most recent 30 from http://mathoverflow.net 2013-06-19T09:52:33Z http://mathoverflow.net/feeds/question/9968 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/9968/how-to-transform-a-plane-into-a-sphere-solved psihodelia 2009-12-28T17:16:04Z 2013-06-07T14:33:08Z

<p>Given a 2-dimensional array of MxN heights, how to transform it to a sphere? Every element of this array is just a 3D point (x,y,z) where z represents some height. One has to transform this array into a sphere, twisting it around the origin so, that only minimal distortions will happen.</p> <p>Representing it by spherical coordinates is not very good, because of the severe distortions. It's probably better if there is no direct one-to-one mapping from 2D plane to a surface of 3D sphere - many plane's points will not be involved. But what is the best possible mapping and how to transform involved points (elements of array)? </p> <p>This is for a 3D-planet terrain simulation. First, fractal landscape is produced, then, it is to be transformed to 3D sphere.</p> <p>Thanks in advance!</p> <p><strong>SOLUTION</strong>: <a href="http://en.wikipedia.org/wiki/Map%5Fprojection" rel="nofollow">Map projection</a></p>

http://mathoverflow.net/questions/9968/how-to-transform-a-plane-into-a-sphere-solved/9970#9970 B. Bischof 2009-12-28T17:30:42Z 2009-12-28T17:30:42Z

<p>I may be misunderstanding your question but if you are asking how to take a data set of points in R^3 and convert them to a surface of a sphere then you can use the transformations given on wikipedia by associating latitude and longitude to your plane. I wrote code to do this myself for the math modeling competition a couple years ago. </p> <p>Sorrry for the limited scope of this answer and the lack of hyperlinks I am updating from the iPhone and that makes it a little bit annoying. </p>

http://mathoverflow.net/questions/9968/how-to-transform-a-plane-into-a-sphere-solved/133076#133076 Zahra 2013-06-07T14:33:08Z 2013-06-07T14:33:08Z

<p>Hi B. Bischof,</p> <p>I need to map 3D points on a unit Gauss sphere. As you mentioned that you already wrote a code for that, can you please help me?</p>