// Matrix3D.java -- Transformation matrix for 3-space
//
// This is based on the class provided by Leonard (as opposed to my own
// Matrix3D.java from earlier projects.)

import Vertex3D;

public class Matrix3D {
    private float m[];
    private float nm[];
    private  boolean matrix_changed;
    public Matrix3D()      // null constructor allows for extension
    {
        m = new float[16];
        nm = new float[9];
        loadIdentity();
	matrix_changed = true;
    }

    public Matrix3D(ZRaster r)
    {
        m = new float[16];
        nm = new float[9];
        float w = r.width / 2;
        float h = r.height / 2;
        float d = ZRaster.MAXZ / 2;
        m[ 0] = w;  m[ 1] = 0;  m[ 2] = 0;  m[ 3] = w;
        m[ 4] = 0;  m[ 5] = h;  m[ 6] = 0;  m[ 7] = h;
        m[ 8] = 0;  m[ 9] = 0;  m[10] = d;  m[11] = d;
        m[12] = 0;  m[13] = 0;  m[14] = 0;  m[15] = 1;
	matrix_changed = true;
    }

    public Matrix3D(Matrix3D copy)    // makes a copy of the matrix
    {
        m = new float[16];
        nm = new float[9];
        System.arraycopy(copy.m, 0, m, 0, 16);
        System.arraycopy(copy.nm, 0, nm, 0, 9);
	matrix_changed = false;
    }


    /*
        ... Methods for setting and getting matrix elements ...
    */
    public void set(int j, int i, float val)
    {
        m[4*j+i] = val;
	matrix_changed = true;
    }

    public float get(int j, int i)
    {
        return m[4*j+i];
    }

    protected void set(int i, float val)
    {
        m[i] = val;
	matrix_changed = true;
    }
    
    protected float get(int i)
    {
        return m[i];
    }


    public final void copy(Matrix3D src)
    {
        System.arraycopy(src.m, 0, m, 0, 16);
        System.arraycopy(src.nm, 0, nm, 0, 9);
    }

  void ComputeInverse() {
    // We can do this, because affine transformations (other than a scale
    // by 0) won't cause the matrix to become singular.
    matrix_changed = false;

    // Find determinant of A'
    float det_a = m[0]*m[5]*m[10] + m[1]*m[6]*m[8]  + m[2]*m[4]*m[9]
                - m[0]*m[6]*m[9]  - m[1]*m[4]*m[10] - m[2]*m[5]*m[8];
    if (det_a == 0) {
      System.out.println("Warning! transformation matrix is singular!");
      // Not correct, but safe:
      nm[0]=1; nm[1]=0; nm[2]=0;
      nm[3]=0; nm[4]=1; nm[5]=0;
      nm[6]=0; nm[7]=0; nm[8]=1;
      return;
    }
   
    // Find cofactors
    nm[0] = (m[4]*m[8] - m[5]*m[7]) / det_a;
    nm[1] = (m[3]*m[8] - m[5]*m[6]) / det_a;
    nm[2] = (m[3]*m[7] - m[4]*m[6]) / det_a;

    nm[3] = (m[1]*m[8] - m[2]*m[7]) / det_a;
    nm[4] = (m[0]*m[8] - m[2]*m[6]) / det_a;
    nm[5] = (m[0]*m[7] - m[1]*m[6]) / det_a;

    nm[6] = (m[1]*m[5] - m[2]*m[4]) / det_a;
    nm[7] = (m[0]*m[5] - m[2]*m[3]) / det_a;
    nm[8] = (m[0]*m[4] - m[1]*m[3]) / det_a;
  }

    public void transform(Vertex3D in[], Vertex3D out[], int vertices)
    {
        for (int i = 0; i < vertices; i++) {
            out[i].x = m[0]*in[i].x + m[1]*in[i].y + m[2]*in[i].z + m[3]*in[i].w;
            out[i].y = m[4]*in[i].x + m[5]*in[i].y + m[6]*in[i].z + m[7]*in[i].w;
            out[i].z = m[8]*in[i].x + m[9]*in[i].y + m[10]*in[i].z + m[11]*in[i].w;
            out[i].w = m[12]*in[i].x + m[13]*in[i].y + m[14]*in[i].z + m[15]*in[i].w;

            if (in[i].hasNormal) {
	      // Lecture 18, Slide 31
	      // n' = transpose(inv(A')) * n
	      // transpose(inv(A')) = C/det(A') 
	      //   where C is the cofactor matrix

	      if (matrix_changed) 
		ComputeInverse();
	    
