/*******************************************************************************
*
* McStas, neutron ray-tracing package
*         Copyright (C) 1997-2008, All rights reserved
*         Risoe National Laboratory, Roskilde, Denmark
*         Institut Laue Langevin, Grenoble, France
*
* Runtime: share/interoff-lib.c
*
* %Identification
* Written by: Reynald Arnerin
* Date:    Jun 12, 2008
* Origin: ILL
* Release: $Revision$
* Version: McStas X.Y
*
* Object File Format intersection library for McStas. Requires the qsort function.
*
* Such files may be obtained with e.g.
*   qhull < points.xyz Qx Qv Tv o > points.off
* where points.xyz has format (it supports comments):
*   3
*   <nb_points>
*   <x> <y> <z>
*   ...
* The resulting file should have its first line being changed from '3' into 'OFF'.
* It can then be displayed with geomview.
* A similar, but somewhat older solution is to use 'powercrust' with e.g.
*   powercrust -i points.xyz
* which will generate a 'pc.off' file to be renamed as suited.
*
*******************************************************************************/

#ifndef INTEROFF_LIB_H
#include "interoff-lib.h"
#endif

#pragma acc routine
double off_F(double x, double y,double z,double A,double B,double C,double D) {
  return ( A*x + B*y + C*z + D );
}

#pragma acc routine
char off_sign(double a) {
  if (a<0)       return(-1);
  else if (a==0) return(0);
  else           return(1);
}

// off_normal ******************************************************************
//gives the normal vector of p
#pragma acc routine
void off_normal(Coords* n, polygon p)
{
  //using Newell method
  int i=0,j=0;
  n->x=0;n->y=0;n->z=0;
  for (i = 0, j = p.npol-1; i < p.npol; j = i++)
  {
    MCNUM x1=p.p[3*i],
          y1=p.p[3*i+1],
          z1=p.p[3*i+2];
    MCNUM x2=p.p[3*j],
          y2=p.p[3*j+1],
          z2=p.p[3*j+2];
    // n is the cross product of v1*v2
    n->x += (y1 - y2) * (z1 + z2);
    n->y += (z1 - z2) * (x1 + x2);
    n->z += (x1 - x2) * (y1 + y2);
  }
} /* off_normal */

// off_pnpoly ******************************************************************
//based on http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
//return 0 if the vertex is out
//    1 if it is in
//   -1 if on the boundary
#pragma acc routine
int off_pnpoly(polygon p, Coords v)
{
  int i=0, c = 0;
  MCNUM minx=FLT_MAX,maxx=-FLT_MAX,miny=FLT_MAX,maxy=-FLT_MAX,minz=FLT_MAX,maxz=-FLT_MAX;
  MCNUM areax=0,areay=0,areaz=0;

  int pol2dx=0,pol2dy=1;          //2d restriction of the poly
  MCNUM x=v.x,y=v.y;

  /*areax: projected area with x-scratched = |v1_yz x v2_yz|, where v1=(x1-x0,0,z1-z0) & v2=(x2-x0,0,z2-z0).*/
  /* In principle, if polygon is triangle area should be scaled by 1/2, but this is irrelevant for finding the maximum area.*/
  /* Similarly for y and z scratched.*/
  areax=coords_len(coords_xp(
        coords_set(0,p.p[3*1+1]-p.p[0+1],p.p[3*1+2]-p.p[0+2]),
        coords_set(0,p.p[3*2+1]-p.p[0+1],p.p[3*2+2]-p.p[0+2])));
  areay=coords_len(coords_xp(
        coords_set(p.p[3*1+0]-p.p[0+0],0,p.p[3*1+2]-p.p[0+2]),
        coords_set(p.p[3*2+0]-p.p[0+0],0,p.p[3*2+2]-p.p[0+2])));
  areaz=coords_len(coords_xp(
        coords_set(p.p[3*1+0]-p.p[0+0],p.p[3*1+1]-p.p[0+1],0),
        coords_set(p.p[3*2+0]-p.p[0+0],p.p[3*2+1]-p.p[0+1],0)));

  if(areaz<areax){
    if(areax<areay){
      /*pick areay - i.e. scratch y*/
      pol2dy=2;
      y=v.z;
    }else{
      /*scratch x*/
      pol2dx=2;
      x=v.z;
    }
  }else if (areaz<areay){
    pol2dy=2;
    y=v.z;
  }

  //trace rays and test number of intersection
  int j;
  for (i = 0, j = p.npol-1; i < p.npol; j = i++) {
    if (((((p.p[3*i+pol2dy])<=y) && (y<(p.p[3*j+pol2dy]))) ||
         (((p.p[3*j+pol2dy])<=y) && (y<(p.p[3*i+pol2dy])))) &&
        (x < ( (p.p[3*j+pol2dx] - p.p[3*i+pol2dx]) * (y - p.p[3*i+pol2dy])
             / (p.p[3*j+pol2dy] - p.p[3*i+pol2dy]) + p.p[3*i+pol2dx]) ))
      c = !c;

    if (((fabs(p.p[3*i+pol2dy]-y)<=OFF_EPSILON) || ((fabs(p.p[3*j+pol2dy]-y)<=OFF_EPSILON))) &&
        fabs(x -((p.p[3*j+pol2dx] - p.p[3*i+pol2dx]) * (y - p.p[3*i+pol2dy])
          / (p.p[3*j+pol2dy] - p.p[3*i+pol2dy]) + p.p[3*i+pol2dx])) < OFF_EPSILON)
    {
      //the point lies on the edge
      c=-1;
      break;
    }
  }

  return c;
} /* off_pnpoly */

// off_intersectPoly ***********************************************************
//gives the intersection vertex between ray [a,b) and polygon p and its parametric value on (a b)
//based on http://geometryalgorithms.com/Archive/algorithm_0105/algorithm_0105.htm
#pragma acc routine
int off_intersectPoly(intersection *inter, Coords a, Coords b, polygon p)
{
  //direction vector of [a,b]
  Coords dir = {b.x-a.x, b.y-a.y, b.z-a.z};

