CubicPWI.h

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/*
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   The MIT License

   Copyright (c) 2009 Scientific Computing and Imaging Institute,
   University of Utah.

   
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///
///@class CubicPWI
///@brief Cubic piecewise interpolation
///
///@author
///       Alexei Samsonov
///       Department of Computer Science
///       University of Utah
/// 
///@date  July 2000
///


#ifndef SCI_CUBICPWI_H__
#define SCI_CUBICPWI_H__

#include <Core/Math/PiecewiseInterp.h>

#include <Core/Containers/Array1.h>
#include <Core/GeometryPrimitives/Point.h>
#include <Core/GeometryPrimitives/Vector.h>
#include <sci_debug.h>

#include <iostream>


#include <Core/Math/share.h>

namespace SCIRun {

enum EndCondition { natural_ends, clamped_ends, bessel_ends, quadratic_ends };

template <class T> std::ostream& 
operator<<(std::ostream& out, Array1<T> a)
{
  for (int i = 0; i < a.size(); i++){
    std::cout << a[i] << std::endl;
  }
  return out;
}

typedef struct Quat {
  double a;
  double b;
  double c;
  double d;
} QUAT;

class SCISHARE CubicPWI: public PiecewiseInterp<double> {
public:
  CubicPWI();
  CubicPWI(const Array1<double>&, const Array1<double>&);
  
  bool set_data(const Array1<double>&, const Array1<double>&);
  inline bool get_value(double, double&);

private:
  Array1<QUAT> p;
};

inline bool CubicPWI::get_value(double w, double& res)
{
  int i = 0;
  if (data_valid && (i = get_interval(w)) >= 0) {
    w -= points[i];
    res = p[i].a + w * (p[i].b + w * (p[i].c + p[i].d * w));
    return true;
  }
  else
    return false;
}

template <class T> class Cubic3DPWI: public PiecewiseInterp<T> {
public:
  Cubic3DPWI() {};
  Cubic3DPWI(const Array1<double>&, const Array1<T>&);
  
  bool set_data(const Array1<double>&, const Array1<T>&);
  bool set_data(const Array1<double>&, const Array1<T>&, 
    const Array1<Core::Geometry::Vector>&);
  inline bool get_value(double, T&);
  
private:
  Array1<QUAT> X;
  Array1<QUAT> Y;
  Array1<QUAT> Z;
};

template <class T> Cubic3DPWI<T>::Cubic3DPWI(const Array1<double>& pts, 
                         const Array1<T>& vals)
{
  set_data(pts, vals);
}

template <class T> inline bool Cubic3DPWI<T>::get_value(double w, T& res)
{
  int i;
  if (this->data_valid && (i = this->get_interval(w)) >= 0) {
    w -= this->points[i];
    res = T(X[i].a + w * (X[i].b + w * (X[i].c + X[i].d * w)), 
              Y[i].a + w * (Y[i].b + w * (Y[i].c + Y[i].d * w)),
              Z[i].a + w * (Z[i].b + w * (Z[i].c + Z[i].d * w)));
    return true;
  }
  else
    return false;
}


SCISHARE bool set_tangents(const Array1<double>&, const Array1<double>&, 
                   Array1<double>&, EndCondition);

template <class T> bool 
Cubic3DPWI<T>::set_data(const Array1<double>& pts, const Array1<T>& vals)
{
  int sz = vals.size();
  this->reset();
  Array1<double> drvX, drvY, drvZ;
  Array1<double> vx, vy, vz;
  vx.resize(sz);
  vy.resize(sz);
  vz.resize(sz);

  for (int i = 0; i < sz; i++) {
    vx[i] = vals[i].x();
    vy[i] = vals[i].y();
    vz[i] = vals[i].z();
  }

  if (set_tangents(pts, vx, drvX, natural_ends) && 
      set_tangents(pts, vy, drvY, natural_ends) 
      && set_tangents(pts, vz, drvZ, natural_ends)) {
#if DEBUG
    std::cout << "Derivatives are done!!!" << std::endl;
#endif
    Array1<Core::Geometry::Vector> drvs;
    drvs.resize(sz);
    for (int i = 0; i < sz; i++) {
      drvs[i] = Core::Geometry::Vector(drvX[i], drvY[i], drvZ[i]);
    }
    return set_data(pts, vals, drvs);          
  }
  else {
    return false;
  }
}

