我正在寻找数学变换来将2D平面[0,1]x[0,1]上的点变换到单位球面上.
最常见的投影将纬度-经度映射通过解释u和v作为球面坐标的角度(映射u到[0,2PI]和v到[-PI/2, PI/2])
这会对球体的极点产生强烈的扭曲.人们可以把这种转变想象成将球体包裹成两端旋转纸张的糖果纸.这会在这两端造成扭曲.
The transformation I'm looking for can be rater thoght of putting the sphere into the middle of a paper and putting all sides around the sphere and twirl them together on a single spot - so you get a little paper-bag with your sphere in it. This yelds minimal distortion on the bottom of the "bag" and maximum distoriton on the top …