import java.awt.*;
import java.util.*;

/************************************************
 *  Implementation of a renderable sphere       *
 *  Original code provided by Leonard McMillan  *
 *                                              *
 *  This is a sample renderable object, to      *
 *  demonstrate the use of the interface.       *
 ************************************************/

class Sphere implements Renderable {
  Surface surface;
  Vector3D center;
  float radius;
  float radSqr;
  
  public Sphere(Surface s, Vector3D c, float r) {
    surface = s;
    center = c;
    radius = r;
    radSqr = r*r;
  }
  
  public float transparency() {
    return surface.kt;
  }

  public boolean intersect(Ray ray) {
    float dx = center.x - ray.origin.x;
    float dy = center.y - ray.origin.y;
    float dz = center.z - ray.origin.z;
    float v = ray.direction.dot(dx, dy, dz);
    
    // Do the following quick check to see if there is even a chance
    // that an intersection here might be closer than a previous one
    if (v - radius > ray.t)
      return false;
    
    // Test if the ray actually intersects the sphere
    float t = radSqr + v*v - dx*dx - dy*dy - dz*dz;
    if (t < 0)
      return false;
    
    // Test if the intersection is in the positive
    // ray direction and it is the closest so far
    if (v*v < t) {
      t = v + ((float) Math.sqrt(t));
    } else
      t = v - ((float) Math.sqrt(t));
    if ((t > ray.t) || (t < 0))
      return false;
    
    ray.t = t;
    ray.object = this;
    return true;
  }
  
  public Color Shade(Ray ray, Vector lights, Vector objects, Color bgnd) {
    // An object shader doesn't really do too much other than
    // supply a few critical bits of geometric information
    // for a surface shader. It must must compute:
    //
    //   1. the point of intersection (p)
    //   2. a unit-length surface normal (n)
    //   3. a unit-length vector towards the ray's origin (v)
    //
    float px = ray.origin.x + ray.t*ray.direction.x;
    float py = ray.origin.y + ray.t*ray.direction.y;
    float pz = ray.origin.z + ray.t*ray.direction.z;
    
    Vector3D p = new Vector3D(px, py, pz);
    Vector3D v = new Vector3D(-ray.direction.x, -ray.direction.y, 
			      -ray.direction.z);
    Vector3D n = new Vector3D(px - center.x, py - center.y, pz - center.z);
    n.normalize();
    
    // The illumination model is applied
    // by the surface's Shade() method
    return surface.Shade(p, n, v, lights, objects, bgnd, ray.depth);
  }
  
  public String toString() {
    return ("sphere "+center+" "+radius);
  }
}