  //the normal vector to the polygon
  Coords normale=p.normal;
  //off_normal(&normale, p); done at the init stage

  //direction vector from a to a vertex of the polygon
  Coords w0 = {a.x-p.p[0], a.y-p.p[1], a.z-p.p[2]};

  //scalar product
  MCNUM nw0  =-scalar_prod(normale.x,normale.y,normale.z,w0.x,w0.y,w0.z);
  MCNUM ndir = scalar_prod(normale.x,normale.y,normale.z,dir.x,dir.y,dir.z);
  inter->time = inter->edge = inter->in_out=0;
  inter->v = inter->normal = coords_set(0,0,1);

  if (fabs(ndir) < OFF_EPSILON)    // ray is parallel to polygon plane
  {
    if (nw0 == 0)              // ray lies in polygon plane (infinite number of solution)
      return 0;
    else return 0;             // ray disjoint from plane (no solution)
  }

  // get intersect point of ray with polygon plane
  inter->time = nw0 / ndir;            //parametric value the point on line (a,b)

  inter->v = coords_set(a.x + inter->time * dir.x,// intersect point of ray and plane
    a.y + inter->time * dir.y,
    a.z + inter->time * dir.z);

  int res=off_pnpoly(p,inter->v);

  inter->edge=(res==-1);
  if (ndir<0)
    inter->in_out=1;  //the negative dot product means we enter the surface
  else
    inter->in_out=-1;

  inter->normal=p.normal;

  return res;         //true if the intersection point lies inside the poly
} /* off_intersectPoly */


// off_getBlocksIndex **********************************************************
/*reads the indexes at the beginning of the off file as this :
line 1  OFF
line 2  nbVertex nbFaces nbEdges
*/
FILE *off_getBlocksIndex(char* filename, long* vtxSize, long* polySize )
{
  FILE* f = Open_File(filename,"r", NULL); /* from read_table-lib: FILE *Open_File(char *name, char *Mode, char *path) */
  if (!f) return (f);

  char line[CHAR_BUF_LENGTH];
  char *ret=0;
  *vtxSize = *polySize = 0;

  /* **************** start to read the file header */
  /* OFF file:
     'OFF' or '3'
   */

  ret=fgets(line,CHAR_BUF_LENGTH , f);// line 1 = "OFF"
  if (ret == NULL)
  {
    fprintf(stderr, "Error: Can not read 1st line in file %s (interoff/off_getBlocksIndex)\n", filename);
    exit(1);
  }
  if (strlen(line)>5)
  {
      fprintf(stderr,"Error: First line in %s is too long (=%lu). Possibly the line is not terminated by '\\n'.\n"
              "       The first line is required to be exactly 'OFF', '3' or 'ply'.\n",
              filename,(long unsigned)strlen(line));
      fclose(f);
      return(NULL);
  }

  if (strncmp(line,"OFF",3) && strncmp(line,"3",1) && strncmp(line,"ply",1))
  {
    fprintf(stderr, "Error: %s is probably not an OFF, NOFF or PLY file (interoff/off_getBlocksIndex).\n"
                    "       Requires first line to be 'OFF', '3' or 'ply'.\n",filename);
    fclose(f);
    return(NULL);
  }

  if (!strncmp(line,"OFF",3) || !strncmp(line,"3",1)) {
    do  /* OFF file: skip # comments which may be there */
    {
      ret=fgets(line,CHAR_BUF_LENGTH , f);
      if (ret == NULL)
      {
        fprintf(stderr, "Error: Can not read line in file %s (interoff/off_getBlocksIndex)\n", filename);
        exit(1);
      }
    } while (line[0]=='#');
    //line = nblines of vertex,faces and edges arrays
    sscanf(line,"%lu %lu",vtxSize,polySize);
  } else {
    do  /* PLY file: read all lines until find 'end_header'
           and locate 'element faces' and 'element vertex' */
    {
      ret=fgets(line,CHAR_BUF_LENGTH , f);
      if (ret == NULL)
      {
        fprintf(stderr, "Error: Can not read line in file %s (interoff/off_getBlocksIndex)\n", filename);
        exit(1);
      }
      if (!strncmp(line,"element face",12))
        sscanf(line,"element face %lu",polySize);
      else if (!strncmp(line,"element vertex",14))
        sscanf(line,"element vertex %lu",vtxSize);
      else if (!strncmp(line,"format binary",13))
        exit(fprintf(stderr,
          "Error: Can not read binary PLY file %s, only 'format ascii' (interoff/off_getBlocksIndex)\n%s\n",
          filename, line));
    } while (strncmp(line,"end_header",10));
  }

