How to create a seamless cubemap noise texture?

Question

I have, so far, been able to create the vertices and UV coords etc for a sphere that would be textured with a cube map. I have also successfully loaded a cube texture from file and applied it to my sphere and it looks awesome.

So now, I want to randomly create a noise cube texture map to apply to my sphere.

I have a class which can create 1d, 2d, 3d and 4d noise. My problem is I don't know the math needed to sample a sphere map out of the cube, and then how to translate this to the 6 textures that make up with my cubemap.

I guess first I need to know how to first sample the points of a sphere in 3d; and then how to translate these to x,y,z coordinates for the 6 sides. I can probably work it out from there.

I would have thought this would be simple enough to Google, but I'm not finding what I need.

SOLUTION

For whomever comes along next, here's the answer. @Jason has the right idea below. Here's how I solved it:

1. March through each of the faces of the cube and each UV coord for that face
2. Normalize each position vector
3. Multiply by the radius of your sphere. You now have the coordinates of the sphere edge
4. These coordinates can be used to sample from your 3D noise function

You'll end up with each faces UV coordinates being filled with the noise that is at the spherical equivalents position in the noise.

(I hope that was in english). I will try to remember to update this later with full code once I've cleaned it up.

Answer 1

To generate noise which is isotropic, you need to sample from 3D space but from the surface of as sphere:

Here the black point is the location in space of the pixel in the image you want to generate the color for. Project it onto the unit sphere (the green point) by normalizing the vector from the origin (red), and then sample from your noise function (scale it up by a constant to get finer noise, or down to get softer noise). You will need functions to compute the x,y,z coordinates of a cube map pixel given the image dimensions, pixel x,y, and which face the pixel is on.

Note that classic Perlin noise has some serious artifacts when taking a 2D slice of 3D noise, so you should use another function, or add a bunch of randomly rotated copies of classic noise (which kinda hides the artifacts).

This noise will look distorted when you look at the raw images, but when rendered as a skybox it will appear uniform in every direction.

Answer 2

I have also successfully loaded a cube texture from file and applied it to my sphere and it looks awesome.

This implies that you've already calculated the UV's on the CPU and stored them in the vertices. Those same UV's should work for any cube textures that are similarly oriented since they all range from 0:1.

A diagram follows, in case it helps, but I think you're already doing this.

The gray sphere represents your skysphere.
The purple cube is just a cube with the same "radius" as the skysphere.
The green cube is a unit cube.

Given some arbitrary "forward" direction that corresponds to the cube map, and the normalized direction from each pixel world-coordinate to sphere-center, a few dot products will tell you which face to sample and how to convert the angle into a UV.

For example, when you are working with the top face, the normalized pixel world X and Z will become the UV. On the face shown below, Y and Z change but X is constant. The dot products range from -1:1 and UV's are 0:1 so you'll also need a linear scaling and translation i.e. (XZ + 1) / 2

The same, from above:

Any point within the face has an angle away from "face-forward" of -45:45. This corresponds to the dot range -1:1. Again, scaling to 0:1 range is trivial. This diagram occurs twice for each point; the face determines which of the 3 axis' go into the UV.

Answer 3

Please confirm that my other answer is not-at-all or, less-, applicable, so I can delete it.

This is one way to "unwrap" a cube, (neglecting the bottom face (assuming there is a terrain of some kind)).

(right-handed)
For face 1:
U+ corresponds to Y+
V+ corresponds to Z+

For face 4:
U+ corresponds to X+
V+ corresponds to Y-

and so on..

Answer 4

As I done in my project Seamles Noise Generator

I suggest to apply a 3d noise (i.e. 3d perlin noise) on the cube surface and unwrap it like already suggested

And use a cube sphere aproach

Answer 5

Your question is similar to what I'm doing , but I'm using libnoise , doing most of the work for me .Can generate 4 faces of a icoespher using libnoise(they fit perfectly in a icoesphere) and saving as bmp, but unfortunately , there must be some wrong in libnoise , which causes distortion in the top faces and down , looked at the code utils::NoiseMapBuilderSphere, which takes two latitudes and two longitudes and turns in an image and everything seems ok , the code looks like the first answer from user41442.

/*snipt from libnoise utils::NoiseMapBuilderSphere.*/
model::Sphere sphereModel;
sphereModel.SetModule (*m_pSourceModule);

double lonExtent = m_eastLonBound  - m_westLonBound ;
double latExtent = m_northLatBound - m_southLatBound;
double xDelta = lonExtent / (double)m_destWidth ;
double yDelta = latExtent / (double)m_destHeight;
double curLon = m_westLonBound ;
double curLat = m_southLatBound;

// Fill every point in the noise map with the output values from the model.
for (int y = 0; y < m_destHeight; y++) 
{
    float* pDest = m_pDestNoiseMap->GetSlabPtr(y);//get pointer to fill one slice of sphere, one at a time
    curLon = m_westLonBound;
    for (int x = 0; x < m_destWidth; x++) 
    {
        float curValue = (float)sphereModel.GetValue (curLat, curLon);
        *pDest++ = curValue;
        curLon += xDelta;
    }
    curLat += yDelta;
}

my code for gen faces Z+ Z- X+ X-:

for each face i change that :

heightMapBuilder.SetBounds (-45.0, 45.0, -45.0, 45.0); //Z+  front
heightMapBuilder.SetBounds (-45.0, 45.0,    45.0, 135.0);//X+ right
heightMapBuilder.SetBounds (-45.0, 45.0,   -225.0, -135.0);//Z- back
heightMapBuilder.SetBounds (-45.0, 45.0,  -135,-45 );//X-     left

just do not understand why it does not work with latitudes 45,90 and longitudes -180,180 for generating face top.