Spherical Coordinates

[sessionbeer]

Hello,

I'm trying to replicate the same deformation as seen in the gif below. After some research I believe it's got something to do with Spherical Coordinates?

I implemented the formula from this site  which is:

radius = sqrt(x^2 + y^2 + z^2)
polar = arccos(z/radius)
azimuthal = atan2(y, x)

x = radius * sin(polar) * cos(azimuthal)
y = radius * sin(polar) * sin(azimuthal)
z = radius * cos(polar)

But this results in some pinching of the cube at both poles, so maybe this isn't right, or I haven't done it correctly?

Has any one got any experience with something like this? Any help would be really appreciated.

Thank you

 

sphere_deform.hip

Edited October 25, 2016 by sessionbeer

[galagast]

Hi, here's my quick take on it. Didn't use Spherical Coordinates though.. also apologies as I was just eye-balling some of the values >_<

H15.5.607 Indie

sphere_wrap.hiplc

[mestela]

Feels similar to the mobius transformation stuff here:

 

 

 

[sessionbeer]

Thanks @galagast and @mestela, Unfortunately I don't think either of those routes are right for this deformation, and after some more research I think I may have titled this post wrong. I'm not sure what the formula is called but I think this is getting pretty close to it:

 

float len = length(@P);
float a   = (fit(len, 0, 2, 0, $PI*0.5));
float r   = chf("radius");

f@x = r * cos(a);
f@y = r * sin(a);

@P.x *= @y;
@P.y *= @y;
@P.z  = @x*2;

I'm basically wrapping a disc shape around a sphere but using the centre point as the front of the sphere, and the sides of the disc as the back of the sphere. This looks like its close but I cant get the points to push out into a proper spherical shape? Can any one spot my silly mistake here and why I can't get the points out into the sphere shape?

Any help would be amazing as I'm so confused why its not working?

Thank you

 

sphere_wrapping_disc.hip

[galagast]

It may not be in-line with the formula you're using.. if you try adding this to the last line of the code, is it what you were after?:

@P = normalize(@P) * r*2;

 

@mestela: Those are gold! thank for the link!

 

 

Edited October 26, 2016 by galagast

[sessionbeer]

@galagast thanks for the quick reply! I just tried that line of code and although it visually looks correct, it seems to only work in that one situation  for example if you placed a box or grid as the input geo, like in the gif above, it breaks the formula. It feels so close though!