package graphics;

public class Quadratic extends Shape
{
  public Matrix3D coefficients;

  //coefficients
  //ax^2 + by^2 + cz^2 + dxy + eyz + fzx + gx + hy + iz + j
  public double a, b, c, d, e, f, g, h, i, j;

  public Quadratic(double a, double b, double c, double d, double e, double f, double g, double h, double i, double j)
  {
    this.a = a; this.b = b; this.c = c;
    this.d = d; this.e = e; this.f = f;
    this.g = g; this.h = h; this.i = i;
    this.j = j;

    double[][] data = new double[4][4];
    data[0][0] = a; data[1][1] = b;  data[2][2] = c;
    data[0][1] = d; data[1][2] = e;  data[0][2] = f;
    data[0][3] = g; data[1][3] = h;  data[2][3] = i;
    data[3][3] = j;

    this.coefficients = new Matrix3D(data);

    this.matrix = new Matrix3D();
  }

  public double equation(double x, double y, double z)
  {
    return a*x*x + b*y*y + c*z*z + d*x*y + e*y*z + f*x*z + g*x + h*y + i*z + j;
  }

  //returns array of t values (roots) or void if no intersection
  //sets point of intersection and normal there
  public double[] testRay(Vector3 v, Vector3 w, Vector3 pos, Vector3 normal)
  {
    //for convenience
    double vx = v.get(0), vy = v.get(1), vz = v.get(2);
    double wx = w.get(0), wy = w.get(1), wz = w.get(2);

    //quadratic coefficients - (A B C) dot (t2 t 1)
    double A = a*wx*wx + b*wy*wy + c*wz*wz + d*wx*wy + e*wy*wz + f*wx*wz;
    double B = 2*a*vx*wx + 2*b*vy*wy + 2*c*vz*wz + 
        d*vx*wy + d*vy*wx + e*vy*wz + e*vz*wy + f*vx*wz + f*vz*wx +
        g*wx + h*wy + i*wz;
    double C = equation(vx, vy, vz);

//System.err.println("a,b,c: ("+A+", "+B+", "+C+")");

    double[] roots = getRoots(A, B, C);
    if (roots == null) return null;

    //pick smaller (nearer) root
    double t = Math.min(roots[0], roots[1]);

    //we don't care about intersections behind the origin
    if (t < 0.001) return null;

    //calculate intersection point and normal
    setIntersectionPoint(v, w, t, pos);

    //for convenience
    double x = pos.get(0), y = pos.get(1), z = pos.get(2);

    normal.set(0, 2*a*x + d*y + f*z + g);
    normal.set(1, 2*b*y + d*x + e*z + h);
    normal.set(2, 2*c*z + e*y + f*x + i);
    normal.normalize();

    return roots;
  }

  //quadratic equation
  protected double[] getRoots(double A, double B, double C)
  {
    double disc = B*B - 4*A*C;
    if (disc < 0) return null;

    double discRt = Math.sqrt(disc);

    double[] roots = new double[2];
    roots[0] = (0-B - discRt)/2*A;
    roots[1] = (0-B + discRt)/2*A;

    return roots;
  }

  public void transform()
  {
    if (this.matrix == null)
    {
      System.err.println("Warning: transformation matrix is null.  Cannot transform Quadratic.");
      return;
    }

    Matrix3D m = new Matrix3D(this.matrix);
    m.invert();
    Matrix3D m2 = new Matrix3D(m); //save copy of inverted matrix
    m.transpose();

//System.err.println("m = " + m);
    m.multiply(this.coefficients); //multiply by coefficient matrix
    m.multiply(m2); //multiply by matrix inverse

    this.coefficients.copy(m);

    fixMatrix();

    a = this.coefficients.get(0, 0);
    b = this.coefficients.get(1, 1);
    c = this.coefficients.get(2, 2);
    d = this.coefficients.get(0, 1);
    e = this.coefficients.get(1, 2);
    f = this.coefficients.get(0, 2);
    g = this.coefficients.get(0, 3);
    h = this.coefficients.get(1, 3);
    i = this.coefficients.get(2, 3);
    j = this.coefficients.get(3, 3);
  }

  //some transformations mess up coefficients matrix
  //this function restores them
  private void fixMatrix()
  {
    for (int i = 0; i < 4; i++)
    for (int j = 0; j < 4; j++)
    {
      if (i < j)
      {
        double ij = this.coefficients.get(i, j);
        double ji = this.coefficients.get(j, i);

        this.coefficients.set(i, j, ij + ji);
        this.coefficients.set(j, i, 0);
      }
    }
  }

  public Quadratic deepCopy()
  {
    return new Quadratic(a, b, c, d, e, f, g, h, i, j);
  }

  public void dump()
  {
    System.err.println("(a, b, c), (d, e, f), (g, h, i, j) = (" + a + ", " + b + ", " + c + "), (" + d + ", " + e + ", " + f + "), (" + g + ", " + h + ", " + i + ", " + j + ")");
  }
}