R: Does R have a package for generating random numbers in multi-dimensional space? For example, suppose I want to generate 1000 points inside a cuboid or a sphere.

12 down vote

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 : GenerateCubiclePoints <- function(nrPoints,nrDim,center=rep(0,nrDim),l=1){     x <-  matrix(runif(nrPoints*nrDim,-1,1),ncol=nrDim)     x <-  as.data.frame(             t(apply(x*(l/2),1,'+',center))           )     names(x) <- make.names(seq_len(nrDim))     x} is in a cube/hypercube of nrDim dimensions with a center and l the length of one side. For an n-sphere with nrDim dimensions, you can do something similar, where r is the radius : GenerateSpherePoints <- function(nrPoints,nrDim,center=rep(0,nrDim),r=1){     #generate the polar coordinates!     x <-  matrix(runif(nrPoints*nrDim,-pi,pi),ncol=nrDim)     x[,nrDim] <- x[,nrDim]/2     #recalculate them to cartesians     sin.x <- sin(x)     cos.x <- cos(x)     cos.x[,nrDim] <- 1  # see the formula for n.spheres     y <- 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 <-  as.data.frame(             t(apply(y,1,'+',center))           )     names(y) <- make.names(seq_len(nrDim))     y} in 2 dimensions, these give : From code :  T1 <- GenerateCubiclePoints(10000,2,c(4,3),5)  T2 <- GenerateSpherePoints(10000,2,c(-5,3),2)  op <- par(mfrow=c(1,2))  plot(T1)  plot(T2)  par(op) link|improve this answer edited Feb 16 '11 at 17:03 Richie Cotton 17.5k11156 answered Feb 16 '11 at 13:50 Joris Meys 22k23265

@Richie: thx for the tweak – Joris Meys Feb 16 '11 at 22:20 Thank you very much for your help and answers... – Pradeep Feb 17 '11 at 6:26 @Pradeep -- If this answers your question better, you should consider accepting this answer rather than the one you did. – Prasad Chalasani Jun 14 '11 at 19:14 feedback

up vote 2 down vote

Cuboid: df <- data.frame(     x = runif(1000),     y = runif(1000),     z = runif(1000) ) head(df)           x           y         z1 0.7522104 0.579833314 0.7878651 2 0.2846864 0.520284731 0.8435828 3 0.2240340 0.001686003 0.2143208 4 0.4933712 0.250840233 0.4618258 5 0.6749785 0.298335804 0.4494820 6 0.7089414 0.141114804 0.3772317 Sphere: df <- data.frame(     radius = runif(1000),     inclination = 2*pi*runif(1000),     azimuth = 2*pi*runif(1000) ) head(df)      radius inclination  azimuth1 0.1233281    5.363530 1.747377 2 0.1872865    5.309806 4.933985 3 0.2371039    5.029894 6.160549 4 0.2438854    2.962975 2.862862 5 0.5300013    3.340892 1.647043 6 0.6972793    4.777056 2.381325 Note: edited to include code for sphere link|improve this answer edited Feb 16 '11 at 13:55 answered Feb 16 '11 at 13:28 Andrie 25.7k33276

1   I want to to generate points within the boundary of a specified shape.. say a cuboid ,cube ,sphere ??.... is there any way to generate such datasets ?? – Pradeep Feb 16 '11 at 13:46 Code added in edit. – Andrie Feb 16 '11 at 13:56 feedback

up vote 1 down vote

A couple of years ago, I made a package called geozoo. It is available on CRAN. install.packages("geozoo") library(geozoo) It has many different functions to produce objects in N-dimensions. p = 4 n = 1000 # Cube with points on it's face.   # A 3D version would be a box with solid walls and a hollow interior. cube.face(p) # Hollow sphere sphere.hollow(p, n) # Solid cube cube.solid.random(p, n) cube.solid.grid(p, 10) # evenly spaced points # Solid Sphere sphere.solid.random(p, n) sphere.solid.grid(p, 10) # evenly spaced points One of my favorite ones to watch animate is a cube with points along its edges, because it was one of the first objects that I made. It also gives you a sense of distance between vertices. # Cube with points along it's edges.   cube.dotline(4) Also, check out the website: http://streaming.stat.iastate.edu/~dicook/geometric-data/. It contains pictures and downloadable data sets. Hope it meets your needs!