VTK-5.0.0/Common/vtkMatrix4x4.cxx

/*=========================================================================

  Program:   Visualization Toolkit
  Module:    $RCSfile: vtkMatrix4x4.cxx,v $

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/
#include "vtkMatrix4x4.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"

#include <stdlib.h>
#include <math.h>

vtkCxxRevisionMacro(vtkMatrix4x4, "$Revision: 1.62 $");
vtkStandardNewMacro(vtkMatrix4x4);

// Useful for viewing a double[16] as a double[4][4]
typedef double (*SqMatPtr)[4];

//----------------------------------------------------------------------------
void vtkMatrix4x4::Zero(double Elements[16])
{
  SqMatPtr elem  = (SqMatPtr)Elements;
  int i,j;
  for (i = 0; i < 4; i++)
    {
    for (j = 0; j < 4; j++)
      {
      elem[i][j] = 0.0;
      }
    }
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::Identity(double Elements[16])
{
  Elements[0] = Elements[5] = Elements[10] = Elements[15] = 1.0;
  Elements[1] = Elements[2] = Elements[3] = Elements[4] = 
    Elements[6] = Elements[7] = Elements[8] = Elements[9] = 
    Elements[11] = Elements[12] = Elements[13] = Elements[14] = 0.0;
}

//----------------------------------------------------------------------------
template<class T1, class T2, class T3>
void vtkMatrixMultiplyPoint(T1 elem[16], T2 in[4], T3 out[4])
{
  T3 v1 = in[0];
  T3 v2 = in[1];
  T3 v3 = in[2];
  T3 v4 = in[3];

  out[0] = v1*elem[0]  + v2*elem[1]  + v3*elem[2]  + v4*elem[3];
  out[1] = v1*elem[4]  + v2*elem[5]  + v3*elem[6]  + v4*elem[7];
  out[2] = v1*elem[8]  + v2*elem[9]  + v3*elem[10] + v4*elem[11];
  out[3] = v1*elem[12] + v2*elem[13] + v3*elem[14] + v4*elem[15];
}  

//----------------------------------------------------------------------------
// Multiply this matrix by a point (in homogeneous coordinates). 
// and return the result in result. The in[4] and result[4] 
// arrays must both be allocated but they can be the same array.
void vtkMatrix4x4::MultiplyPoint(const double Elements[16], 
                                 const float in[4], float result[4])
{
  vtkMatrixMultiplyPoint(Elements,in,result);
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::MultiplyPoint(const double Elements[16], 
                                 const double in[4], double result[4])
{
  vtkMatrixMultiplyPoint(Elements,in,result);
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::PointMultiply(const double Elements[16], 
                                 const float in[4], float result[4])
{
  double newElements[16];
  vtkMatrix4x4::Transpose(Elements,newElements);
  vtkMatrix4x4::MultiplyPoint(newElements,in,result);
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::PointMultiply(const double Elements[16], 
                                 const double in[4], double result[4])
{
  double newElements[16];
  vtkMatrix4x4::Transpose(Elements,newElements);
  vtkMatrix4x4::MultiplyPoint(newElements,in,result);
}

//----------------------------------------------------------------------------
// Multiplies matrices a and b and stores the result in c.
void vtkMatrix4x4::Multiply4x4(const double a[16], const double b[16], 
                               double c[16])
{
  SqMatPtr aMat = (SqMatPtr) a;
  SqMatPtr bMat = (SqMatPtr) b;
  SqMatPtr cMat = (SqMatPtr) c;
  int i, k;
  double Accum[4][4];

  for (i = 0; i < 4; i++) 
    {
    for (k = 0; k < 4; k++) 
      {
      Accum[i][k] = aMat[i][0] * bMat[0][k] +
                    aMat[i][1] * bMat[1][k] +
                    aMat[i][2] * bMat[2][k] +
                    aMat[i][3] * bMat[3][k];
      }
    }

  // Copy to final dest
  for (i = 0; i < 4; i++)
    {
    cMat[i][0] = Accum[i][0];
    cMat[i][1] = Accum[i][1];
    cMat[i][2] = Accum[i][2];
    cMat[i][3] = Accum[i][3];
    }

}

//----------------------------------------------------------------------------
// Matrix Inversion (adapted from Richard Carling in "Graphics Gems," 
// Academic Press, 1990).
void vtkMatrix4x4::Invert(const double inElements[16], 
                          double outElements[16])
{
  SqMatPtr outElem = (SqMatPtr)outElements;

  // inverse( original_matrix, inverse_matrix )
  // calculate the inverse of a 4x4 matrix
  //
  //     -1     
  //     A  = ___1__ adjoint A
  //         det A
  //
  
  int i, j;
  double det;

  // calculate the 4x4 determinent
  // if the determinent is zero, 
  // then the inverse matrix is not unique.

  det = vtkMatrix4x4::Determinant(inElements);
  if ( det == 0.0 ) 
    {
    return;
    }

  // calculate the adjoint matrix
  vtkMatrix4x4::Adjoint(inElements, outElements );

  // scale the adjoint matrix to get the inverse
  for (i=0; i<4; i++)
    {
    for(j=0; j<4; j++)
      {
      outElem[i][j] = outElem[i][j] / det;
      }
    }
}

//----------------------------------------------------------------------------
double vtkMatrix4x4::Determinant(const double Elements[16])
{
  SqMatPtr elem = (SqMatPtr)Elements;

  double a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;