  /* The FILE is left opened ready to read 'vtxSize' vertices (vtxSize *3 numbers)
     and then polySize polygons (rows) */

  return(f);
} /* off_getBlocksIndex */

// off_init_planes *************************************************************
//gives the equations of 2 perpandicular planes of [ab]
#pragma acc routine
void off_init_planes(Coords a, Coords b,
  MCNUM* A1, MCNUM* C1, MCNUM* D1, MCNUM *A2, MCNUM* B2, MCNUM* C2, MCNUM* D2)
{
  //direction vector of [a b]
  Coords dir={b.x-a.x, b.y-a.y, b.z-a.z};

  //the plane parallel to the 'y' is computed with the normal vector of the projection of [ab] on plane 'xz'
  *A1= dir.z;
  *C1=-dir.x;
  if(*A1!=0 || *C1!=0)
    *D1=-(a.x)*(*A1)-(a.z)*(*C1);
  else
  {
    //the plane does not support the vector, take the one parallel to 'z''
    *A1=1;
    //B1=dir.x=0
    *D1=-(a.x);
  }
  //the plane parallel to the 'x' is computed with the normal vector of the projection of [ab] on plane 'yz'
  *B2= dir.z;
  *C2=-dir.y;
  *A2= 0;
  if (*B2==0 && *C2==0)
  {
    //the plane does not support the vector, take the one parallel to 'z'
    *B2=1;
    //B1=dir.x=0
    *D2=-(a.y);
  }
  else {
    if (dir.z==0)
    {
      //the planes are the same, take the one parallel to 'z'
      *A2= dir.y;
      *B2=-dir.x;
      *D2=-(a.x)*(*A2)-(a.y)*(*B2);
    }
    else
      *D2=-(a.y)**B2-(a.z)**C2;
  }
} /* off_init_planes */

// off_clip_3D_mod *************************************************************
#pragma acc routine
int off_clip_3D_mod(intersection* t, Coords a, Coords b,
  Coords* vtxArray, unsigned long vtxSize, unsigned long* faceArray,
  unsigned long faceSize, Coords* normalArray)
{
  MCNUM A1=0, C1=0, D1=0, A2=0, B2=0, C2=0, D2=0;      //perpendicular plane equations to [a,b]
  off_init_planes(a, b, &A1, &C1, &D1, &A2, &B2, &C2, &D2);

  int t_size=0;
  MCNUM popol[3*4]; /*3 dimensions and max 4 vertices to form a polygon*/
  unsigned long i=0,indPoly=0;

  //exploring the polygons :
  i=indPoly=0;
  while (i<faceSize)
  {
    polygon pol;
    pol.npol  = faceArray[i];                //nb vertex of polygon
    pol.p     = popol;
    pol.normal= coords_set(0,0,1);
    pol.D     = 1;
    unsigned long indVertP1=faceArray[++i];  //polygon's first vertex index in vtxTable
    int j=1;
    /*check whether vertex is left or right of plane*/
    char sg0=off_sign(off_F(vtxArray[indVertP1].x,vtxArray[indVertP1].y,vtxArray[indVertP1].z,A1,0,C1,D1));
    while (j<pol.npol)
    {
      //polygon's j-th vertex index in vtxTable
      unsigned long indVertP2=faceArray[i+j];
      /*check whether vertex is left or right of plane*/
      char sg1=off_sign(off_F(vtxArray[indVertP2].x,vtxArray[indVertP2].y,vtxArray[indVertP2].z,A1,0,C1,D1));
      if (sg0!=sg1) //if the plane intersect the polygon
        break;

      ++j;
    }

    if (j<pol.npol)          //ok, let's test with the second plane
    {
      char sg1=off_sign(off_F(vtxArray[indVertP1].x,vtxArray[indVertP1].y,vtxArray[indVertP1].z,A2,B2,C2,D2));//tells if vertex is left or right of the plane

      j=1;
      while (j<pol.npol)
      {
        //unsigned long indVertPi=faceArray[i+j];  //polyg's j-th vertex index in vtxTable
        Coords vertPi=vtxArray[faceArray[i+j]];
        if (sg1!=off_sign(off_F(vertPi.x,vertPi.y,vertPi.z,A2,B2,C2,D2)))//if the plane intersect the polygon
          break;
        ++j;
      }
      if (j<pol.npol)
      {
#ifdef OFF_LEGACY
        if (t_size>OFF_INTERSECT_MAX)
        {
#ifndef OPENACC
          fprintf(stderr, "Warning: number of intersection exceeded (%d) (interoff-lib/off_clip_3D_mod)\n", OFF_INTERSECT_MAX);
#endif
            return (t_size);
        }
#endif
        //both planes intersect the polygon, let's find the intersection point
        //our polygon :
        int k;
        for (k=0; k<pol.npol; ++k)
        {
          Coords vertPk=vtxArray[faceArray[i+k]];
          pol.p[3*k]  =vertPk.x;
          pol.p[3*k+1]=vertPk.y;
          pol.p[3*k+2]=vertPk.z;
        }
        pol.normal=normalArray[indPoly];
        intersection x;
        if (off_intersectPoly(&x, a, b, pol))
        {
          x.index = indPoly;
#ifdef OFF_LEGACY
          t[t_size++]=x;
#else
	  /* Check against our 4 existing times, starting from [-FLT_MAX, FLT_MAX, FLT_MAX, FLT_MAX] */
	  /* Case 1, negative time? */
	  if (t_size < 4) t_size++;	  
	  if (x.time < 0) {
	    if (x.time > t[0].time) {
	      t[0]=x;
	    }
	  } else {
	    /* Case 2, positive time */
	    intersection xtmp;
	    if (x.time < t[3].time) {
	      t[3]=x;
	      if (t[3].time < t[2].time) {
		xtmp = t[2];
		t[2] = t[3];
		t[3] = xtmp;
	      }
	      if (t[2].time < t[1].time) {
		xtmp = t[1];
		t[1] = t[2];
		t[2] = xtmp;
	      }
	    } 
	  }
#endif
	}
      } /* if (j<pol.npol) */
    } /* if (j<pol.npol) */
    i += pol.npol;
    indPoly++;
  } /* while i<faceSize */
  return t_size;
} /* off_clip_3D_mod */

