Random Points on Cylinder Surface

/// <summary>Returns a random point on the surface of a cylinder</summary>
/// <param name="randomNumberGenerator">Random number generator that will be used</param>
/// <param name="orientation">Orientation of the cylinder</param>
/// <param name="radius">Radius of the cylinder</param>
/// <param name="length">Length of the cylinder</param>
/// <returns>A random point on the volume's surface</returns>
public static Vector3 GenerateRandomPointOnSurface(
  System.Random randomNumberGenerator,
  Matrix orientation, float radius, float length
) {

  // Calculate the surface areas of the three sections our cylinder has:
  // Upper cap, side and lower cap
  float capArea = MathHelper.Pi * (radius * radius);
  float sideArea = 2.0f * MathHelper.Pi * radius * length;
  float capAndSideArea = capArea + sideArea;

  // We need a phi value (angle of the random point) in any of the cases
  float phi = (float)randomNumberGenerator.NextDouble() * MathHelper.TwoPi;

  // Choose the section that the random point will be generated on in relation
  // to its surface area so the probability is constant on the entire surface
  float section = (float)randomNumberGenerator.NextDouble() * (capArea * 2.0f + sideArea);

  // Depending on the section, these two values are calculated differently
  float randomRadius;
  float randomZ;

  // Upper cap: Generate a random radius
  if(section < capArea) {
    randomZ = length / 2.0f;
    randomRadius = (float)Math.Sqrt(randomNumberGenerator.NextDouble()) * radius;

  // Side: Generate a random height
  } else if(section < capAndSideArea) {
    randomZ = ((float)randomNumberGenerator.NextDouble() - 0.5f) * length;
    randomRadius = radius;

  // Lower cap: Generate a random radius
  } else {
    randomZ = -length / 2.0f;
    randomRadius = (float)Math.Sqrt(randomNumberGenerator.NextDouble()) * radius;
  }

  // Now transform the point to cartesian coordinates and rotate it into
  // the global coordinate frame
  return Vector3.Transform(
    new Vector3(
      randomRadius * (float)Math.Cos(phi),
      randomRadius * (float)Math.Sin(phi),
      randomZ
    ),
    orientation
  );

}