Field.cpp

// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.
//
// Contributor(s):
//   Jonathan Lambrechts
//

#include <list>
#include <math.h>
#include <fstream>
#include <string>
#include <sstream>

#ifdef HAVE_MATH_EVAL
#include "matheval.h"
#endif
#ifdef HAVE_ANN
#include "ANN/ANN.h"
#endif

#include "Context.h"
#include "Field.h"
#include "GeoInterpolation.h"
#include "GModel.h"
#include "Message.h"

#if !defined(HAVE_NO_POST)
#include "OctreePost.h"
#include "PViewDataList.h"
#endif

#define MAX_LC 1.e22

extern Context_T CTX;

class FieldOptionDouble : public FieldOption
{
 public:
  double &val;
  FieldOptionType get_type(){ return FIELD_OPTION_DOUBLE; }
  FieldOptionDouble(double &_val, bool *_status=0) : FieldOption(_status), val(_val){}
  double numerical_value() const { return val; }
  void numerical_value(double v){ modified(); val = v; }
  void get_text_representation(std::string &v_str)
  {
    std::ostringstream sstream;
    sstream.precision(16);
    sstream << val;
    v_str = sstream.str();
  }
};

class FieldOptionInt : public FieldOption
{
 public:
  int &val;
  FieldOptionType get_type(){ return FIELD_OPTION_INT; }
  FieldOptionInt(int &_val, bool *_status=0) : FieldOption(_status), val(_val){}
  double numerical_value() const { return val; }
  void numerical_value(double v){ modified(); val = (int)v; }
  void get_text_representation(std::string & v_str)
  {
    std::ostringstream sstream;
    sstream << val;
    v_str = sstream.str();
  }
};

class FieldOptionList : public FieldOption
{
 public:
  std::list<int> &val;
  FieldOptionType get_type(){ return FIELD_OPTION_LIST; }
  FieldOptionList(std::list<int> &_val, bool *_status=0) 
    : FieldOption(_status), val(_val) {}
  std::list<int> &list(){ modified(); return val; }
  const std::list<int>& list() const { return val; }
  void get_text_representation(std::string & v_str)
  {
    std::ostringstream sstream;
    sstream << "{";
    for(std::list<int>::iterator it = val.begin(); it != val.end(); it++) {
      if(it != val.begin())
        sstream << ", ";
      sstream << *it;
    }
    sstream << "}";
    v_str = sstream.str();
  }
};

class FieldOptionString:public FieldOption
{
 public:
  std::string & val;
  virtual FieldOptionType get_type(){ return FIELD_OPTION_STRING; }
  FieldOptionString(std::string &_val, bool *_status=0)
    : FieldOption(_status), val(_val) {}
  std::string &string() { modified(); return val; }
  const std::string &string() const { return val; }
  void get_text_representation(std::string &v_str)
  {
    std::ostringstream sstream;
    sstream << "\"" << val << "\"";
    v_str = sstream.str();
  }
};
class FieldOptionPath:public FieldOptionString
{
 public:
  virtual FieldOptionType get_type(){ return FIELD_OPTION_PATH; }
  FieldOptionPath(std::string &_val, bool *_status=0)
    : FieldOptionString(_val,_status) {}
};

class FieldOptionBool : public FieldOption
{
 public:
  bool & val;
  FieldOptionType get_type(){ return FIELD_OPTION_BOOL; }
  FieldOptionBool(bool & _val, bool *_status=0)
    : FieldOption(_status), val(_val) {}
  double numerical_value() const { return val; }
  void numerical_value(double v){ modified(); val = v; }
  void get_text_representation(std::string & v_str)
  {
    std::ostringstream sstream;
    sstream << val;
    v_str = sstream.str();
  }
};

void FieldManager::reset()
{
  for(std::map<int, Field *>::iterator it = begin(); it != end(); it++) {
    delete it->second;
  }
  clear();
}

Field *FieldManager::get(int id)
{
  iterator it = find(id);
  if(it == end()) {
    return 0;
  }
  return it->second;
}

