Ivan Reese
06/26/2019, 2:36 AMwtaysom
06/26/2019, 4:24 AMshalabh
06/26/2019, 4:30 AM>>> 2 * sympy.sqrt(2)
2*sqrt(2)
>>> 2 * sympy.sqrt(2) == sympy.sqrt(8)
True
It appears to keep the symbolic expressions in some normal form so it can do equality checks when the same irrational is computed differently (at least in the above case)Ivan Reese
06/26/2019, 4:39 AMwtaysom
06/26/2019, 5:38 AMIvan Reese
06/26/2019, 5:58 AMsometimes continuous time works well between discrete collisionsYeah, that's exactly what I'm planning to do ā if I suck and end up using discrete representations of time and space, I'll interpolate so as to recover some measure of continuity, which will be perfectly lossless when away from collision events (thanks for nothing, Nyquist!). As for linear approximations ā totally, yes, that's pretty much my only option for working with them in bounded time, as far as I'm aware, unless there's some fast implementation of constructible numbers Conal is withholding from us.
Joshua Horowitz
06/26/2019, 8:26 AMwtaysom
06/26/2019, 9:44 AMKonrad Hinsen
06/26/2019, 2:44 PMIvan Reese
06/26/2019, 3:44 PMjarm
06/26/2019, 6:01 PMIvan Reese
06/26/2019, 11:07 PMThe second and deeper problem is that numerical weapons are per se less effective in geometric computing than they are in other fields. In geometry, we don't compute numbers but structures: convex hulls, triangulations, etc. In building these structures, the underlying algorithms ask questions like "is a point to the left, to the right, or on the line through two other points?" Such questions have no answers that are "slightly off". Either you get it right, or you don't. And if you don't, the algorithm might go completely astray. Even the most fancy roundoff control techniques don't help here: it's primarily a combinatorial problem, not a numerical one.
We concentrate on the geometry (after all, that's what we do best), and the CGAL algorithms themselves don't contain any numerical security measures to keep them from going astray.That's perfect. And I think I can do just as well by restricting my domain to things that are simple, cleanly representable, and closed-form. Fingers crossed!
Doug Moen
06/27/2019, 1:02 PMDeklan Webster
06/27/2019, 3:14 PMDoug Moen
06/27/2019, 4:31 PMKonrad Hinsen
06/27/2019, 4:52 PMwtaysom
06/27/2019, 4:58 PMDoug Moen
06/27/2019, 5:26 PMDeklan Webster
06/27/2019, 5:31 PMwtaysom
06/27/2019, 6:43 PMhttps://www.youtube.com/watch?v=cyW5z-M2yzwā¾
shalabh
06/27/2019, 8:25 PMDoug Moen
06/27/2019, 9:38 PM