Uniform Sampling from Parametrized Submanifolds in Scala

Here is the code for yesterday’s post but written in scala language instead of lisp.

import scala.collection.immutable

def writeSampleToFile(n: Int, fn: () => IndexedSeq[Double], filename:String) = {
  val      out = new java.io.PrintWriter(filename)
  val mySample = (1 to n) map (x => fn())

  for(point <- mySample) 
     out.println(point.foldLeft("")( (a,b) => "%s %4.3f " format(a,b) ))

  out.close
}


def sampleFromSimplex() = {
  val x = math.sqrt(math.random)
  val y = math.random

  IndexedSeq(x*y,x-x*y,1-x)
}


def sampleFromSphere() = {
  val   rho = math.pow(math.random,1/3)
  val   phi = math.acos(2*(math.random - 0.5))
  val theta = 2*math.Pi*math.random

  IndexedSeq(rho*math.cos(theta)*math.sin(phi),
             rho*math.sin(theta)*math.sin(phi),
             rho*math.cos(phi))
}


def sampleFromTorus(a:Double, b:Double) = {
  val theta = 2*math.Pi*math.random
  val   phi = 2*math.Pi*math.random
  val   rho = a + b*math.cos(theta)

  IndexedSeq(rho*math.cos(phi),
             rho*math.sin(phi),
             rho*math.sin(theta))
} 

writeSampleToFile(400,sampleFromSimplex,"./simplex.csv")
writeSampleToFile(400,sampleFromSphere,"./sphere.csv")
writeSampleToFile(2000,(()=>sampleFromTorus(6.0,1.0)),"./torus-large.csv")
writeSampleToFile(2000,(()=>sampleFromTorus(2.1,1.0)),"./torus-small.csv")