Let's say that I need to reconstruct a surface that could be cloned 6 times to create a perfect sphere.
It is sampled in some finite N elements per side so the patch will have NxN elements (vertex)
So I will iterate from -0.5 to 0.5 in XY axis being 0 0 the center of my patch.
Ideally I was about iterating like that
sphericalTheta = xpos * (pi / 2.0);
sphericalPhi = ypos * (pi / 2.0);
Being xpos and ypos the iterators over that -0.5 0.5 range
so I expected that this should work:
mX = cos(sphericalPhi) * sin(sphericalTheta);
mY = cos(sphericalPhi) * cos(sphericalTheta);
mZ = sin(sphericalPhi);
but obviously it didn't work
Seeing that result intuitively I notice that I should modify my iterators since -0.5 0.5 only works when the other coordinate in the pair is 0
newypos = ypos * cos(abs(xpos)* (pi / 3.0));
newxpos = xpos * cos(abs(ypos)* (pi / 3.0));
sphericalTheta = newxpos * (pi / 2.0);
sphericalPhi = newypos * (pi / 2.0);
It gets better but still it has some overlaps.
Side note: this is NOT the same as Sphere parameterization with 6 patches
Thank you in advance.