Field *FieldManager::new_field(int id, std::string type_name)
{
  if(find(id) != end()) {
    Msg::Error("Field id %i is already defined.", id);
    return 0;
  }
  if(map_type_name.find(type_name) == map_type_name.end()) {
    Msg::Error("Unknown field type \"%s\".", type_name.c_str());
    return 0;
  }
  Field *f = (*map_type_name[type_name]) ();
  if(!f)
    return 0;
  f->id = id;
  (*this)[id] = f;
  return f;
}

int FieldManager::new_id()
{
  int i = 0;
  iterator it = begin();
  while(1) {
    i++;
    while(it != end() && it->first < i)
      it++;
    if(it == end() || it->first != i)
      break;
  }
  return std::max(i, 1);
}

int FieldManager::max_id()
{
  if(!empty())
    return rbegin()->first;
  else
    return 0;
}

void FieldManager::delete_field(int id)
{
  iterator it = find(id);
  if(it == end()) {
    Msg::Error("Cannot delete field id %i, it does not exist.", id);
    return;
  }
  delete it->second;
  erase(it);
}

// StructuredField
class StructuredField : public Field
{
  double o[3], d[3];
  int n[3];
  double *data;
  bool error_status;
  bool text_format;
  std::string file_name;
 public:
  StructuredField()
  {
    options["FileName"] = new FieldOptionPath(file_name, &update_needed);
    text_format = false;
    options["TextFormat"] = new FieldOptionBool(text_format, &update_needed);
    data = 0;
  }
  const char *get_name()
  {
    return "Structured";
  }
  virtual ~ StructuredField() {
    if(data)
      delete[]data;
  }
  double operator() (double x, double y, double z)
  {
    if(update_needed) {
      error_status = false;
      try {
        std::ifstream input;
        if(text_format)
          input.open(file_name.c_str());
        else
          input.open(file_name.c_str(),std::ios::binary);
        if(!input.is_open())
          throw(1);
        input.
          exceptions(std::ifstream::eofbit | std::ifstream::failbit | std::
                     ifstream::badbit);
        if(!text_format) {
          input.read((char *)o, 3 * sizeof(double));
          input.read((char *)d, 3 * sizeof(double));
          input.read((char *)n, 3 * sizeof(int));
          int nt = n[0] * n[1] * n[2];
          if(data)
            delete[]data;
          data = new double[nt];
          input.read((char *)data, nt * sizeof(double));
        }
        else {
          input >> o[0] >> o[1] >> o[2] >> d[0] >> d[1] >> d[2] >> n[0] >>
            n[1] >> n[2];
          int nt = n[0] * n[1] * n[2];
          if(data)
            delete[]data;
          data = new double[nt];
          for(int i = 0; i < nt; i++)
            input >> data[i];
        }
        input.close();
      }
      catch(...) {
        error_status = true;
        Msg::Error("Field %i : error reading file %s", this->id,
		   file_name.c_str());
      }
      update_needed = false;
    }
    if(error_status)
      return MAX_LC;
    //tri-linear
    int id[2][3];
    double xi[3];
    double xyz[3] = { x, y, z };
    for(int i = 0; i < 3; i++) {
      id[0][i] = (int)floor((xyz[i] - o[i]) / d[i]);
      id[1][i] = id[0][i] + 1;
      id[0][i] = std::max(std::min(id[0][i], n[i] - 1), 0);
      id[1][i] = std::max(std::min(id[1][i], n[i] - 1), 0);
      xi[i] = (xyz[i] - (o[i] + id[0][i] * d[i])) / d[i];
      xi[i] = std::max(std::min(xi[i], 1.), 0.);
    }
    double v = 0;
    for(int i = 0; i < 2; i++)
      for(int j = 0; j < 2; j++)
        for(int k = 0; k < 2; k++) {
          v += data[id[i][0] * n[1] * n[2] + id[j][1] * n[2] + id[k][2]]
            * (i * xi[0] + (1 - i) * (1 - xi[0]))
            * (j * xi[1] + (1 - j) * (1 - xi[1]))
            * (k * xi[2] + (1 - k) * (1 - xi[2]));
        }
    return v;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

