/* Matrix3D.java */


/** A fairly conventional 3D matrix object that can transform sets of
    3D points and perform a variety of manipulations on the transform */

class Matrix3D {
  float xx, xy, xz, xo;
  float yx, yy, yz, yo;
  float zx, zy, zz, zo;
  static final double pi = 3.14159265;

  /** Create a new unit matrix */
  Matrix3D () {
    xx = (float) 1.0;
    yy = (float) 1.0;
    zz = (float) 1.0;
  }

  /** Scale by f in all dimensions */
  void scale(float f) {
    xx *= f;
    xy *= f;
    xz *= f;
    xo *= f;
    yx *= f;
    yy *= f;
    yz *= f;
    yo *= f;
    zx *= f;
    zy *= f;
    zz *= f;
    zo *= f;
  }

  /** Scale along each axis independently */
  void scale(float xf, float yf, float zf) {
    xx *= xf;
    xy *= xf;
    xz *= xf;
    xo *= xf;
    yx *= yf;
    yy *= yf;
    yz *= yf;
    yo *= yf;
    zx *= zf;
    zy *= zf;
    zz *= zf;
    zo *= zf;
  }

  /** Translate the origin */
  void translate(float x, float y, float z) {
    xo += x;
    yo += y;
    zo += z;
  }
  
  /** rotate theta degrees about the y axis */
  void yrot(double theta) {
    theta *= (pi / 180);
    double ct = Math.cos(theta);
    double st = Math.sin(theta);

    float Nxx = (float) (xx * ct + zx * st);
    float Nxy = (float) (xy * ct + zy * st);
    float Nxz = (float) (xz * ct + zz * st);
    float Nxo = (float) (xo * ct + zo * st);

    float Nzx = (float) (zx * ct - xx * st);
    float Nzy = (float) (zy * ct - xy * st);
    float Nzz = (float) (zz * ct - xz * st);
    float Nzo = (float) (zo * ct - xo * st);

    xo = Nxo;
    xx = Nxx;
    xy = Nxy;
    xz = Nxz;
    zo = Nzo;
    zx = Nzx;
    zy = Nzy;
    zz = Nzz;
  }

  /** rotate theta degrees about the x axis */
  void xrot(double theta) {
    theta *= (pi / 180);
    double ct = Math.cos(theta);
    double st = Math.sin(theta);

    float Nyx = (float) (yx * ct + zx * st);
    float Nyy = (float) (yy * ct + zy * st);
    float Nyz = (float) (yz * ct + zz * st);
    float Nyo = (float) (yo * ct + zo * st);

    float Nzx = (float) (zx * ct - yx * st);
    float Nzy = (float) (zy * ct - yy * st);
    float Nzz = (float) (zz * ct - yz * st);
    float Nzo = (float) (zo * ct - yo * st);

    yo = Nyo;
    yx = Nyx;
    yy = Nyy;
    yz = Nyz;
    zo = Nzo;
    zx = Nzx;
    zy = Nzy;
    zz = Nzz;
  }

  /** rotate theta degrees about the z axis */
  void zrot(double theta) {
    theta *= (pi / 180);
    double ct = Math.cos(theta);
    double st = Math.sin(theta);

    float Nyx = (float) (yx * ct + xx * st);
    float Nyy = (float) (yy * ct + xy * st);
    float Nyz = (float) (yz * ct + xz * st);
    float Nyo = (float) (yo * ct + xo * st);

    float Nxx = (float) (xx * ct - yx * st);
    float Nxy = (float) (xy * ct - yy * st);
    float Nxz = (float) (xz * ct - yz * st);
    float Nxo = (float) (xo * ct - yo * st);

    yo = Nyo;
    yx = Nyx;
    yy = Nyy;
    yz = Nyz;
    xo = Nxo;
    xx = Nxx;
    xy = Nxy;
    xz = Nxz;
  }

  /** Multiply this matrix by a second: M = M*R */
  void mult(Matrix3D rhs) {
    float lxx = xx * rhs.xx + yx * rhs.xy + zx * rhs.xz;
    float lxy = xy * rhs.xx + yy * rhs.xy + zy * rhs.xz;
    float lxz = xz * rhs.xx + yz * rhs.xy + zz * rhs.xz;
    float lxo = xo * rhs.xx + yo * rhs.xy + zo * rhs.xz + rhs.xo;

    float lyx = xx * rhs.yx + yx * rhs.yy + zx * rhs.yz;
    float lyy = xy * rhs.yx + yy * rhs.yy + zy * rhs.yz;
    float lyz = xz * rhs.yx + yz * rhs.yy + zz * rhs.yz;
    float lyo = xo * rhs.yx + yo * rhs.yy + zo * rhs.yz + rhs.yo;

    float lzx = xx * rhs.zx + yx * rhs.zy + zx * rhs.zz;
    float lzy = xy * rhs.zx + yy * rhs.zy + zy * rhs.zz;
    float lzz = xz * rhs.zx + yz * rhs.zy + zz * rhs.zz;
    float lzo = xo * rhs.zx + yo * rhs.zy + zo * rhs.zz + rhs.zo;

    xx = lxx;
    xy = lxy;
    xz = lxz;
    xo = lxo;

    yx = lyx;
    yy = lyy;
    yz = lyz;
    yo = lyo;

    zx = lzx;
    zy = lzy;
    zz = lzz;
    zo = lzo;
  }

  /** Reinitialize to the unit matrix */
  void unit() {
    xo = 0;
    xx = 1;
    xy = 0;
    xz = 0;
    yo = 0;
    yx = 0;
    yy = 1;
    yz = 0;
    zo = 0;
    zx = 0;
    zy = 0;
    zz = 1;
  }

  /** Transform nvert points from v into tv.  v contains the input
      coordinates in floating point. tv ends up holding the transformed
      points. */
  void transform(Vertex v[], Vertex tv[], int nvert) {
    for (int i=0; i<nvert; i++) {
      float x = v[i].x;
      float y = v[i].y;
      float z = v[i].z;

      tv[i].x = x*xx + y*xy + z*xz + xo;
      tv[i].y = x*yx + y*yy + z*yz + yo;
      tv[i].z = x*zx + y*zy + z*zz + zo;
    }
  }

  public String toString() {
    return ("[" + xo + "," + xx + "," + xy + "," + xz + ";"
	  + yo + "," + yx + "," + yy + "," + yz + ";"
	  + zo + "," + zx + "," + zy + "," + zz + "]");
  }
}