A basis for the implicit representation of planar rational cubic Bézier curves · HackerPapers discussionshttps://hackerpaper.kaipfister.de/p/1605.08669/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMTA basis for the implicit representation of planar rational cubic Bézier curves — mentioned by Lichtsohttps://news.ycombinator.com/item?id=45628349urn:hackerpapers:mention:1605.08669:45628349Sat, 18 Oct 2025 16:00:00 GMT<p>&gt; &quot;a³-bcd ≤ 0&quot; 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... &gt; The winding number logic is usually super involved, especially when multiple sub-shapes start overlap and subtracting each…</p><p><a href="https://hackerpaper.kaipfister.de/p/1605.08669/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.NA