	      out[i].hasNormal = true;
	      out[i].nx = nm[0]*in[i].nx + nm[1]*in[i].ny + nm[2]*in[i].nz;
	      out[i].ny = nm[3]*in[i].nx + nm[4]*in[i].ny + nm[5]*in[i].nz;
	      out[i].nz = nm[6]*in[i].nx + nm[7]*in[i].ny + nm[8]*in[i].nz;
            }
        }
    }

    public Vertex3D transform(Vertex3D v)
    {
        float x, y, z, w;
        x = m[0]*v.x + m[1]*v.y + m[2]*v.z + m[3]*v.w;
        y = m[4]*v.x + m[5]*v.y + m[6]*v.z + m[7]*v.w;
        z = m[8]*v.x + m[9]*v.y + m[10]*v.z + m[11]*v.w;
        w = m[12]*v.x + m[13]*v.y + m[14]*v.z + m[15]*v.w;

        w = 1 / w;
        Vertex3D result = new Vertex3D(x*w, y*w, z*w);
 
        if (v.hasNormal) {
	  if (matrix_changed) 
	    ComputeInverse();
	  
	  result.hasNormal = true;
	  result.nx = nm[0]*v.nx + nm[1]*v.ny + nm[2]*v.nz;
	  result.ny = nm[3]*v.nx + nm[4]*v.ny + nm[5]*v.nz;
	  result.nz = nm[6]*v.nx + nm[7]*v.ny + nm[8]*v.nz;
        }
        
        return result;
    }

    public final void compose(Matrix3D s)
    {
        float t0, t1, t2, t3;
        for (int i = 0; i < 16; i += 4) {
            t0 = m[i  ];
            t1 = m[i+1];
            t2 = m[i+2];
            t3 = m[i+3];
            m[i  ] = t0*s.get(0) + t1*s.get(4) + t2*s.get( 8) + t3*s.get(12);
            m[i+1] = t0*s.get(1) + t1*s.get(5) + t2*s.get( 9) + t3*s.get(13);
            m[i+2] = t0*s.get(2) + t1*s.get(6) + t2*s.get(10) + t3*s.get(14);
            m[i+3] = t0*s.get(3) + t1*s.get(7) + t2*s.get(11) + t3*s.get(15);
        }
	matrix_changed = true;
    }

    public void loadIdentity()
    {
        for (int i = 0; i < 16; i++)
            if ((i >> 2) == (i & 3))
                m[i] = 1;
            else
                m[i] = 0;
	matrix_changed = true;
    }

    public void translate(float tx, float ty, float tz)
    {
        m[ 3] += m[ 0]*tx + m[ 1]*ty + m[ 2]*tz;
        m[ 7] += m[ 4]*tx + m[ 5]*ty + m[ 6]*tz;
        m[11] += m[ 8]*tx + m[ 9]*ty + m[10]*tz;
        m[15] += m[12]*tx + m[13]*ty + m[14]*tz;
	matrix_changed = true;
    }

    public void scale(float sx, float sy, float sz)
    {
        m[ 0] *= sx; m[ 1] *= sy; m[ 2] *= sz;
        m[ 4] *= sx; m[ 5] *= sy; m[ 6] *= sz;
        m[ 8] *= sx; m[ 9] *= sy; m[10] *= sz;
        m[12] *= sx; m[13] *= sy; m[14] *= sz;
	matrix_changed = true;
    }

    public void rotate(float ax, float ay, float az, float angle)
    {
        float t0, t1, t2;

        if (angle == 0) return;          // return with m unmodified

        t0 = ax*ax + ay*ay + az*az;
        if (t0 == 0) return;

        float cosx = (float) Math.cos(angle);
        float sinx = (float) Math.sin(angle);
        t0 = 1f / ((float) Math.sqrt(t0));
        ax *= t0;
        ay *= t0;
        az *= t0;
        t0 = 1f - cosx;

        float r11 = ax*ax*t0 + cosx;
        float r22 = ay*ay*t0 + cosx;
        float r33 = az*az*t0 + cosx;

        t1 = ax*ay*t0;
        t2 = az*sinx;
        float r12 = t1 - t2;
        float r21 = t1 + t2;

        t1 = ax*az*t0;
        t2 = ay*sinx;
        float r13 = t1 + t2;
        float r31 = t1 - t2;

        t1 = ay*az*t0;
        t2 = ax*sinx;
        float r23 = t1 - t2;
        float r32 = t1 + t2;

        for (int i = 0; i < 16; i += 4) {
            t0 = m[i];
            t1 = m[i+1];
            t2 = m[i+2];
            m[i  ] = t0*r11 + t1*r21 + t2*r31;
            m[i+1] = t0*r12 + t1*r22 + t2*r32;
            m[i+2] = t0*r13 + t1*r23 + t2*r33;
        }
	matrix_changed = true;
    }

    public void lookAt(float eyex, float eyey, float eyez,
                       float atx,  float aty,  float atz,
                       float upx,  float upy,  float upz)
    {
        float t0, t1, t2;

