Fast calculation of the distance to cubic Bezier curves on the GPU

> The next step is to work with chains of Bézier curves to make up complex shapes (such as font glyphs). It will lead us to build a signed distance field. This is not trivial at all and mandates one or several dedicated articles. We will hopefully study these subjects in the not-so-distant future.

If you only want to fill a path of bezier curves (e.g. for text rendering) you can do without the "distance" part from "signed distance field" [0], leaving you with a "signed field" aka. an implicit curve [1].

Meaning not having to calculate the exact distance but only the sign (inside or outside) can be done without all the crazy iterative root finding in an actually cheap manner with only four multiplications and one addition per pixel / fragment / sample for a rational cubic curve [3].

[0]: https://en.wikipedia.org/wiki/Signed_distance_function

[1]: https://en.wikipedia.org/wiki/Implicit_curve

[2]: https://github.com/Lichtso/contrast_renderer/blob/a189d64a13...

Cool. Maybe the next step can be to compute a set of bezier curves that (by a good approximation) closely cover the point-set that is exactly a given distance away from a given set of bezier curves.

Ok now all we need is an AI transformer model which can handle bezier curve embeddings as primitives instead of vector embeddings.