// off_clip_3D_mod_grav *************************************************************
/*******************************************************************************
version of off_clip_3D_mod_grav
*******************************************************************************/
#pragma acc routine seq
int off_clip_3D_mod_grav(intersection* t, Coords pos, Coords vel, Coords acc,
  Coords* vtxArray, unsigned long vtxSize, unsigned long* faceArray,
  unsigned long faceSize, Coords* normalArray, double* DArray)
{
  int t_size=0;
  MCNUM popol[3*CHAR_BUF_LENGTH];
  double plane_Eq [4];
  double quadratic [3];
  unsigned long i=0,indPoly=0;
  //exploring the polygons :
  i=indPoly=0;
  while (i<faceSize)
  {
    polygon pol;
    pol.npol  = faceArray[i];                //nb vertex of polygon
    pol.p     = popol;
    pol.normal= coords_set(0,0,1);
    unsigned long indVertP1=faceArray[++i];  //polygon's first vertex index in vtxTable
    
    if (t_size>CHAR_BUF_LENGTH)
      {
#ifndef OPENACC
	fprintf(stderr, "Warning: number of intersection exceeded (%d) (interoff-lib/off_clip_3D_mod)\n", CHAR_BUF_LENGTH);
#endif
	return (t_size);
      }
    //both planes intersect the polygon, let's find the intersection point
    //our polygon :
    int k;
    for (k=0; k<pol.npol; ++k)
      {
	Coords vertPk=vtxArray[faceArray[i+k]];
	pol.p[3*k]  =vertPk.x;
	pol.p[3*k+1]=vertPk.y;
	pol.p[3*k+2]=vertPk.z;
      }
    pol.normal=normalArray[indPoly];
    pol.D=DArray[indPoly];
    p_to_quadratic(pol.normal, pol.D, acc, pos, vel, quadratic);
    double x1, x2;
    int nsol = quadraticSolve(quadratic, &x1, &x2);

    if (nsol >= 1) {
      double time = 1.0e36;
      if (x1 < time && x1 > 0.0) {
	time = x1;
      }
      if (nsol == 2 && x2 < time && x2 > 0.0) {
	time = x2;
      }
      if (time != 1.0e36) {
	intersection inters;
	double t2 = time * time * 0.5;
	double tx = pos.x + time * vel.x;
	if (acc.x != 0.0) {
	  tx = tx + t2 * acc.x;
	}
	double ty = pos.y + time * vel.y;
	if (acc.y != 0.0) {
	  ty = ty + t2 * acc.y;
	}
	double tz = pos.z + time * vel.z;
	if (acc.z != 0.0) {
	  tz = tz + t2 * acc.z;
	}
	inters.v = coords_set(tx, ty, tz);
	Coords tvel = coords_set(vel.x + time * acc.x,
				 vel.y + time * acc.y,
				 vel.z + time * acc.z);
	inters.time = time;
	inters.normal = pol.normal;
	inters.index = indPoly;
	int res=off_pnpoly(pol,inters.v);
	if (res != 0) {
	  inters.edge=(res==-1);
	  MCNUM ndir = scalar_prod(pol.normal.x,pol.normal.y,pol.normal.z,tvel.x,tvel.y,tvel.z);
	  if (ndir<0) {
	    inters.in_out=1;  //the negative dot product means we enter the surface
	  } else {
	    inters.in_out=-1;
	  }
#ifdef OFF_LEGACY
          t[t_size++]=inters;
#else
    /* Check against our 4 existing times, starting from [-FLT_MAX, FLT_MAX, FLT_MAX, FLT_MAX] */
    /* Case 1, negative time? */
    if (t_size < 4) t_size++;
    if (inters.time < 0) {
      if (inters.time > t[0].time) {
        t[0]=inters;
      }
    } else {
      /* Case 2, positive time */
      intersection xtmp;
      if (inters.time < t[3].time) {
      t[3]=inters;
        if (t[3].time < t[2].time) {
    xtmp = t[2];
    t[2] = t[3];
    t[3] = xtmp;
        }
        if (t[2].time < t[1].time) {
    xtmp = t[1];
    t[1] = t[2];
    t[2] = xtmp;
        }
      }
    }
#endif
	}
      }
    }
    i += pol.npol;
    indPoly++;
  } /* while i<faceSize */
  return t_size;
} /* off_clip_3D_mod_grav */

