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Common/vtkMath.h

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

  Program:   Visualization Toolkit
  Module:    $RCSfile: vtkMath.h,v $
  Language:  C++


Copyright (c) 1993-2001 Ken Martin, Will Schroeder, Bill Lorensen 
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

 * Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.

 * Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.

 * Neither name of Ken Martin, Will Schroeder, or Bill Lorensen nor the names
   of any contributors may be used to endorse or promote products derived
   from this software without specific prior written permission.

 * Modified source versions must be plainly marked as such, and must not be
   misrepresented as being the original software.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS''
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

=========================================================================*/
#ifndef __vtkMath_h
#define __vtkMath_h

#include "vtkObject.h"

class VTK_COMMON_EXPORT vtkMath : public vtkObject
{
public:
  static vtkMath *New();
  vtkTypeMacro(vtkMath,vtkObject);
  

  static float Pi() {return 3.14159265358979;};
  static float DegreesToRadians() {return 0.017453292;};

  static double DoubleDegreesToRadians() {return 0.017453292519943295;};


  static float Dot(const float x[3], const float y[3]) {
    return (x[0]*y[0] + x[1]*y[1] + x[2]*y[2]);};


  static double Dot(const double x[3], const double y[3]) {
    return (x[0]*y[0] + x[1]*y[1] + x[2]*y[2]);};
  
  static void Cross(const float x[3], const float y[3], float z[3]);

  static void Cross(const double x[3], const double y[3], double z[3]);

  static float Norm(const float* x, int n); 


  static float Norm(const float x[3]) {
    return sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);};
  

  static double Norm(const double x[3]) {
    return sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);};
  
  static float Normalize(float x[3]);

  static double Normalize(double x[3]);


  static void Perpendiculars(const double x[3], double y[3], double z[3], 
                             double theta);
  static void Perpendiculars(const float x[3], float y[3], float z[3],
                             double theta);

  static float Distance2BetweenPoints(const float x[3], const float y[3]);

  static double Distance2BetweenPoints(const double x[3], const double y[3]);


  static float Dot2D(const float x[3], const float y[3]) {
    return (x[0]*y[0] + x[1]*y[1]);};
  

  static double Dot2D(const double x[3], const double y[3]) {
    return (x[0]*y[0] + x[1]*y[1]);};


  static float Norm2D(const float x[3]) {
    return sqrt(x[0]*x[0] + x[1]*x[1]);};


  static double Norm2D(const double x[3]) {
    return sqrt(x[0]*x[0] + x[1]*x[1]);};

  static float Normalize2D(float x[3]);

  static double Normalize2D(double x[3]);


  static float Determinant2x2(const float c1[2], const float c2[2]) {
    return (c1[0]*c2[1] - c2[0]*c1[1]);};


  static double Determinant2x2(double a, double b, double c, double d) {
    return (a * d - b * c);};


  static void LUFactor3x3(float A[3][3], int index[3]);
  static void LUFactor3x3(double A[3][3], int index[3]);


  static void LUSolve3x3(const float A[3][3], const int index[3], 
                         float x[3]);
  static void LUSolve3x3(const double A[3][3], const int index[3], 
                         double x[3]);


  static void LinearSolve3x3(const float A[3][3], const float x[3], 
                             float y[3]);
  static void LinearSolve3x3(const double A[3][3], const double x[3], 
                             double y[3]);


  static void Multiply3x3(const float A[3][3], const float in[3], 
                          float out[3]);
  static void Multiply3x3(const double A[3][3], const double in[3], 
                          double out[3]);
  

  static void Multiply3x3(const float A[3][3], const float B[3][3], 
                          float C[3][3]);
  static void Multiply3x3(const double A[3][3], const double B[3][3], 
                          double C[3][3]);


  static void Transpose3x3(const float A[3][3], float AT[3][3]);
  static void Transpose3x3(const double A[3][3], double AT[3][3]);


  static void Invert3x3(const float A[3][3], float AI[3][3]);
  static void Invert3x3(const double A[3][3], double AI[3][3]);


  static void Identity3x3(float A[3][3]);
  static void Identity3x3(double A[3][3]);


  static double Determinant3x3(float A[3][3]);
  static double Determinant3x3(double A[3][3]);


  static float Determinant3x3(const float c1[3], 
                              const float c2[3], 
                              const float c3[3]);


  static double Determinant3x3(double a1, double a2, double a3, 
                               double b1, double b2, double b3, 
                               double c1, double c2, double c3);


  static void QuaternionToMatrix3x3(const float quat[4], float A[3][3]); 
  static void QuaternionToMatrix3x3(const double quat[4], double A[3][3]); 


  static void Matrix3x3ToQuaternion(const float A[3][3], float quat[4]);
  static void Matrix3x3ToQuaternion(const double A[3][3], double quat[4]);
  

  static void Orthogonalize3x3(const float A[3][3], float B[3][3]);
  static void Orthogonalize3x3(const double A[3][3], double B[3][3]);


  static void Diagonalize3x3(const float A[3][3], float w[3], float V[3][3]);
  static void Diagonalize3x3(const double A[3][3],double w[3],double V[3][3]);


  static void SingularValueDecomposition3x3(const float A[3][3],
                                            float U[3][3], float w[3],
                                            float VT[3][3]);
  static void SingularValueDecomposition3x3(const double A[3][3],
                                            double U[3][3], double w[3],
                                            double VT[3][3]);

  static int SolveLinearSystem(double **A, double *x, int size);

  static int InvertMatrix(double **A, double **AI, int size);


  static int InvertMatrix(double **A, double **AI, int size,
                          int *tmp1Size, double *tmp2Size);

