Random points on a unit sphere without biasing 2005-06-14 - By Andy Jones
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This is interesting. I haven't done the math on quaternions to see if
this should work, but when I run the script, my eye is telling me
there's a slight bias around the X-axis equator. Of course, I don't
think every possible value of a 2x2 matrix in [-1,1] defines a valid
quaternion, so it could be that the bias is coming from the particular
mapping the quaternion set method is using to go from that matrix space
to the space of valid quaternions.
-Andy
Bradley R. Gabe wrote:
> It's an interesting exercise. I'm not a mathematician by any stretch,
> but here's a little jscript that'll distribute points in a unit sphere
> by randomly calculating a quaternion rotation, then transforming 1
> unit from origin. I use a particle cloud to visualize the point
> distribution.
>
> // SPHERICAL POINT DIST
> var radius = 0.5;
> var pnts = 1000;
>
> // Create New particle Type
> var pTypeColl = CreateParticleType();
> pType = pTypeColl(0);
>
> // Create Cloud
> var cloud = ActiveSceneRoot.AddParticleCloud();
> var cloudPrim = cloud.ActivePrimitive;
> cloudPrim.AddParticles(pnts, pType);
> particles = cloudPrim.Particles;
>
>
> // For each particle, set a random distribution
> for(var i=0; i<pnts; i++){
>
> // Get XSIMath objects for calculating random rot
> var rot = XSIMath.CreateRotation();
> var q1 = XSIMath.CreateQuaternion();
> var trans = XSIMath.CreateTransform();
> var pos = XSIMath.CreateVector3();
> var radPos = XSIMath.CreateVector3();
> radPos.Set(radius, 0,0);
>
> // Calculate random quaternions
> var W = Math.random() * 2 - 1;
> var X = Math.random() * 2 - 1;
> var Y = Math.random() * 2 - 1;
> var Z = Math.random() * 2 - 1;
> q1.set(W,X,Y,Z);
>
> // Create a unit transform from quaternion rotation
> rot.SetFromQuaternion(q1);
> trans.SetRotation(rot);
> trans.AddLocalTranslation(radPos);
> trans.GetTranslation(pos);
>
> // Set particle to unit transform;
> particles(i).position = pos;
>
> }
>
>
>
>> Hi All,
>>
>> This is to the maths geniuses in the room. I want to generate X number
>> of points on a unit sphere, but be sure I won't have any biasing
>> involved.
>>
>> My first thought was just to use a couple of random numbers (let's
>> assume they don't have any bias) and then use those with a few sin and
>> cos function etc to generate the points. Though I have a feeling that
>> would give me more points around the poles.
>>
>> Anyone have some good suggestions?
>>
>> Cheers,
>>
>> Alan.
>>
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