class UTMField : public Field
{
  int field_id, zone;
  double a, b, n, n2, n3, n4, n5, e, e2, e1, e12, e13, e14, J1, J2, J3, J4,
    Ap, Bp, Cp, Dp, Ep, e4, e6, ep, ep2, ep4, k0, mu_fact;
 public:
  UTMField()
  {
    field_id = 1;
    zone = 0;
    options["IField"] = new FieldOptionInt(field_id);
    options["Zone"] = new FieldOptionInt(zone);
    a = 6378137;                /* Equatorial Radius */
    b = 6356752.3142;           /* Rayon Polar Radius */
    /* see http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.HTM */
    n = (a - b) / (a + b);
    n2 = n * n;
    n3 = n * n * n;
    n4 = n * n * n * n;
    n5 = n * n * n * n * n;
    e = sqrt(1 - b * b / a / a);
    e2 = e * e;
    e1 = (1 - sqrt(1 - e2)) / (1 + sqrt(1 - e2));
    e12 = e1 * e1;
    e13 = e1 * e1 * e1;
    e14 = e1 * e1 * e1 * e1;
    J1 = (3 * e1 / 2 - 27 * e13 / 32);
    J2 = (21 * e12 / 16 - 55 * e14 / 32);
    J3 = 151 * e13 / 96;
    J4 = 1097 * e14 / 512;
    Ap = a * (1 - n + (5. / 4.) * (n2 - n3) + (81. / 64.) * (n4 - n5));
    Bp = -3 * a * n / 2 * (1 - n + (7. / 8.) * (n2 - n3) +
                           (55. / 64.) * (n4 - n5));
    Cp = 14 * a * n2 / 16 * (1 - n + (3. / 4) * (n2 - n3));
    Dp = -35 * a * n3 / 48 * (1 - n + 11. / 16. * (n2 - n3));
    Ep = +315 * a * n4 / 51 * (1 - n);
    e4 = e2 * e2;
    e6 = e2 * e2 * e2;
    ep = e * a / b;
    ep2 = ep * ep;
    ep4 = ep2 * ep2;
    k0 = 0.9996;
    mu_fact = 1 / (k0 * a * (1 - e2 / 4 - 3 * e4 / 64 - 5 * e6 / 256));
  }
  const char *get_name()
  {
    return "UTM";
  }
  double operator() (double x, double y, double z)
  {
    double r = sqrt(x * x + y * y + z * z);
    double lon = atan2(y, x);
    double lat = asin(z / r);
    double meridionalarc = Ap * lat + Bp * sin(2 * lat)
      + Cp * sin(4 * lat) + Dp * sin(6 * lat) + Ep;
    double slat = sin(lat);
    double clat = cos(lat);
    double slat2 = slat * slat;
    double clat2 = clat * clat;
    double clat3 = clat2 * clat;
    double clat4 = clat3 * clat;
    double tlat2 = slat2 / clat2;
    double nu = a / sqrt(1 - e * e * slat2);
    double p = lon - ((zone - 0.5) / 30 - 1) * M_PI;
    double p2 = p * p;
    double p3 = p * p2;
    double p4 = p2 * p2;
    double utm_x =
      k0 * nu * clat * p + (k0 * nu * clat3 / 6) * (1 - tlat2 +
                                                    ep2 * clat2) * p3 + 5e5;
    double utm_y =
      meridionalarc * k0 + k0 * nu * slat * clat / 2 * p2 +
      k0 * nu * slat * clat3 / 24 * (5 - tlat2 + 9 * ep2 * clat2 +
                                     4 * ep4 * clat4) * p4;
    return (*GModel::current()->getFields()->get(field_id)) (utm_x, utm_y, 0);
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

class LonLatField : public Field
{
  int field_id;
 public:
  LonLatField()
  {
    field_id = 1;
    options["IField"] = new FieldOptionInt(field_id);
  }
  const char *get_name()
  {
    return "LonLat";
  }
  double operator() (double x, double y, double z)
  {
    return (*GModel::current()->getFields()->get(field_id))
      (atan2(y, x), asin(z / sqrt(x * x + y * y + z * z)), 0);
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

