Create points evenly on a sphere

Question

Create points evenly on a sphere

I am interested in creating points that are “evenly” (and not coincidentally) distributed around a sphere, like the dimples of a golf ball or the vertices of hexagons on a soccer ball. Are there any specific algorithms for this?

Note. I know that the points are not really "evenly" distributed over the sphere, but they are distributed in such a way that the distribution of the points looks the same from any direction that looks directly at any of the points - this is what interests me.

+3

algorithm

astrofrog Dec 03 '10 at 20:49

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7 answers

Mads Elvheim · Answer 1 · 2010-12-03T20:59:11+0000

. . .

psuedo ++, :

/* Assume 'data' initially holds vertices for eight triangles (an octahedron) */
void GenerateSphere(float radius, std::vector<Vector3f>& data, int accum=10)
{
    assert( !(data.size() % 3) );

    std::vector<Vector3f> newData;

    for(int i=0; i<data.size(); i+=3){
        /* Tesselate each triangle into three new ones */
        Vector3f centerPoint = (data[i] + data[i+1] + data[i+2]) / 3.0f;

        /* triangle 1*/
        newData.push_back(data[i+0]);
        newData.push_back(data[i+1]);
        newData.push_back(centerPoint);
        /* triangle 2*/
        newData.push_back(data[i+1]);
        newData.push_back(data[i+2]);
        newData.push_back(centerPoint);
        /* triangle 3*/
        newData.push_back(centerPoint);
        newData.push_back(data[i+2]);
        newData.push_back(data[i+0]);
    }
    data = newData;
    if(!accum){
        /* We're done. Normalize the vertices,
             multiply by the radius and return. */
        for(int i=0; i<data.size(); ++i){
            data[i].normalize();
            data[i] *= radius;
        }
    } else {
        /* Decrease recursion counter and iterate again */
        GenerateSphere(radius, data, accum-1);
    }
    return;
}