SCR_SpherePointGenerator.c

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class SCR_SpherePointGenerator
{
    const float GOLDEN_RATIO = 1.618033988749895; // limited to 16 places, rounded away from zero
    const float INV_GOLDEN_RADIO_RAD = 3.883222077450933; // 2 * Pi / GOLDEN_RATIO limited to 16 places, rounded away from zero
    const float PI4 = 12.56637061435917; // 4 * Pi limited to 16 places, rounded away from zero
    const float POINT_DIST_SPHERE_EXP = 2.231; // Significantly improves accuracy of spacing predictions. This number was manually goal-searched by optimising for Root Mean Square Error on GetPointOnUnitSphere's results and predictions that use this exponent.
    const float INV_POINT_DIST_SPHERE_EXP = 0.4482294935006723; // 1 / 2.231 limited to 16 places, rounded away from zero
 
    //------------------------------------------------------------------------------------------------
    static vector GetPointOnUnitSphereFromEquator(int amount, int index)
    {
        int isIndexOdd = 1 & index;
        int centerOffset = index >> 1;
        if (isIndexOdd)
            centerOffset = -(centerOffset + 1);
        int centeredIndex = ((int)(0.5 * amount)) + centerOffset;
        return GetPointOnUnitSphere(amount, centeredIndex);
    }
 
    //------------------------------------------------------------------------------------------------
    static vector GetPointOnUnitSphere(int amount, int index)
    {
        if (amount < 1)
            return vector.Zero;
 
        float theta = index * INV_GOLDEN_RADIO_RAD;
        float phi = Math.Acos(1 - 2 * index / amount); // Math.Acos already limits the domain to [-1, 1], which is acceptable. No additional bounds checking is needed.
        return { Math.Cos(theta) * Math.Sin(phi), Math.Cos(phi), Math.Sin(theta) * Math.Sin(phi) };
    }
 
    //------------------------------------------------------------------------------------------------
    static int EstimatePointsFromSpacingOnUnitSphere(float spacing)
    {
        if (float.AlmostEqual(spacing, 0))
            return float.INFINITY;
 
        float areaPerPoint = Math.Pow(spacing, POINT_DIST_SPHERE_EXP);
        float pointsEst = PI4 / areaPerPoint;
        return Math.Ceil(pointsEst);
    }
 
    //------------------------------------------------------------------------------------------------
    static float EstimateSpacingFromPointsOnUnitSphere(int amount)
    {
        if (amount < 1)
            return -1;
 
        float areaPerPoint = PI4 / amount;
        return Math.Pow(areaPerPoint, INV_POINT_DIST_SPHERE_EXP);
    }
}