Test for inconsistencies between place() and intersects() #112
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We’re looking for cases where place(a, b, c) will place c so it intersects with a or b.
The old place(a, b, c) function would sometimes place c so it overlapped with a and/or b, if c had a much larger radius than a and b. This version doesn’t seem to. As per discussion on d3#111. This commit also updates the tests in find-place-bugs.js to use the new function, and updates the intersection test in siblings-test.js to match Note that flare-test.js fails. I haven’t investigated why: I hope it is simply a result of the changes in numerical precision causing slightly different circle placements.
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I like the idea of choosing the larger of the two circles as the starting center. I’ve written up some notes here and will take a crack at merging our two implementations soon: https://beta.observablehq.com/@mbostock/tangent-to-two-circles |
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The idea behind my code is to use a coordinate frame in which the first circle (say a) is centred at the origin, and the second (say b) at (1, 0). In this frame the equations are easy to solve, then we transform the result back to the original coordinate system. Subtracting the equations gives 1 - 2x = (rb + rc)^2 - (ra + rc)^2 = (rb - ra)(ra + rb + 2rc), which gives x; then y = ±sqrt((ra + rc)^2 - x^2). |
Since the values that had been divided by scale = sqrt(dc) are only being used in pairs, we can avoid the square root and just divide by dc instead. This should help with the precision, marginally, I hope.
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Our approaches are equivalent:
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Improved
place(a, b, c)function that avoids overlaps between c and a or b.Note that
flare-test.jsfails. I haven’t investigated why: I hope it is simply a result of the changes in numerical precision causing slightly different circle placements.See discussion on #111. Fixes #109.