        /*
            .... a unit vector along the line of sight ....
        */
        atx -= eyex;
        aty -= eyey;
        atz -= eyez;

        t0 = atx*atx + aty*aty + atz*atz;
        if (t0 == 0) return;                // at and eye at same point
        t0 = (float) (1 / Math.sqrt(t0));
        atx *= t0;
        aty *= t0;
        atz *= t0;

        /*
            .... a unit vector to the right ....
        */
        float rightx, righty, rightz;
        rightx = aty*upz - atz*upy;
        righty = atz*upx - atx*upz;
        rightz = atx*upy - aty*upx;
        t0 = rightx*rightx + righty*righty + rightz*rightz;
        if (t0 == 0) return;                // up is the same as at
        t0 = (float) (1 / Math.sqrt(t0));
        rightx *= t0;
        righty *= t0;
        rightz *= t0;


        /*
            .... a unit up vector ....
        */
        upx = righty*atz - rightz*aty;
        upy = rightz*atx - rightx*atz;
        upz = rightx*aty - righty*atx;


        /*
            .... find camera translation ....
        */
        float tx, ty, tz;
        tx = rightx*eyex + righty*eyey + rightz*eyez;
        ty = upx*eyex + upy*eyey + upz*eyez;
        tz = atx*eyex + aty*eyey + atz*eyez;

        /*
            .... do transform ....
        */
        for (int i = 0; i < 16; i += 4) {
            t0 = m[i];
            t1 = m[i+1];
            t2 = m[i+2];
            m[i  ] = t0*rightx + t1*upx - t2*atx;
            m[i+1] = t0*righty + t1*upy - t2*aty;
            m[i+2] = t0*rightz + t1*upz - t2*atz;
            m[i+3] -= t0*tx + t1*ty - t2*tz;
        }
	matrix_changed = true;
    }

    public void perspective(float left, float right,
                            float bottom, float top,
                            float near, float far)
    {
        float t0, t1, t2, t3;

        t0 = 1f / (right - left);
        t1 = 1f / (bottom - top);
        t2 = 1f / (far - near);

        float m13 = -t0*(right + left);
        float m23 = -t1*(bottom + top);
        float m33 = t2*(far + near);

        near *= 2;
        float m11 = t0*near;
        float m22 = t1*near;
        float m34 = -t2*far*near;

        for (int i = 0; i < 16; i += 4) {
            t0 = m[i];
            t1 = m[i+1];
            t2 = m[i+2];
            m[i  ] = t0*m11;
            m[i+1] = t1*m22;
            m[i+2] = t0*m13 + t1*m23 + t2*m33 + m[i+3];
            m[i+3] = t2*m34;
        }
	matrix_changed = true;
    }
    
    public void orthographic(float left, float right,
                             float bottom, float top,
                             float near, float far)
    {
        float t0, t1, t2, t3;

        t0 = 1f / (right - left);
        t1 = 1f / (bottom - top);
        t2 = 1f / (far - near);

        float m11 = 2*t0;
        float m22 = 2*t1;
        float m33 = 2*t2;
        float m14 = -t0*(right + left);
        float m24 = -t1*(bottom + top);
        float m34 = -t2*(far + near);

        for (int i = 0; i < 16; i += 4) {
            t0 = m[i];
            t1 = m[i+1];
            t2 = m[i+2];
            m[i  ] = t0*m11;
            m[i+1] = t1*m22;
            m[i+2] = t2*m33;
            m[i+3] = t0*m14 + t1*m24 + t2*m34 + m[i+3];
        }
	matrix_changed = true;
    }

    public String toString()
    {
        return ("[ ["+m[ 0]+", "+m[ 1]+", "+m[ 2]+", "+m[ 3]+" ], ["+
                      m[ 4]+", "+m[ 5]+", "+m[ 6]+", "+m[ 7]+" ], ["+
                      m[ 8]+", "+m[ 9]+", "+m[10]+", "+m[11]+" ], ["+
                      m[12]+", "+m[13]+", "+m[14]+", "+m[15]+" ] ]");
    }
}