Comment by Lichtso

> "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 anti-aliasing, composite shapes of more than one bezier curve and boolean operators for masking / clipping. Using the stencil buffer for counting the winding number allows to do all of that very easily without tessellation or decomposition at path intersections.

> Can you elaborate on it or provide resources?

If you are interested in the theory behind implicit curve rendering and how to handle the edge cases of cubic bezier curves checkout these papers:

Loop, Charles, and Jim Blinn. "Resolution independent curve rendering using programmable graphics hardware." https://www.microsoft.com/en-us/research/wp-content/uploads/...

BARROWCLOUGH, Oliver JD. "A basis for the implicit representation of planar rational cubic Bézier curves." https://arxiv.org/abs/1605.08669

> The distance is only irrelevant for plain 2D text rendering, right?

Yes, as I said it is relevant for text rendering, but not necessarily 2D. It can also be embedded in a 3D perspective as long as the text itself is planar. Meaning you can directly render text in a 3D scene this way without rendering to a texture first.

> But real shadows and lighting would require the distance aspect, no?

I think the difference is in stroke vs fill, not the illumination (as you could still use shadow mapping / projection). In stroking you need to calculate an offset curve either explicitly or implicitly sample it from a signed distance field. Thus the exact distance matters for stroking, for filling it does not.