Issue #43 #51
Issue #43 #51
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…e a majority vote) Solves #43.
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Cleaner version. The fixes for voronoi will be in d3-delaunay (d3/d3-delaunay#86). |
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That's such an awesome fix! It will probably still have some edge cases, especially considering that asymmetric orientation tests can occur within a set of points > 3 (where pairwise they're stable but inconsistent as a system), and that inCircle tests may be unstable too. But if it makes the library more robust without affecting performance much, I'm up for it!
index.js
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| @@ -379,7 +379,14 @@ function dist(ax, ay, bx, by) { | |||
| } | |||
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| function orient(px, py, qx, qy, rx, ry) { | |||
| return (qy - py) * (rx - qx) - (qx - px) * (ry - qy) < 0; | |||
| const d = cross(px, py, qx, qy, rx, ry); | |||
| if (Math.abs(d) > 1e-6) return d < 0; | |||
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I wonder how much we could lower the 1e-6? That may be too high for the purpose.
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In all the examples I had either large numbers, or very small ones (for triangles that were definitely problematic). In those examples it looked like the small value was ~1e-11 or less, but I don't know when the precision stops being a problem.
(In any case the cost for such small triangles is just +2 area computations.)
An asymmetric (but consistent) method could be to start with the top-left point of the set — but for triangles it would be less elegant (and probably more code).
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Did some exploration of the topic and came up with an alternative approach ("More precise" in the notebook) — @Fil check it out and let me know what you think: https://observablehq.com/@mourner/non-robust-arithmetic-as-art |
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👍 I like the fact that it separates And the notebook is ⚡️ |
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It may be a little slower than the voting approach because of the extra operations for bounds checking, but the advantage is that it's a proven error bound — with arbitrary ones like |
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Actually somehow it looks ~15-20% faster — here are my results if you change The tests failed at first but that turned out to be because of non-robust convex check. :) Updated to use the same formula there too and it passes now. Pushed my commit here. |
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Fantastic work! 👏👏👏 |
Based on mapbox/delaunator#51 Along with the last missing test case "issue44".
* Robust orient2d checks * Add example to display triangulation in SVG * Clean up svg.rs example * Split fixture tests into separate test cases * Add test case for #10 * Copy remaining robustness tests from js repo * Add point label to svg example to easy investigations * Add grid test fixture * Add hull convex check to tests Based on mapbox/delaunator#51 Along with the last missing test case "issue44". * Remove invalid test code for connectivity
This PR contains a fix and test for #43: the idea is that the cross-product ABxAC is not stable, so we have a majority vote on the sign of ABxAC, BCxBA, CAxCB. The formula for the majority vote is symmetric, so it always gives the same answer for a given triangle. (For performance, we don't call the vote if ABxAC is not too small.)
I've also included a fix and test files for related issues with the voronoi (https://observablehq.com/d/bd8a95abd9a01c79 & https://observablehq.com/d/b219d92fae85fc9b), but as these issues only show in voronoi (ie in d3-delaunay)—the tests don't actually fail. I'm not sure what to do with this part — I don't see a way of fixing that in d3-delaunay directly though, so I've stuck it here for discussion.With these two, all the test notebooks are fixed.