Generating uniformly random distribution of points inside a sphere

 This code generates uniform random points within a sphere. The sphere is centred at the origin with a variable radius. The generation is by direct calculation, rather than by exclusion. I found many examples for this in python, mathematica etc. but none for Igor. Hopefully it's useful for somebody. 
////    @param  num     number of points to be generated
////    @param  Radius  radius of sphere
Function UniformSphere(num,Radius)
    Variable num,Radius
    
    Make/O/N=(num) xw,yw,zw
    Variable phi,theta,rr
    
    Variable i
    
    for(i = 0; i < num; i += 1)
        phi = pi + enoise(pi)
        theta = acos(enoise(1))
        rr = Radius * ((0.5 + enoise(0.5))^(1/3))
        xw[i] = rr * sin(theta) * cos(phi)
        yw[i] = rr * sin(theta) * sin(phi)
        zw[i] = rr * cos(theta)
    endfor
    DoWindow/K xyPlot
    Display/N=xyPlot yw vs xw
    ModifyGraph/W=xyPlot mode=3,marker=8
    ModifyGraph/W=xyPlot width={Plan,1,bottom,left}
    DoWindow/K yzPlot
    Display/N=yzPlot zw vs yw
    ModifyGraph/W=yzPlot mode=3,marker=8
    ModifyGraph/W=yzPlot width={Plan,1,bottom,left}
    DoWindow/K xzPlot
    Display/N=xzPlot zw vs xw
    ModifyGraph/W=xzPlot mode=3,marker=8
    ModifyGraph/W=xzPlot width={Plan,1,bottom,left}
End
It might be useful to add the following (requires IP7)
JointHistogram xw,yw,zw


Also, to visualize the distribution why not display it in Gizmo:
Concatenate {xw,yw,zw},triplet
NewGizmo
AppendToGizmo defaultScatter=triplet


Depending on the number of points you may want to either display them as a cloud or simply reduce the radius:
ModifyGizmo ModifyObject=scatter0,objectType=scatter,property={ size,0.2}

May 31, 2016 at 08:47 am - Permalink

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