// off_compare *****************************************************************
#pragma acc routine
int off_compare (void const *a, void const *b)
{
   intersection const *pa = a;
   intersection const *pb = b;

   return off_sign(pa->time - pb->time);
} /* off_compare */

// off_cleanDouble *************************************************************
//given an array of intersections throw those which appear several times
//returns 1 if there is a possibility of error
#pragma acc routine
int off_cleanDouble(intersection* t, int* t_size)
{
  int i=1;
  intersection prev=t[0];
  while (i<*t_size)
  {
    int j=i;
    //for each intersection with the same time
    while (j<*t_size && fabs(prev.time-t[j].time)<OFF_EPSILON)
    {
      //if the intersection is the exact same erase it
      if (prev.in_out==t[j].in_out)
      {
        int k;
        for (k=j+1; k<*t_size; ++k)
        {
          t[k-1]=t[k];
        }
        *t_size-=1;
      }
      else
        ++j;
    }
    prev=t[i];
    ++i;

  }
  return 1;
} /* off_cleanDouble */

// off_cleanInOut **************************************************************
//given an array of intesections throw those which enter and exit in the same time
//Meaning the ray passes very close to the volume
//returns 1 if there is a possibility of error
#pragma acc routine
int off_cleanInOut(intersection* t, int* t_size)
{
  int i=1;
  intersection prev=t[0];
  while (i<*t_size)
  {
    //if two intersection have the same time but one enters and the other exits erase both
    //(such intersections must be adjacent in the array : run off_cleanDouble before)
    if (fabs(prev.time-t[i].time)<OFF_EPSILON && prev.in_out!=t[i].in_out)
    {
      int j=0;
      for (j=i+1; j<*t_size; ++j)
      {
        t[j-2]=t[j];
      }
      *t_size-=2;
      prev=t[i-1];
    }
    else
    {
      prev=t[i];
      ++i;
    }
  }
  return (*t_size);
} /* off_cleanInOut */

/* PUBLIC functions ******************************************************** */

/*******************************************************************************
* long off_init(  char *offfile, double xwidth, double yheight, double zdepth, off_struct* data)
* ACTION: read an OFF file, optionally center object and rescale, initialize OFF data structure
* INPUT: 'offfile' OFF file to read
*        'xwidth,yheight,zdepth' if given as non-zero, apply bounding box.
*           Specifying only one of these will also use the same ratio on all axes
*        'notcenter' center the object to the (0,0,0) position in local frame when set to zero
* RETURN: number of polyhedra and 'data' OFF structure
*******************************************************************************/
long off_init(  char *offfile, double xwidth, double yheight, double zdepth,
                int notcenter, off_struct* data)
{
  // data to be initialized
  long    vtxSize =0, polySize=0, i=0, ret=0, faceSize=0;
  Coords* vtxArray        =NULL;
  Coords* normalArray     =NULL;
  double* DArray          =NULL;
  unsigned long* faceArray=NULL;
  FILE*   f               =NULL; /* the FILE with vertices and polygons */
  double minx=FLT_MAX,maxx=-FLT_MAX,miny=FLT_MAX,maxy=-FLT_MAX,minz=FLT_MAX,maxz=-FLT_MAX;

  // get the indexes
  if (!data) return(0);

  MPI_MASTER(
  printf("Loading geometry file (OFF/PLY): %s\n", offfile);
  );

  f=off_getBlocksIndex(offfile,&vtxSize,&polySize);
  if (!f) return(0);

  // read vertex table = [x y z | x y z | ...] =================================
  // now we read the vertices as 'vtxSize*3' numbers and store it in vtxArray
  MPI_MASTER(
  printf("  Number of vertices: %ld\n", vtxSize);
  );
  vtxArray   = malloc(vtxSize*sizeof(Coords));
  if (!vtxArray) return(0);
  i=0;
  while (i<vtxSize && ~feof(f))
  {
    double x,y,z;
    ret=fscanf(f, "%lg%lg%lg", &x,&y,&z);
    if (!ret) {
      // invalid line: we skip it (probably a comment)
      char line[CHAR_BUF_LENGTH];
      char *s=fgets(line, CHAR_BUF_LENGTH, f);
      continue;
    }
    if (ret != 3) {
      fprintf(stderr, "Error: can not read [xyz] coordinates for vertex %li in file %s (interoff/off_init). Read %li values.\n",
        i, offfile, ret);
      exit(2);
    }
    vtxArray[i].x=x;
    vtxArray[i].y=y;
    vtxArray[i].z=z;

    //bounding box
    if (vtxArray[i].x<minx) minx=vtxArray[i].x;
    if (vtxArray[i].x>maxx) maxx=vtxArray[i].x;
    if (vtxArray[i].y<miny) miny=vtxArray[i].y;
    if (vtxArray[i].y>maxy) maxy=vtxArray[i].y;
    if (vtxArray[i].z<minz) minz=vtxArray[i].z;
    if (vtxArray[i].z>maxz) maxz=vtxArray[i].z;
    i++; // inquire next vertex
  }

