Re: [math-fun] Computational geometry software
I suspect that Jim wants to do exact (or at least very high precision) calculations. Some computational geometry problems merely want the *sign* of a determinant, but they need quite high (quad?) precision in order to make sure that that sign is correct. At 08:36 AM 11/20/2017, Andy Latto wrote:
If you want to do a lot of this sort of computation, I'll bet this is the sort of thing graphics processors are optimized to do fast.
Andy
On Mon, Nov 20, 2017 at 10:01 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of software (preferably in Mathematica) that computes the intersection of polytopes, or at least polygons?
I'd like to explore some more random-nonempty-intersection problems, and it'd be very helpful to be able to do numerical experiments in a flexible setting.
For instance, how many sides on average does the intersection of P, Q+v, and R+w have, conditioned on the event that the intersection is nonempty, where P, Q, and R are fixed parallelograms, and v and w are random translation vectors? (The usual caveats and clarifications about "random translation vectors" apply.) The answer might be that it depends on P, Q, and R, or it might be 4 (no matter what), or it might be some other number; maybe one of you can see a non-experimental approach, but I don't, so doing experiments is the next step for me. But I don't trust myself to write correct infrastructural code for handling polygons.
Jim Propp
PS: I'm still mulling over Veit's two puzzles about averages. I'm guessing that a key tool for solving his first puzzle is "V-E+F=2", or rather "V-E+F is negligible when V, E, and F are large", but I don't see what the answer is.
<< Represent your polygons (polytopes) as disjoint unions of triangles (simplices). >> Which I seem to recall is not in general possible for dimension greater than planar --- tho' obviously possible if convex. WFL On 11/20/17, Henry Baker <hbaker1@pipeline.com> wrote:
I suspect that Jim wants to do exact (or at least very high precision) calculations. Some computational geometry problems merely want the *sign* of a determinant, but they need quite high (quad?) precision in order to make sure that that sign is correct.
At 08:36 AM 11/20/2017, Andy Latto wrote:
If you want to do a lot of this sort of computation, I'll bet this is the sort of thing graphics processors are optimized to do fast.
Andy
On Mon, Nov 20, 2017 at 10:01 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of software (preferably in Mathematica) that computes the intersection of polytopes, or at least polygons?
I'd like to explore some more random-nonempty-intersection problems, and it'd be very helpful to be able to do numerical experiments in a flexible setting.
For instance, how many sides on average does the intersection of P, Q+v, and R+w have, conditioned on the event that the intersection is nonempty, where P, Q, and R are fixed parallelograms, and v and w are random translation vectors? (The usual caveats and clarifications about "random translation vectors" apply.) The answer might be that it depends on P, Q, and R, or it might be 4 (no matter what), or it might be some other number; maybe one of you can see a non-experimental approach, but I don't, so doing experiments is the next step for me. But I don't trust myself to write correct infrastructural code for handling polygons.
Jim Propp
PS: I'm still mulling over Veit's two puzzles about averages. I'm guessing that a key tool for solving his first puzzle is "V-E+F=2", or rather "V-E+F is negligible when V, E, and F are large", but I don't see what the answer is.
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