class BoxField : public Field
{
  double v_in, v_out, x_min, x_max, y_min, y_max, z_min, z_max;
 public:
  BoxField()
  {
    v_in = v_out = x_min = x_max = y_min = y_max = z_min = z_max = 0;
    options["VIn"] = new FieldOptionDouble(v_in);
    options["VOut"] = new FieldOptionDouble(v_out);
    options["XMin"] = new FieldOptionDouble(x_min);
    options["XMax"] = new FieldOptionDouble(x_max);
    options["YMin"] = new FieldOptionDouble(y_min);
    options["YMax"] = new FieldOptionDouble(y_max);
    options["ZMin"] = new FieldOptionDouble(z_min);
    options["ZMax"] = new FieldOptionDouble(z_max);
  }
  const char *get_name()
  {
    return "Box";
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
  double operator() (double x, double y, double z)
  {
    return (x <= x_max && x >= x_min && y <= y_max && y >= y_min && z <= z_max
            && z >= z_min) ? v_in : v_out;
  }
};

class ThresholdField : public Field
{
  int iField;
  double dmin, dmax, lcmin, lcmax;
  bool sigmoid;
 public:
  const char *get_name()
  {
    return "Threshold";
  }
  ThresholdField()
  {
    iField = 0;
    dmin = 1;
    dmax = 10;
    lcmin = 0.1;
    lcmax = 1;
    sigmoid = false;
    options["IField"] = new FieldOptionInt(iField);
    options["DistMin"] = new FieldOptionDouble(dmin);
    options["DistMax"] = new FieldOptionDouble(dmax);
    options["LcMin"] = new FieldOptionDouble(lcmin);
    options["LcMax"] = new FieldOptionDouble(lcmax);
    options["Sigmoid"] = new FieldOptionBool(sigmoid);
  }
  double operator() (double x, double y, double z)
  {
    Field *field = GModel::current()->getFields()->get(iField);
    double r = ((*field) (x, y, z) - dmin) / (dmax - dmin);
    r = std::max(std::min(r, 1.), 0.);
    double lc;
    if(sigmoid){
      double s = exp(12. * r - 6.) / (1. + exp(12. * r - 6.));
      lc = lcmin * (1. - s) + lcmax * s;
    }
    else{ // linear
      lc = lcmin * (1 - r) + lcmax * r;
    }
    return lc;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

class GradientField : public Field
{
  int iField, kind;
  double delta;
 public:
  const char *get_name()
  {
    return "Gradient";
  }
  GradientField() : iField(0), kind(3), delta(CTX.lc / 1e4)
  {
    options["IField"] = new FieldOptionInt(iField);
    options["Kind"] = new FieldOptionInt(kind);
    options["Delta"] = new FieldOptionDouble(delta);
  }
  double operator() (double x, double y, double z)
  {
    Field *field = GModel::current()->getFields()->get(iField);
    double gx, gy, gz;
    switch (kind) {
    case 0:    /* x */
      return ((*field) (x + delta / 2, y, z) -
              (*field) (x - delta / 2, y, z)) / delta;
    case 1:    /* y */
      return ((*field) (x, y + delta / 2, z) -
              (*field) (x, y - delta / 2, z)) / delta;
    case 2:    /* z */
      return ((*field) (x, y, z + delta / 2) -
              (*field) (x, y, z - delta / 2)) / delta;
    case 3:    /* norm */
      gx =
        ((*field) (x + delta / 2, y, z) -
         (*field) (x - delta / 2, y, z)) / delta;
      gy =
        ((*field) (x, y + delta / 2, z) -
         (*field) (x, y - delta / 2, z)) / delta;
      gz =
        ((*field) (x, y, z + delta / 2) -
         (*field) (x, y, z - delta / 2)) / delta;
      return sqrt(gx * gx + gy * gy + gz * gz);
    default:
      Msg::Error("Field %i : Unknown kind (%i) of gradient.", this->id,
		 kind);
      return MAX_LC;
    }
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

