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Groups > comp.lang.c > #144762
| From | "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> |
|---|---|
| Newsgroups | comp.lang.c |
| Subject | Re: Choosing a random point on a sphere surface |
| Date | 2019-06-12 00:42 -0700 |
| Organization | Aioe.org NNTP Server |
| Message-ID | <qdqadj$lf3$2@gioia.aioe.org> (permalink) |
| References | <random-sphere-20190610162901@ram.dialup.fu-berlin.de> <h4XLE.29681$6X.21034@fx43.iad> <ln4l4vr3ie.fsf@kst-u.example.com> <qdpo39$mto$1@dont-email.me> |
On 6/11/2019 7:30 PM, James Kuyper wrote: > On 6/11/19 9:33 PM, Keith Thompson wrote: >> Clifford Heath <no.spam@please.net> writes: > ... >>> I just came up with a very nice alternate way to uniformly choose a >>> point on a unit sphere, with arbitrary granularity. Use a hierarchical >>> triangular mesh with a random binary bit-string of 3+2n bits. Convert >>> the HTM value into your chosen coordinate system, job done. >>> >>> HTM is a generalised coordinate system for points on the globe, based on >>> an iterated triangular subdivision of the sides of an octahedron. >>> >>> <http://www.skyserver.org/htm/> >>> <https://www.microsoft.com/en-us/research/publication/indexing-the-sphere-with-the-hierarchical-triangular-mesh/> >> >> I don't believe the selection is uniform. >> >> Quoting from your second link (emphasis added): >> >> We describe a method to subdivide the surface of a sphere into >> spherical triangles of similar, *but not identical*, shapes >> and sizes. >> >> We start with the surface of the sphere partitioned into 8 identical >> spherical triangles, with 90-degree vertices. Considering one >> of the 8 triangles, we draw great circle segments connecting the >> midpoints of the edges, partitioning it into 4 smaller triangles. >> I believe the outer 3 triangles are congruent to each other, but >> the central one is not. >> >> It looks like a useful way to define a coordinate system on the >> surface of a sphere, but it doesn't produce equal-area triangles >> (and it's not intended to). >> >> I don't quite have the math to confirm or refute this. Anyone else? > > The document itself says that, at any given level of sub-division, the > biggest triangles have roughly twice the area of the smallest triangles, > so it's definitely not a way to produce a spherically uniform set of points. > Sounds very fractal... Humm...
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Re: Choosing a random point on a sphere surface Clifford Heath <no.spam@please.net> - 2019-06-12 09:47 +1000
Re: Choosing a random point on a sphere surface Keith Thompson <kst-u@mib.org> - 2019-06-11 18:33 -0700
Re: Choosing a random point on a sphere surface James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-11 22:30 -0400
Re: Choosing a random point on a sphere surface Clifford Heath <no.spam@please.net> - 2019-06-12 12:54 +1000
Re: Choosing a random point on a sphere surface "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-12 00:42 -0700
Re: Choosing a random point on a sphere surface fir <profesor.fir@gmail.com> - 2019-06-18 11:21 -0700
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