  static int LUFactorLinearSystem(double **A, int *index, int size);


  static int LUFactorLinearSystem(double **A, int *index, int size,
                                  double *tmpSize);


  static void LUSolveLinearSystem(double **A, int *index, 
                                  double *x, int size);

  static double EstimateMatrixCondition(double **A, int size);

  static void RandomSeed(long s);  

  static float Random();  

  static float Random(float min, float max);


  static int Jacobi(float **a, float *w, float **v);
  static int Jacobi(double **a, double *w, double **v);


  static int JacobiN(float **a, int n, float *w, float **v);
  static int JacobiN(double **a, int n, double *w, double **v);

  static double* SolveCubic(double c0, double c1, double c2, double c3);

  static double* SolveQuadratic(double c0, double c1, double c2);

  static double* SolveLinear(double c0, double c1);


  static int SolveCubic(double c0, double c1, double c2, double c3, 
                        double *r1, double *r2, double *r3, int *num_roots);


  static int SolveQuadratic(double c0, double c1, double c2, 
                            double *r1, double *r2, int *num_roots);
  
  static int SolveLinear(double c0, double c1, double *r1, int *num_roots);



  static int SolveLeastSquares(int numberOfSamples, double **xt, int xOrder,
                               double **yt, int yOrder, double **mt);
  
protected:
  vtkMath() {};
  ~vtkMath() {};
  
  static long Seed;
private:
  vtkMath(const vtkMath&);  // Not implemented.
  void operator=(const vtkMath&);  // Not implemented.
};

inline float vtkMath::Normalize(float x[3])
{
  float den; 
  if ( (den = vtkMath::Norm(x)) != 0.0 )
    {
    for (int i=0; i < 3; i++)
      {
      x[i] /= den;
      }
    }
  return den;
}
inline double vtkMath::Normalize(double x[3])
{
  double den; 
  if ( (den = vtkMath::Norm(x)) != 0.0 )
    {
    for (int i=0; i < 3; i++)
      {
      x[i] /= den;
      }
    }
  return den;
}

inline float vtkMath::Normalize2D(float x[3])
{
  float den; 
  if ( (den = vtkMath::Norm2D(x)) != 0.0 )
    {
    for (int i=0; i < 2; i++)
      {
      x[i] /= den;
      }
    }
  return den;
}

inline double vtkMath::Normalize2D(double x[3])
{
  double den; 
  if ( (den = vtkMath::Norm2D(x)) != 0.0 )
    {
    for (int i=0; i < 2; i++)
      {
      x[i] /= den;
      }
    }
  return den;
}

inline float vtkMath::Determinant3x3(const float c1[3], 
                                     const float c2[3], 
                                     const float c3[3])
{
  return c1[0]*c2[1]*c3[2] + c2[0]*c3[1]*c1[2] + c3[0]*c1[1]*c2[2] -
         c1[0]*c3[1]*c2[2] - c2[0]*c1[1]*c3[2] - c3[0]*c2[1]*c1[2];
}

inline double vtkMath::Determinant3x3(double a1, double a2, double a3, 
                                      double b1, double b2, double b3, 
                                      double c1, double c2, double c3)
{
    return ( a1 * vtkMath::Determinant2x2( b2, b3, c2, c3 )
           - b1 * vtkMath::Determinant2x2( a2, a3, c2, c3 )
           + c1 * vtkMath::Determinant2x2( a2, a3, b2, b3 ) );
}

inline float vtkMath::Distance2BetweenPoints(const float x[3], 
                                             const float y[3])
{
  return ((x[0]-y[0])*(x[0]-y[0]) + (x[1]-y[1])*(x[1]-y[1]) +
          (x[2]-y[2])*(x[2]-y[2]));
}
inline double vtkMath::Distance2BetweenPoints(const double x[3], 
                                              const double y[3])
{
  return ((x[0]-y[0])*(x[0]-y[0]) + (x[1]-y[1])*(x[1]-y[1]) +
          (x[2]-y[2])*(x[2]-y[2]));
}

inline float vtkMath::Random(float min, float max)
{
  return (min + vtkMath::Random()*(max-min));
}

// Cross product of two 3-vectors. Result vector in z[3].
inline void vtkMath::Cross(const float x[3], const float y[3], float z[3])
{
  float Zx = x[1]*y[2] - x[2]*y[1]; 
  float Zy = x[2]*y[0] - x[0]*y[2];
  float Zz = x[0]*y[1] - x[1]*y[0];
  z[0] = Zx; z[1] = Zy; z[2] = Zz; 
}

// Cross product of two 3-vectors. Result vector in z[3].
inline void vtkMath::Cross(const double x[3], const double y[3], double z[3])
{
  double Zx = x[1]*y[2] - x[2]*y[1]; 
  double Zy = x[2]*y[0] - x[0]*y[2];
  double Zz = x[0]*y[1] - x[1]*y[0];
  z[0] = Zx; z[1] = Zy; z[2] = Zz; 
}

//BTX
//----------------------------------------------------------------------------
template<class T>
static inline double vtkDeterminant3x3(T A[3][3])
{
  return A[0][0]*A[1][1]*A[2][2] + A[1][0]*A[2][1]*A[0][2] + 
         A[2][0]*A[0][1]*A[1][2] - A[0][0]*A[2][1]*A[1][2] - 
         A[1][0]*A[0][1]*A[2][2] - A[2][0]*A[1][1]*A[0][2];
}
//ETX

inline double vtkMath::Determinant3x3(float A[3][3])
{
  return vtkDeterminant3x3(A);
}

inline double vtkMath::Determinant3x3(double A[3][3])
{
  return vtkDeterminant3x3(A);
}


#endif

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