From: dwells@nrao.edu (Don Wells) Newsgroups: sci.math.num-analysis,comp.graphics.algorithms Subject: Re: Covering a sphere with points Date: 07 Feb 1997 23:14:26 GMT "HS" == Hartmut Schmider writes: HS> I am trying to cover a sphere with a sensible large grid of HS> points. Each of the points will be "representative" for a small area around HS> it. For integration, it is clear that a "cos(theta)/phi" grid of kinds HS> will do the job, but for my purposes (interpolation) this leads to large HS> errors near the poles. So I guess i am looking for a **simple** way of HS> constructing an even grid on a sphere, that allows quick assignment of HS> neighboring points. The main point is it has to be simple (ie, it needs to HS> be fast to assign any point on the sphere to the nearest gridpoint). In a recent issue of "The Mathematical Intelligencer", I saw a discussion of the concept of "generalized spiral points", which cover the sphere with an even distribution of points. A Web search for "generalized spiral" found the URL http://pascal.math.nwu.edu:80/talk1/paper/node13.html which is part of a paper titled "Arranging Points on the Sphere" (follow the "Up" link of the URL above). It appears that this paper does not discuss the problem of finding the nearest point of the set of generalized spiral points. My suggestion is to construct a lookup table to get close to the answer, so that you only have to make distance calculations for a small set of points (probably four). The table might be simple grid of longitude/latitude; an equal-area mapping to a lookup table (e.g., the quadrilateralized spherical cube) is probably overkill in this era of abundant RAM. -- Donald C. Wells Associate Scientist dwells@nrao.edu http://fits.cv.nrao.edu/~dwells National Radio Astronomy Observatory +1-804-296-0277 520 Edgemont Road, Charlottesville, Virginia 22903-2475 USA ==============================================================================