class CurvatureField : public Field
{
  int iField;
  double delta;
 public:
  const char *get_name()
  {
    return "Curvature";
  }
  CurvatureField() : iField(0), delta(CTX.lc / 1e4)
  {
    options["IField"] = new FieldOptionInt(iField);
    options["Delta"] = new FieldOptionDouble(delta);
  }
  void grad_norm(Field &f,double x,double y,double z, double *g)
  {
    g[0]=f(x+delta/2,y,z)-f(x-delta/2,y,z);
    g[1]=f(x,y+delta/2,z)-f(x,y-delta/2,z);
    g[2]=f(x,y,z+delta/2)-f(x,y,z-delta/2);
    double n=sqrt(g[0]*g[0]+g[1]*g[1]+g[2]*g[2]);
    g[0]/=n;
    g[1]/=n;
    g[2]/=n;
  }
  double operator() (double x, double y, double z)
  {
    Field *field = GModel::current()->getFields()->get(iField);
    double grad[6][3];
    grad_norm(*field,x+delta/2,y,z,grad[0]);
    grad_norm(*field,x-delta/2,y,z,grad[1]);
    grad_norm(*field,x,y+delta/2,z,grad[2]);
    grad_norm(*field,x,y-delta/2,z,grad[3]);
    grad_norm(*field,x,y,z+delta/2,grad[4]);
    grad_norm(*field,x,y,z-delta/2,grad[5]);
    return (grad[0][0]-grad[1][0]+grad[2][1]-grad[3][1]+grad[4][2]-grad[5][2])/delta;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

#if defined(HAVE_GSL)
#include <gsl/gsl_math.h>
#include <gsl/gsl_eigen.h>
class MaxEigenHessianField : public Field
{
  int iField;
  double delta;
  gsl_eigen_symm_workspace *gslwork;
  gsl_matrix *gslmat;
  gsl_vector *eigenvalues;
 public:
  const char *get_name()
  {
    return "MaxEigenHessian";
  }
  MaxEigenHessianField() : iField(0), delta(CTX.lc / 1e4)
  {
    options["IField"] = new FieldOptionInt(iField);
    options["Delta"] = new FieldOptionDouble(delta);
    gslwork=gsl_eigen_symm_alloc(3);
    eigenvalues=gsl_vector_alloc(3);
    gslmat=gsl_matrix_alloc(3,3);
  }
  ~MaxEigenHessianField()
  {
    gsl_eigen_symm_free(gslwork);
    gsl_vector_free(eigenvalues);
    gsl_matrix_free(gslmat);
  }
  double operator() (double x, double y, double z)
  {
    Field *field = GModel::current()->getFields()->get(iField);
    gsl_matrix_set(gslmat,1,0,
          (*field) (x + delta/2 , y+delta/2, z)
        + (*field) (x - delta/2 , y-delta/2, z)
        - (*field) (x - delta/2 , y+delta/2, z)
        - (*field) (x + delta/2 , y-delta/2, z));
    gsl_matrix_set(gslmat,2,0,
          (*field) (x + delta/2 , y, z+delta/2)
        + (*field) (x - delta/2 , y, z-delta/2)
        - (*field) (x - delta/2 , y, z+delta/2)
        - (*field) (x + delta/2 , y, z-delta/2));
    gsl_matrix_set(gslmat,2,1,
          (*field) (x, y + delta/2 , z+delta/2)
        + (*field) (x, y - delta/2 , z-delta/2)
        - (*field) (x, y - delta/2 , z+delta/2)
        - (*field) (x, y + delta/2 , z-delta/2));
    double f=(*field)(x,y,z);
    gsl_matrix_set(gslmat,0,0,
        (*field) (x + delta , y, z)+ (*field) (x - delta , y, z) -2*f);
    gsl_matrix_set(gslmat,1,1,
        (*field) (x, y + delta, z)+ (*field) (x , y - delta, z) -2* f);
    gsl_matrix_set(gslmat,2,2,
        (*field) (x, y ,z + delta)+ (*field) (x , y, z - delta)-2*f);
    gsl_eigen_symm(gslmat,eigenvalues,gslwork);
    return std::max(
      fabs(gsl_vector_get(eigenvalues,0)),
      std::max(
      fabs(gsl_vector_get(eigenvalues,0)),
      fabs(gsl_vector_get(eigenvalues,1))))/(delta*delta);
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};
#endif

class LaplacianField : public Field
{
  int iField;
  double delta;
 public:
  const char *get_name()
  {
    return "Laplacian";
  }
  LaplacianField() : iField(0), delta(CTX.lc / 1e4)
  {
    options["IField"] = new FieldOptionInt(iField);
    options["Delta"] = new FieldOptionDouble(delta);
  }
  double operator() (double x, double y, double z)
  {
    Field *field = GModel::current()->getFields()->get(iField);
      return (
        (*field) (x + delta , y, z)+ (*field) (x - delta , y, z)
        +(*field) (x, y + delta , z)+ (*field) (x, y - delta , z)
        +(*field) (x, y, z + delta )+ (*field) (x, y, z - delta )
        -6* (*field) (x , y, z)
        ) / (delta*delta);
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

