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    <p>I have some functions for hypercube and n-sphere selection that generate dataframes with cartesian coordinates and guarantee a uniform distribution through the hypercube or n-sphere for an arbitrary amount of dimensions :</p> <pre><code>GenerateCubiclePoints &lt;- function(nrPoints,nrDim,center=rep(0,nrDim),l=1){ x &lt;- matrix(runif(nrPoints*nrDim,-1,1),ncol=nrDim) x &lt;- as.data.frame( t(apply(x*(l/2),1,'+',center)) ) names(x) &lt;- make.names(seq_len(nrDim)) x } </code></pre> <p>is in a cube/hypercube of <code>nrDim</code> dimensions with a <code>center</code> and <code>l</code> the length of one side. </p> <p>For an n-sphere with <code>nrDim</code> dimensions, you can do something similar, where <code>r</code> is the radius :</p> <pre><code>GenerateSpherePoints &lt;- function(nrPoints,nrDim,center=rep(0,nrDim),r=1){ #generate the polar coordinates! x &lt;- matrix(runif(nrPoints*nrDim,-pi,pi),ncol=nrDim) x[,nrDim] &lt;- x[,nrDim]/2 #recalculate them to cartesians sin.x &lt;- sin(x) cos.x &lt;- cos(x) cos.x[,nrDim] &lt;- 1 # see the formula for n.spheres y &lt;- sapply(1:nrDim, function(i){ if(i==1){ cos.x[,1] } else { cos.x[,i]*apply(sin.x[,1:(i-1),drop=F],1,prod) } })*sqrt(runif(nrPoints,0,r^2)) y &lt;- as.data.frame( t(apply(y,1,'+',center)) ) names(y) &lt;- make.names(seq_len(nrDim)) y } </code></pre> <p>in 2 dimensions, these give :</p> <p><img src="https://i.stack.imgur.com/2c2kY.png" alt="enter image description here"></p> <p>From code :</p> <pre><code> T1 &lt;- GenerateCubiclePoints(10000,2,c(4,3),5) T2 &lt;- GenerateSpherePoints(10000,2,c(-5,3),2) op &lt;- par(mfrow=c(1,2)) plot(T1) plot(T2) par(op) </code></pre>
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    1. POGenerating multidimensional data
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    1. USRichie Cotton
    1. USJoris Meys
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    1. CO@Richie: thx for the tweak
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      1. USJoris Meys
    2. COThank you very much for your help and answers...
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      1. USPradeep
    3. CO@Pradeep -- If this answers your question better, you should consider accepting this answer rather than the one you did.
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      1. USPrasad Chalasani
 

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