// takes sorted array of points
template <class T> bool 
Cubic3DPWI<T>::set_data(const Array1<double>& pts, const Array1<T>& vals, 
                        const Array1<Core::Geometry::Vector>& drvs){
  int sz = 0;
  this->reset();
  
  if (this->fill_data(pts) && (sz = this->points.size()) > 1 && 
      sz == vals.size() && sz == drvs.size()) {
#if DEBUG
    std::cout << "Inside set_data!!!" << std::endl;
#endif
    X.resize(sz);
    Y.resize(sz);
    Z.resize(sz);
    
    Array1<double> drvX, drvY, drvZ;
    Array1<double> vx, vy, vz;
    vx.resize(sz);
    vy.resize(sz);
    vz.resize(sz);
    drvX.resize(sz);
    drvY.resize(sz);
    drvZ.resize(sz);
    
    for (int i=0; i < sz; i++) {
      vx[i] = vals[i].x();
      vy[i] = vals[i].y();
      vz[i] = vals[i].z();
      drvX[i] = drvs[i].x();
      drvY[i] = drvs[i].y();
      drvZ[i] = drvs[i].z();
    }
    
    this->data_valid = true;
    double delta, a, b, c, d;
    
    for (int i = 0; i < sz-1; i++)
      if ( (delta = this->points[i+1] - this->points[i]) > 10e-9) {
        a = vx[i];
        b = drvX[i];
        c = ((3 * (vx[i+1] - vx[i]) / delta) - 2 * drvX[i] - drvX[i+1]) / delta;
        d = (drvX[i] + drvX[i+1] - (2 * (vx[i+1] - vx[i]) / delta)) / (delta * delta);
        
        X[i].a = a;
        X[i].b = b;
        X[i].c = c;
        X[i].d = d;
#if DEBUG
        std::cout << "Interval: " << this->points[i] << ", " << this->points[i+1] << std::endl;
        std::cout << "Coeff. are for X: " << X[i].a << std::endl << X[i].b 
                  << std::endl << X[i].c << std::endl << X[i].d << std::endl;
#endif
        a = vy[i];
        b = drvY[i];
        c = (3 * (vy[i+1] - vy[i]) / delta - 2 * drvY[i] - drvY[i+1]) / delta;
        d = (drvY[i] + drvY[i+1] - 2 * (vy[i+1] - vy[i]) / delta) / (delta * delta);
        
        Y[i].a = a;
        Y[i].b = b;
        Y[i].c = c;
        Y[i].d = d;
#if DEBUG
        std::cout << "Interval: " << this->points[i] << ", " << this->points[i+1] << std::endl;
        std::cout << "Coeff. are for Y: " << Y[i].a << std::endl << Y[i].b 
                  << std::endl << Y[i].c << std::endl << Y[i].d << std::endl;
#endif        
        a = vz[i];
        b = drvZ[i];
        c = (3* (vz[i+1] - vz[i]) / delta- 2 * drvZ[i] - drvZ[i+1]) / delta;
        d = (drvZ[i] + drvZ[i+1] - 2 * (vz[i+1] - vz[i]) / delta) / (delta * delta);
        
        Z[i].a = a;
        Z[i].b = b;
        Z[i].c = c;
        Z[i].d = d;
      }
      else {
#if DEBUG
        std::cout << "Delta is small!!! " << std::endl;
#endif
        this->reset();
        break;
      }
  }
  return this->data_valid;
}
  
} // End namespace SCIRun

#endif //SCI_CUBICPWI_H__