class MeanField : public Field
{
  int iField;
  double delta;
  int n;
 public:
  const char *get_name()
  {
    return "Mean";
  }
  MeanField() : iField(0), delta(CTX.lc / 1e4)
  {
    options["IField"] = new FieldOptionInt(iField);
    options["Delta"] = new FieldOptionDouble(delta);
    //options["N"] = new FieldOptionInt(n);
  }
  double operator() (double x, double y, double z)
  {
    Field *field = GModel::current()->getFields()->get(iField);
    return (
      (*field) (x + delta , y, z)+ (*field) (x - delta , y, z)
      +(*field) (x, y + delta , z)+ (*field) (x, y - delta , z)
      +(*field) (x, y, z + delta )+ (*field) (x, y, z - delta )
      + (*field) (x , y, z)
      ) / 5;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};

#if defined(HAVE_MATH_EVAL)
class MathEvalExpression
{
  bool error_status;
  std::list<Field*> *list;
  int nvalues;
  char **names;
  double *values;
  void *eval;
  int *evaluators_id;
  std::string function;
  char *c_str_function;
 public:
  double evaluate(double x, double y, double z)
  {
    if(error_status)
      return MAX_LC;
    for(int i = 0; i < nvalues; i++)
    {
      Field *f;
      switch (evaluators_id[i]) {
      case -1:
        values[i] = x;
        break;
        case -2:values[i] = y;
        break;
        case -3:values[i] = z;
        break;
        default:
        {
          f = GModel::current()->getFields()->get(evaluators_id[i]);
          values[i] = f ? (*f) (x, y, z) : MAX_LC;
        }
      }
    }
    return evaluator_evaluate(eval, nvalues, names, values);
  }
  MathEvalExpression()
  {
    eval = 0;
    values = 0;
    c_str_function = 0;
    evaluators_id = 0;
  }
  bool set_function(const std::string & f)
  {
    free_members();
    error_status = false;
    c_str_function = strdup(f.c_str());
    eval = evaluator_create(c_str_function);
    if(!eval) {
      error_status = true;
      return false;
    }
    evaluator_get_variables(eval, &names, &nvalues);
    values = new double[nvalues];
    evaluators_id = new int[nvalues];
    for(int i = 0; i < nvalues; i++) {
      int id;
      if(!strcmp("x", names[i]))
        evaluators_id[i] = -1;
      else if(!strcmp("y", names[i]))
        evaluators_id[i] = -2;
      else if(!strcmp("z", names[i]))
        evaluators_id[i] = -3;
      else if(sscanf(names[i], "F%i", &id) == 1)
        evaluators_id[i] = id;
      else {
        Msg::Error("Unknown matheval argument \"%s\"\n", names[i]);
        error_status = true;
        return false;
      }
    }
    return true;
  }
  void free_members()
  {
    if(c_str_function)
      free(c_str_function);
    if(eval)
      evaluator_destroy(eval);
    if(values)
      delete[]values;
    if(evaluators_id)
      delete evaluators_id;
  }
  ~MathEvalExpression() {
    free_members();
  }
};

class MathEvalField : public Field
{
  MathEvalExpression expr;
  std::string f;
 public:
  MathEvalField()
  {
    options["F"] = new FieldOptionString(f, &update_needed);
  }
  double operator() (double x, double y, double z)
  {
    if(update_needed) {
      if(!expr.set_function(f))
        Msg::Error("Field %i : Invalid matheval expression \"%s\"",
		   this->id, f.c_str());
      update_needed = false;
    }
    return expr.evaluate(x, y, z);
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
  const char *get_name()
  {
    return "MathEval";
  }
};

class ParametricField:public Field
{
  MathEvalExpression expr[3];
  std::string f[3];
  int ifield;
 public:
  ParametricField()
  {
    options["IField"] = new FieldOptionInt(ifield);
    options["FX"] = new FieldOptionString(f[0], &update_needed);
    options["FY"] = new FieldOptionString(f[1], &update_needed);
    options["FZ"] = new FieldOptionString(f[2], &update_needed);
  }
  double operator() (double x, double y, double z)
  {
    if(update_needed) {
      for(int i = 0; i < 3; i++) {
        if(!expr[i].set_function(f[i]))
          Msg::Error("Field %i : Invalid matheval expression \"%s\"",
		     this->id, f[i].c_str());
      }
      update_needed = false;
    }
    return (*GModel::current()->getFields()->get(ifield))
      (expr[0].evaluate(x, y, z), expr[1].evaluate(x, y, z),
       expr[2].evaluate(x, y, z));
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
  const char *get_name()
  {
    return "Param";
  }
};
#endif