  // resizing and repositioning params
  double centerx=0, centery=0, centerz=0;
  if (!notcenter) {
    centerx=(minx+maxx)*0.5;
    centery=(miny+maxy)*0.5;
    centerz=(minz+maxz)*0.5;
  }

  double rangex=-minx+maxx,
         rangey=-miny+maxy,
         rangez=-minz+maxz;

  double ratiox=1,ratioy=1,ratioz=1;

  if (xwidth && rangex)
  {
    ratiox=xwidth/rangex;
    ratioy=ratiox;
    ratioz=ratiox;
  }

  if (yheight && rangey)
  {
    ratioy=yheight/rangey;
    if(!xwidth)  ratiox=ratioy;
    ratioz=ratioy;
  }

  if (zdepth && rangez)
  {
    ratioz=zdepth/rangez;
    if(!xwidth)  ratiox=ratioz;
    if(!yheight) ratioy=ratioz;
  }

  rangex *= ratiox;
  rangey *= ratioy;
  rangez *= ratioz;

  //center and resize the object
  for (i=0; i<vtxSize; ++i)
  {
    vtxArray[i].x=(vtxArray[i].x-centerx)*ratiox+(!notcenter ? 0 : centerx);
    vtxArray[i].y=(vtxArray[i].y-centery)*ratioy+(!notcenter ? 0 : centery);
    vtxArray[i].z=(vtxArray[i].z-centerz)*ratioz+(!notcenter ? 0 : centerz);
  }

  // read face table = [nbvertex v1 v2 vn | nbvertex v1 v2 vn ...] =============
  MPI_MASTER(
  printf("  Number of polygons: %ld\n", polySize);
  );
  normalArray= malloc(polySize*sizeof(Coords));
  faceArray  = malloc(polySize*10*sizeof(unsigned long)); // we assume polygons have less than 9 vertices
  DArray     = malloc(polySize*sizeof(double));
  if (!normalArray || !faceArray || !DArray) return(0);

  // fill faces
  faceSize=0;
  i=0;
  while (i<polySize && ~feof(f)) {
    int  nbVertex=0, j=0;
    // read the length of this polygon
    ret=fscanf(f, "%d", &nbVertex);
    if (!ret) {
      // invalid line: we skip it (probably a comment)
      char line[CHAR_BUF_LENGTH];
      char *s=fgets(line, CHAR_BUF_LENGTH, f);
      continue;
    }
    if (ret != 1) {
      fprintf(stderr, "Error: can not read polygon %li length in file %s (interoff/off_init)\n",
        i, offfile);
      exit(3);
    }
    if (faceSize > polySize*10) {
      fprintf(stderr, "Error: %li exceeded allocated polygon array[%li] in file %s (interoff/off_init)\n",
        faceSize, polySize*10, offfile);
    }
    faceArray[faceSize++] = nbVertex; // length of the polygon/face
    // then read the vertex ID's
    for (j=0; j<nbVertex; j++) {
      double vtx=0;
      ret=fscanf(f, "%lg", &vtx);
      faceArray[faceSize++] = vtx;   // add vertices index after length of polygon
    }
    i++;
  }

  // precomputes normals
  long indNormal=0;//index in polyArray
  i=0;    //index in faceArray
  while (i<faceSize)
  {
    int    nbVertex=faceArray[i];//nb of vertices of this polygon
    double *vertices=malloc(3*nbVertex*sizeof(double));
    int j;

    for (j=0; j<nbVertex; ++j)
    {
      unsigned long indVertPj=faceArray[i+j+1];
      vertices[3*j]  =vtxArray[indVertPj].x;
      vertices[3*j+1]=vtxArray[indVertPj].y;
      vertices[3*j+2]=vtxArray[indVertPj].z;
    }

    polygon p;
    p.p   =vertices;
    p.npol=nbVertex;
    p.D=1;
    off_normal(&(p.normal),p);

    normalArray[indNormal]=p.normal;
    p.D = scalar_prod(p.normal.x,p.normal.y,p.normal.z,
		      vertices[0],vertices[1],vertices[2]);
    DArray[indNormal]=p.D;

    i += nbVertex+1;
    indNormal++;
    free(vertices);
  }

  MPI_MASTER(
  if (ratiox!=ratioy || ratiox!=ratioz || ratioy!=ratioz)
    printf("Warning: Aspect ratio of the geometry %s was modified.\n"
           "         If you want to keep the original proportions, specifiy only one of the dimensions.\n",
           offfile);
  if ( xwidth==0 && yheight==0 && zdepth==0 ) {
    printf("Warning: Neither xwidth, yheight or zdepth are defined.\n"
	   "           The file-defined (non-scaled) geometry the OFF geometry %s will be applied!\n",
           offfile);
  }
  printf("  Bounding box dimensions for geometry %s:\n", offfile);
  printf("    Length=%f (%.3f%%)\n", rangex, ratiox*100);
  printf("    Width= %f (%.3f%%)\n", rangey, ratioy*100);
  printf("    Depth= %f (%.3f%%)\n", rangez, ratioz*100);
  );

  data->vtxArray   = vtxArray;
  data->normalArray= normalArray;
  data->DArray     = DArray;
  data->faceArray  = faceArray;
  data->vtxSize    = vtxSize;
  data->polySize   = polySize;
  data->faceSize   = faceSize;
  data->filename   = offfile;
  #ifdef OPENACC
  acc_attach((void *)&vtxArray);
  acc_attach((void *)&normalArray);
  acc_attach((void *)&faceArray);
  #endif

  return(polySize);
} /* off_init */

#pragma acc routine
int Min_int(int x, int y) {
  return (x<y)? x :y;
}

 
#pragma acc routine
void merge(intersection *arr, int l, int m, int r)
{
int i, j, k;
int n1 = m - l + 1;
int n2 =  r - m;

