contrast_renderer

> "a³-bcd ≤ 0" formula These are the coefficients of the implicit curve, finding them can be done once upfront. For integral quadratic bezier curves that is trivial as they are constant, see: https://www.shadertoy.com/view/fsXcDj For rational cubic bezier curves it is more involved, see: https://www.shadertoy.com/view/ttVfzh And for the full complexity of dealing with self intersecting loops and cusps see: https://github.com/Lichtso/contrast_renderer/blob/main/src/f... > The winding number logic is usually super involved, especially when multiple sub-shapes start overlap and subtracting each other. Is this covered or orthogonal to what you are talking about? Orthogonal: The implicit curve only tells you if you are inside or outside (the sign of the SDF), so that is technically sufficient, but usually you want more things: Some kind of ant

> 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_functi