#if !defined(HAVE_NO_POST)
class PostViewField : public Field
{
  OctreePost *octree;
 public:
  int view_index;
  double operator() (double x, double y, double z)
  {
    // FIXME: should test unique view num instead, but that would be slower
    if(view_index < 0 || view_index >= (int)PView::list.size())
      return MAX_LC;
    if(update_needed){
      if(octree) delete octree;
      octree = new OctreePost(PView::list[view_index]);
      update_needed = false;
    }
    double l = 0.;
    if(!octree->searchScalar(x, y, z, &l, 0)) {
      // try really hard to find an element around the point
      /*
	double fact[4] = {1.e-6, 1.e-5, 1.e-4, 1.e-3};
	for(int i = 0; i < 4; i++){
	  double eps = CTX.lc * fact[i];
	  printf("approx search witg eps=%g\n", eps);
	  if(octree->searchScalar(x + eps, y, z, &l, 0)) break;
	  if(octree->searchScalar(x - eps, y, z, &l, 0)) break;
	  if(octree->searchScalar(x, y + eps, z, &l, 0)) break;
	  if(octree->searchScalar(x, y - eps, z, &l, 0)) break;
	  if(octree->searchScalar(x, y, z + eps, &l, 0)) break;
	  if(octree->searchScalar(x, y, z - eps, &l, 0)) break;
	  if(octree->searchScalar(x + eps, y - eps, z - eps, &l, 0)) break;
	  if(octree->searchScalar(x + eps, y + eps, z - eps, &l, 0)) break;
	  if(octree->searchScalar(x - eps, y - eps, z - eps, &l, 0)) break;
	  if(octree->searchScalar(x - eps, y + eps, z - eps, &l, 0)) break;
	  if(octree->searchScalar(x + eps, y - eps, z + eps, &l, 0)) break;
	  if(octree->searchScalar(x + eps, y + eps, z + eps, &l, 0)) break;
	  if(octree->searchScalar(x - eps, y - eps, z + eps, &l, 0)) break;
	  if(octree->searchScalar(x - eps, y + eps, z + eps, &l, 0)) break;
	}
      */
    }
    if(l <= 0) return MAX_LC;
    return l;
  }
  const char *get_name()
  {
    return "PostView";
  }
  PostViewField()
  {
    octree = 0;
    options["IView"] = new FieldOptionInt(view_index, &update_needed);
  }
  ~PostViewField()
  {
    if(octree)
      delete octree;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
};
#endif

class MinField : public Field
{
  std::list<int> idlist;
 public:
  MinField()
  {
    options["FieldsList"] = new FieldOptionList(idlist, &update_needed);
  }
  double operator() (double x, double y, double z)
  {
    double v = MAX_LC;
    for(std::list<int>::iterator it = idlist.begin(); it != idlist.end();
        it++) {
      Field *f = (GModel::current()->getFields()->get(*it));
      if(f)
        v = std::min(v, (*f) (x, y, z));
    }
    return v;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
  const char *get_name()
  {
    return "Min";
  }
};

class MaxField : public Field
{
  std::list<int> idlist;
 public:
  MaxField()
  {
    options["FieldsList"] = new FieldOptionList(idlist, &update_needed);
  }
  double operator() (double x, double y, double z)
  {
    double v = -MAX_LC;
    for(std::list<int>::iterator it = idlist.begin(); it != idlist.end();
        it++) {
      Field *f = (GModel::current()->getFields()->get(*it));
      if(f)
        v = std::max(v, (*f) (x, y, z));
    }
    return v;
  }
  FieldDialogBox *&dialog_box()
  {
    static FieldDialogBox *dialogBox = 0;
    return dialogBox;
  }
  const char *get_name()