/* create temp arrays */
intersection *L, *R;
 L = (intersection *)malloc(sizeof(intersection) * n1);
 R = (intersection *)malloc(sizeof(intersection) * n2);
/* Copy data to temp arrays L[] and R[] */
 #pragma acc loop independent
for (i = 0; i < n1; i++)
    L[i] = arr[l + i];
 #pragma acc loop independent
for (j = 0; j < n2; j++)
    R[j] = arr[m + 1+ j];

/* Merge the temp arrays back into arr[l..r]*/
i = 0;
j = 0;
k = l;

while (i < n1 && j < n2)
{
    if (L[i].time <= R[j].time)
    {
        arr[k] = L[i];
        i++;
    }
    else
    {
        arr[k] = R[j];
        j++;
    }
    k++;
}

/* Copy the remaining elements of L[], if there are any */

while (i < n1)
{
    arr[k] = L[i];
    i++;
    k++;
}

/* Copy the remaining elements of R[], if there are any */
while (j < n2)
{
    arr[k] = R[j];
    j++;
    k++;
}
free(L);
free(R);
}


#ifdef USE_OFF
#pragma acc routine
void gpusort(intersection *arr, int size)
{
  int curr_size;  // For current size of subarrays to be merged
  // curr_size varies from 1 to n/2
  int left_start; // For picking starting index of left subarray
  // to be merged
  // pcopying (R[0:n2])
  {
    for (curr_size=1; curr_size<=size-1; curr_size = 2*curr_size)
      {
	// Pick starting point of different subarrays of current size
	for (left_start=0; left_start<size-1; left_start += 2*curr_size)
	  {
	    // Find ending point of left subarray. mid+1 is starting
	    // point of right
	    int mid = left_start + curr_size - 1;

	    int right_end = Min_int(left_start + 2*curr_size - 1, size-1);

	    // Merge Subarrays arr[left_start...mid] & arr[mid+1...right_end]
	    if (mid < right_end) merge(arr, left_start, mid, right_end);
	  }
      }
  }
}
#endif

/*******************************************************************************
void p_to_quadratic(double eq[], Coords acc,
                    Coords pos, Coords vel,
                    double* teq)
* ACTION: define the quadratic for the intersection of a parabola with a plane
* INPUT: 'eq' plane equation
*        'acc' acceleration vector
*        'vel' velocity of the particle
*        'pos' position of the particle
*         equation of plane A * x + B * y + C * z - D = 0
*         eq[0] = (C*az)/2+(B*ay)/2+(A*ax)/2
*         eq[1] = C*vz+B*vy+A*vx
*         eq[2] = C*z0+B*y0+A*x0-D
* RETURN: equation of parabola: teq(0) * t^2 + teq(1) * t + teq(2)
*******************************************************************************/
void p_to_quadratic(Coords norm, MCNUM d, Coords acc, Coords pos, Coords vel,
		    double* teq)
{
  teq[0] = scalar_prod(norm.x, norm.y, norm.z, acc.x, acc.y, acc.z) * 0.5;
  teq[1] = scalar_prod(norm.x, norm.y, norm.z, vel.x, vel.y, vel.z);
  teq[2] = scalar_prod(norm.x, norm.y, norm.z, pos.x, pos.y, pos.z) - d;
  return;
}

/*******************************************************************************
int quadraticSolve(double eq[], double* x1, double* x2);
* ACTION: solves the quadratic for the roots x1 and x2 
*         eq[0] * t^2 + eq[1] * t + eq[2] = 0
* INPUT: 'eq' the coefficients of the parabola
* RETURN: roots x1 and x2 and the number of solutions
*******************************************************************************/
int quadraticSolve(double* eq, double* x1, double* x2)
{
  if (eq[0] == 0.0) { // This is a linear equation
    if (eq[1] != 0.0) { // one solution
      *x1 = -eq[2]/eq[1];
      *x2 = 1.0e36;
      return 1;
    }else { // no solutions, 1.0e36 will be ignored.
      *x1 = 1.0e36;
      *x2 = 1.0e36;
      return 0;
    }
  }
  double delta = eq[1]*eq[1]-4.0*eq[0]*eq[2];
  if (delta < 0.0) { // no solutions, both are imaginary
    *x1 = 1.0e36;
    *x2 = 1.0e36;
    return 0;
  }
  double s = 1.0;
  if (eq[1] < 0) {
    s = -1.0;
  }
  *x1 = (-eq[1] - s * sqrt(delta))/(2.0*eq[0]);
  if (eq[0] != 0.0) { //two solutions
    *x2 = eq[2]/(eq[0]*(*x1));
    return 2;
  } else { //one solution
    *x2 = 1.0e36;
    return 1;
  }
}

