vtkMath.h

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

  Program:   Visualization Toolkit
  Module:    $RCSfile: vtkMath.h,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.

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

#include "vtkObject.h"

class VTK_COMMON_EXPORT vtkMath : public vtkObject
{
public:
  static vtkMath *New();
  vtkTypeRevisionMacro(vtkMath,vtkObject);
  void PrintSelf(ostream& os, vtkIndent indent);


  static float Pi() {return 3.14159265358979f;};
  static float DegreesToRadians() {return 0.017453292f;};
  static float RadiansToDegrees() {return 57.2957795131f;};


  static double DoubleDegreesToRadians() {return 0.017453292519943295;};
  static double DoublePi() {return 3.1415926535897932384626;};
  static double DoubleRadiansToDegrees() {return 57.29577951308232;};


  static int Round(float f) {
    return static_cast<int>(f + (f >= 0 ? 0.5 : -0.5)); }
  static int Round(double f) {
    return static_cast<int>(f + (f >= 0 ? 0.5 : -0.5)); }

  static int Floor(double x);
  

  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 double Norm(const double* x, int n); 


  static float Norm(const float x[3]) {
    return static_cast<float> (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 static_cast<float> (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 double Determinant2x2(const double c1[2], const double c2[2]) {
    return (c1[0]*c2[1] - c2[0]*c1[1]);};


  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(const double c1[3], 
                               const double c2[3], 
                               const double 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 double Random();  

  static double Random(double min, double 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 SolveHomogeneousLeastSquares(int numberOfSamples, double **xt, int xOrder,
                                double **mt);



  static int SolveLeastSquares(int numberOfSamples, double **xt, int xOrder,
                               double **yt, int yOrder, double **mt, int checkHomogeneous=1);


  static void RGBToHSV(float rgb[3], float hsv[3])
    { 
    RGBToHSV(rgb[0], rgb[1], rgb[2], hsv, hsv+1, hsv+2);
    }
  static void RGBToHSV(float r, float g, float b, 
                       float *h, float *s, float *v);
  static void RGBToHSV(double rgb[3], double hsv[3])
    { 
    RGBToHSV(rgb[0], rgb[1], rgb[2], hsv, hsv+1, hsv+2);
    }
  static void RGBToHSV(double r, double g, double b, 
                       double *h, double *s, double *v);


  static void HSVToRGB(float hsv[3], float rgb[3])
    { 
    HSVToRGB(hsv[0], hsv[1], hsv[2], rgb, rgb+1, rgb+2);
    }
  static void HSVToRGB(float h, float s, float v, 
                       float *r, float *g, float *b);
  static void HSVToRGB(double hsv[3], double rgb[3])
    { 
    HSVToRGB(hsv[0], hsv[1], hsv[2], rgb, rgb+1, rgb+2);
    }
  static void HSVToRGB(double h, double s, double v, 
                       double *r, double *g, double *b);


  static void UninitializeBounds(double bounds[6]){
    bounds[0] = 1.0;
    bounds[1] = -1.0;
    bounds[2] = 1.0;
    bounds[3] = -1.0;
    bounds[4] = 1.0;
    bounds[5] = -1.0;
  }
  

  static int AreBoundsInitialized(double bounds[6]){
    if (bounds[1]-bounds[0]<0.0)
      {
      return 0;
      }
    return 1;
  }


  static void ClampValue(double *value, const double range[2]);
  static void ClampValue(double value, const double range[2], double *clamped_value);
  static void ClampValues(
    double *values, int nb_values, const double range[2]);
  static void ClampValues(
    const double *values, int nb_values, const double range[2], double *clamped_values);

protected:
  vtkMath() {};
  ~vtkMath() {};
  
  static long Seed;
private:
  vtkMath(const vtkMath&);  // Not implemented.
  void operator=(const vtkMath&);  // Not implemented.
};

//----------------------------------------------------------------------------
inline int vtkMath::Floor(double x)
{
#if defined i386 || defined _M_IX86
  double tempval;
  // use 52-bit precision of IEEE double to round (x - 0.25) to 
  // the nearest multiple of 0.5, according to prevailing rounding
  // mode which is IEEE round-to-nearest,even
  tempval = (x - 0.25) + 3377699720527872.0; // (2**51)*1.5
  // extract mantissa, use shift to divide by 2 and hence get rid
  // of the bit that gets messed up because the FPU uses
  // round-to-nearest,even mode instead of round-to-nearest,+infinity
  return ((int*)&tempval)[0] >> 1;
#else
  return (int)floor(x);
#endif
}

//----------------------------------------------------------------------------
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(const double c1[3], 
                                      const double c2[3], 
                                      const double 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 double vtkMath::Random(double min, double 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>
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);
}

//----------------------------------------------------------------------------
inline void vtkMath::ClampValue(double *value, const double range[2])
{
  if (value && range)
    {
    if (*value < range[0])
      {
      *value = range[0];
      }
    else if (*value > range[1])
      {
      *value = range[1];
      }
    }
}

//----------------------------------------------------------------------------
inline void vtkMath::ClampValue(
  double value, const double range[2], double *clamped_value)
{
  if (range && clamped_value)
    {
    if (value < range[0])
      {
      *clamped_value = range[0];
      }
    else if (value > range[1])
      {
      *clamped_value = range[1];
      }
    else
      {
      *clamped_value = value;
      }
    }
}

#endif

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