left and Right constraints were confusing to use and removed them in this implementation.
In code I find this confusion is because they're named according to the order of the array which is easily confused with left and right as screen coordinates. I suggest calling them CurveToLine and LineToCurve and re-adding them to spline-research as they continue to be a useful way to weld lines to curves. The implementation is easy by translating them to a corner with an explicit tangent early in solve. This terminology may help in Spiro too.

To solve the confusion in a GUI, you may need to show this as a new type of explicit tangent.

(context: i'm translating this library to F# to here: https://github.com/terryspitz/dactyl-font/tree/spline-research/spline-research)