  // assign to individual variable names to aid selecting
  //  correct elements

  a1 = elem[0][0]; b1 = elem[0][1]; 
  c1 = elem[0][2]; d1 = elem[0][3];

  a2 = elem[1][0]; b2 = elem[1][1]; 
  c2 = elem[1][2]; d2 = elem[1][3];

  a3 = elem[2][0]; b3 = elem[2][1]; 
  c3 = elem[2][2]; d3 = elem[2][3];

  a4 = elem[3][0]; b4 = elem[3][1]; 
  c4 = elem[3][2]; d4 = elem[3][3];

  return a1 * vtkMath::Determinant3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4)
       - b1 * vtkMath::Determinant3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4)
       + c1 * vtkMath::Determinant3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4)
       - d1 * vtkMath::Determinant3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4);
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::Adjoint(const double inElements[16], double outElements[16])
{
  SqMatPtr inElem = (SqMatPtr) inElements;
  SqMatPtr outElem = (SqMatPtr) outElements;

  // 
  //   adjoint( original_matrix, inverse_matrix )
  // 
  //     calculate the adjoint of a 4x4 matrix
  //
  //      Let  a   denote the minor determinant of matrix A obtained by
  //           ij
  //
  //      deleting the ith row and jth column from A.
  //
  //                    i+j
  //     Let  b   = (-1)    a
  //          ij            ji
  //
  //    The matrix B = (b  ) is the adjoint of A
  //                     ij
  //
  double a1, a2, a3, a4, b1, b2, b3, b4;
  double c1, c2, c3, c4, d1, d2, d3, d4;

  // assign to individual variable names to aid
  // selecting correct values

  a1 = inElem[0][0]; b1 = inElem[0][1]; 
  c1 = inElem[0][2]; d1 = inElem[0][3];

  a2 = inElem[1][0]; b2 = inElem[1][1]; 
  c2 = inElem[1][2]; d2 = inElem[1][3];

  a3 = inElem[2][0]; b3 = inElem[2][1];
  c3 = inElem[2][2]; d3 = inElem[2][3];

  a4 = inElem[3][0]; b4 = inElem[3][1]; 
  c4 = inElem[3][2]; d4 = inElem[3][3];


  // row column labeling reversed since we transpose rows & columns

  outElem[0][0]  =   
    vtkMath::Determinant3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4);
  outElem[1][0]  = 
    - vtkMath::Determinant3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4);
  outElem[2][0]  =   
    vtkMath::Determinant3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4);
  outElem[3][0]  = 
    - vtkMath::Determinant3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4);

  outElem[0][1]  = 
    - vtkMath::Determinant3x3( b1, b3, b4, c1, c3, c4, d1, d3, d4);
  outElem[1][1]  =   
    vtkMath::Determinant3x3( a1, a3, a4, c1, c3, c4, d1, d3, d4);
  outElem[2][1]  = 
    - vtkMath::Determinant3x3( a1, a3, a4, b1, b3, b4, d1, d3, d4);
  outElem[3][1]  =   
    vtkMath::Determinant3x3( a1, a3, a4, b1, b3, b4, c1, c3, c4);
        
  outElem[0][2]  =   
    vtkMath::Determinant3x3( b1, b2, b4, c1, c2, c4, d1, d2, d4);
  outElem[1][2]  = 
    - vtkMath::Determinant3x3( a1, a2, a4, c1, c2, c4, d1, d2, d4);
  outElem[2][2]  =   
    vtkMath::Determinant3x3( a1, a2, a4, b1, b2, b4, d1, d2, d4);
  outElem[3][2]  = 
    - vtkMath::Determinant3x3( a1, a2, a4, b1, b2, b4, c1, c2, c4);
        
  outElem[0][3]  = 
    - vtkMath::Determinant3x3( b1, b2, b3, c1, c2, c3, d1, d2, d3);
  outElem[1][3]  =   
    vtkMath::Determinant3x3( a1, a2, a3, c1, c2, c3, d1, d2, d3);
  outElem[2][3]  = 
    - vtkMath::Determinant3x3( a1, a2, a3, b1, b2, b3, d1, d2, d3);
  outElem[3][3]  =   
    vtkMath::Determinant3x3( a1, a2, a3, b1, b2, b3, c1, c2, c3);
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::DeepCopy(double Elements[16], const double newElements[16])
{
  for (int i = 0; i < 16; i++)
    {
    Elements[i] = newElements[i];
    }
}

//----------------------------------------------------------------------------
// Transpose the matrix and put it into out.   
void vtkMatrix4x4::Transpose(const double inElements[16], 
                              double outElements[16])
{
  SqMatPtr inElem = (SqMatPtr)inElements;
  SqMatPtr outElem = (SqMatPtr)outElements;
  int i, j;
  double temp;

  for (i=0; i<4; i++)
    {
    for(j=i; j<4; j++)
      {
      temp = inElem[i][j];
      outElem[i][j] = inElem[j][i];
      outElem[j][i] = temp;
      }
    }
}

//----------------------------------------------------------------------------
void vtkMatrix4x4::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os, indent);

  int i, j;

  os << indent << "Elements:\n";
  for (i = 0; i < 4; i++) 
    {
    os << indent << indent;
    for (j = 0; j < 4; j++) 
      {
      os << this->Element[i][j] << " ";
      }
    os << "\n";
    }
}