| ▲ | ux 18 hours ago | |||||||
Finding the sign of the distance has been extremely challenging to me in many ways, so I'm very curious about the approach you're presenting. The snippet you shared has a "a³-bcd ≤ 0" formula which is all I get without more context. Can you elaborate on it or provide resources? 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? | ||||||||
| ▲ | Lichtso 16 hours ago | parent [-] | |||||||
> "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 | ||||||||
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