normalCurve2.frink

View or download normalCurve2.frink in plain text format


// This program draws the normal curve or "bell curve" used in statistics.
// It's a bit slow because calculating inverseErf for very high sigmas is
// quite slow.

use statistics.frink

plotNormal[mean, sigma, steps, g is graphics] :=
{
   low = 1/steps             // Use rational numbers so that the exactly
   high = 1-low              // right number of points is plotted.
   println["low is $low"]
   minSigma = inversePhi[low, 8]
   println["minsigma is $minSigma"]
   maxSigma = inversePhi[high, 8]
   println["maxsigma is $maxSigma"]
   
   vscale = 8 sigma^2           // Found experimentally to look good.
   ceilingH = normalDensity[mean + sigma * maxSigma, mean, sigma]
   scaledCeilingH = ceilingH * vscale
   r = scaledCeilingH

   println["ceiling H is $ceilingH"]
   println["scaled ceiling is $scaledCeilingH"]
   
   g.color[0.5,0.5,0.5]
   g.line[mean + (minSigma * sigma), 0, mean + (maxSigma * sigma), 0]
   width = maxSigma - minSigma

   // This polyline is the normal curve.
   c = new polyline
   for s=minSigma to maxSigma+0.001 step (width/100)
   {
      x = mean + (sigma * s)
      y = -normalDensity[x, mean, sigma] * vscale
      c.addPoint[x,y]
   }

   g.add[c]

   g.color[0,0,0]

   wheel = r/2
   first = true
   points = 0
   for phi = high to low step ((low-high)/(steps-1))
   {
//      s = now[]
      x = inversePhi[phi,100,15]

      n = normalDensity[x, mean, sigma]
      do
      {
         wheel = (wheel + 0.618034) mod 1
      } while wheel > n
      
      h = wheel
      if first
      {
         g.color[1,0,0]         // Draw the "you" circle in red.
         g.fillEllipseCenter[x, -1/2 r, r, r]
         g.color[0,0,0]
         g.font["SansSerif", 4]
         g.text["You are here.", x, 7]

         g.line[x, 5, x, 1]     // Arrow body
         // Arrowhead
         p=new filledPolygon
         p.addPoint[x,.65]
         p.addPoint[x+0.3,2.5]
         p.addPoint[x-0.3,2.5]
         g.add[p]
         
         first = false
      } else
         g.fillEllipseCenter[x, -h*vscale, r, r]

      points = points+1
//      e = now[]
//      println["point $points, time is " + format[e-s,"ms",3]]
   }
   println["$points points plotted."]
}

g = new graphics
points = 1000

// You can pass in a number of points as the sole argument.
if length[ARGS] > 0
   points = eval[ARGS@0]

plotNormal[100, 15, points, g]
g.show[]
g.write["normal$points.svg", 1024, undef]
g.write["normal$points.png", 2000, undef]
g.write["normal$points.html", 800, undef]
//g.print[]


View or download normalCurve2.frink in plain text format


This is a program written in the programming language Frink.
For more information, view the Frink Documentation or see More Sample Frink Programs.

Alan Eliasen was born 17955 days, 21 hours, 33 minutes ago.