Picking in 3D through ray tracing method

Hello,

I have been trying to write a code for being able to pick objects or select points in 3D by using a ray tracing method, based on the guidelines I read from this source: http://schabby.de/picking-opengl-ray-tracing/

However, I have no idea how to check intersection between the ray and the object in the scene, and also I am not sure that the code is 100% correct. I am posting the code below. If anyone could help it would be great!

import peasy.*;
import toxi.geom.*;

float x;
float y;

// -- camera parameters ---------
PeasyCam cam;
Vec3D camTarget;
Vec3D camPosition;
Vec3D view = new Vec3D();
Vec3D camHorizontal = new Vec3D();
Vec3D camVertical = new Vec3D();
Vec3D pos;
Vec3D dir;
float fov = 1; //PI/5
float aspect = float(width)/float(height);
float nearClip = 1;
float farClip = 100000;

Cube cube0;

// ------------------------------

void setup() {
  size(800, 800, OPENGL);
  createCamera();
  Vec3D start = new Vec3D(0, 0, 0);
  cube0 = new Cube(start, 30);
}

// ------------------------------

void draw() {
  smooth();
  background(255);
  cube0.run();
  raytracing();
  testIntersection();
}

// ------------------------------

void createCamera() {
  cam = new PeasyCam(this, 300);
  perspective(fov, aspect, nearClip, farClip);
}

// ------------------------------

void raytracing() {
  x = mouseX;
  y = mouseY;

  // --- get camera target position
  float a[] = cam.getLookAt();
  float a1 = a[0];
  float a2 = a[1];
  float a3 = a[2];
  camTarget = new Vec3D(a1, a2, a3);

  // --- get camera position
  float b[] = cam.getPosition();
  float b1 = b[0];
  float b2 = b[1];
  float b3 = b[2];
  camPosition = new Vec3D(b1, b2, b3);

  // --- get view
  view = camTarget.sub(camPosition);
  view.normalize();

  // -- get cameraUp vector
  Vec3D Zaxis = new Vec3D(0, 0, 1);
  Vec3D rotAxis = view.cross(Zaxis);
  float theta = -PI/2;
  Vec3D camUp = view.getRotatedAroundAxis(rotAxis, theta);

  // -- calculate screenHorizontally and screenVertically
  camHorizontal = view.cross(camUp);
  camHorizontal.normalize();
  camVertical = camHorizontal.cross(view);
  camVertical.normalize();

  float vLength = tan(fov/2)*nearClip;
  float hLength = vLength*aspect;
  camVertical.scaleSelf(vLength);
  camHorizontal.scaleSelf(hLength);

  // translate mouse coordinates so that the origin lies in the center
  x -= width/2;
  y -= height/2;
  x /= (width/2);
  y /= (height/2);

  // compute intersection of picking ray with viewport plane
  float posX = camPosition.x + view.x*nearClip + camHorizontal.x*x + camVertical.x*y;
  float posY = camPosition.y + view.y*nearClip + camHorizontal.y*x + camVertical.y*y;
  float posZ = camPosition.z + view.x*nearClip + camHorizontal.z*x + camVertical.z*y;
  pos = new Vec3D(posX, posY, posZ);
  dir = pos.sub(camPosition);
}

// ------------------------------

void testIntersection() {
}

There is also a simple cube class just for displaying and getting the location vector of the cube. Thank you very much for your help! :)