/*******************************************************************************
* int off_intersect_all(double* t0, double* t3,
     Coords *n0, Coords *n3,
     double x, double y, double z,
     double vx, double vy, double vz,
     double ax, double ay, double az,
     off_struct *data )
* ACTION: computes intersection of neutron trajectory with an object.
* INPUT:  x,y,z and vx,vy,vz are the position and velocity of the neutron
*         ax, ay, az are the local acceleration vector
*         data points to the OFF data structure
* RETURN: the number of polyhedra which trajectory intersects
*         t0 and t3 are the smallest incoming and outgoing intersection times
*         n0 and n3 are the corresponding normal vectors to the surface
*         data is the full OFF structure, including a list intersection type
*******************************************************************************/
int off_intersect_all(double* t0, double* t3,
     Coords *n0, Coords *n3,
     double x,  double y,  double z,
     double vx, double vy, double vz,
     double ax, double ay, double az,
     off_struct *data )
{

    int t_size = 0;
#ifdef OFF_LEGACY

    if(mcgravitation) {
      Coords pos={ x,  y,  z};
      Coords vel={vx, vy, vz};
      Coords acc={ax, ay, az};
      t_size=off_clip_3D_mod_grav(data->intersects, pos, vel, acc,
				  data->vtxArray, data->vtxSize, data->faceArray,
				  data->faceSize, data->normalArray, data->DArray );
    } else {
    ///////////////////////////////////
    // non-grav
      Coords A={x, y, z};
      Coords B={x+vx, y+vy, z+vz};
      t_size=off_clip_3D_mod(data->intersects, A, B,
			     data->vtxArray, data->vtxSize, data->faceArray,
			     data->faceSize, data->normalArray );
    }
    #ifndef OPENACC
    qsort(data->intersects, t_size, sizeof(intersection),  off_compare);
    #else
    #ifdef USE_OFF
    gpusort(data->intersects, t_size);
    #endif
    #endif
    off_cleanDouble(data->intersects, &t_size);
    off_cleanInOut(data->intersects,  &t_size);

    /*find intersections "closest" to 0 (favouring positive ones)*/
    if(t_size>0){
      int i=0;
      if(t_size>1) {
        for (i=1; i < t_size-1; i++){
          if (data->intersects[i-1].time > 0 && data->intersects[i].time > 0)
            break;
        }

	data->nextintersect=i-1;
	data->numintersect=t_size;

        if (t0) *t0 = data->intersects[i-1].time;
        if (n0) *n0 = data->intersects[i-1].normal;
        if (t3) *t3 = data->intersects[i].time;
        if (n3) *n3 = data->intersects[i].normal;
      } else {
        if (t0) *t0 = data->intersects[0].time;
	      if (n0) *n0 = data->intersects[0].normal;
      }
      /* should also return t[0].index and t[i].index as polygon ID */
      data->nextintersect=(data->intersects[data->nextintersect]).index;
      return t_size;
    }
#else
    intersection intersect4[4];
    intersect4[0].time=-FLT_MAX;
    intersect4[1].time=FLT_MAX;
    intersect4[2].time=FLT_MAX;
    intersect4[3].time=FLT_MAX;
    if(mcgravitation) {
      Coords pos={ x,  y,  z};
      Coords vel={vx, vy, vz};
      Coords acc={ax, ay, az};
      t_size=off_clip_3D_mod_grav(intersect4, pos, vel, acc,
				  data->vtxArray, data->vtxSize, data->faceArray,
				  data->faceSize, data->normalArray, data->DArray);
    } else {
    ///////////////////////////////////
    // non-grav
      Coords A={x, y, z};
      Coords B={x+vx, y+vy, z+vz};
      t_size=off_clip_3D_mod(intersect4, A, B,
	  data->vtxArray, data->vtxSize, data->faceArray, data->faceSize, data->normalArray );
    }
    if(t_size>0){
      int i=0;
      if (intersect4[0].time == -FLT_MAX) i=1;
      data->numintersect=t_size;
      if (t0) *t0 = intersect4[i].time;
      if (n0) *n0 = intersect4[i].normal;
      if (t3) *t3 = intersect4[i+1].time;
      if (n3) *n3 = intersect4[i+1].normal;

      if (intersect4[1].time == FLT_MAX)
      {
        if (t3) *t3 = 0.0;
      }

      /* should also return t[0].index and t[i].index as polygon ID */
      data->nextintersect=(int)intersect4[i].index;
      return t_size;
    }
#endif
    return 0;
} /* off_intersect */

/*******************************************************************************
* int off_intersect(double* t0, double* t3,
     Coords *n0, Coords *n3,
     double x, double y, double z,
     double vx, double vy, double vz,
     off_struct data )
* ACTION: computes intersection of neutron trajectory with an object.
* INPUT:  x,y,z and vx,vy,vz are the position and velocity of the neutron
*         data points to the OFF data structure
* RETURN: the number of polyhedra which trajectory intersects
*         t0 and t3 are the smallest incoming and outgoing intersection times
*         n0 and n3 are the corresponding normal vectors to the surface
*******************************************************************************/
int off_intersect(double* t0, double* t3,
     Coords *n0, Coords *n3,
     double x,  double y,  double z,
     double vx, double vy, double vz,
     double ax, double ay, double az,
     off_struct data )
{
  return off_intersect_all(t0, t3, n0, n3, x, y, z, vx, vy, vz, ax, ay, az, &data );
} /* off_intersect */

/*****************************************************************************
* int off_x_intersect(double* l0, double* l3,
     Coords *n0, Coords *n3,
     double x, double y, double z,
     double kx, double ky, double kz,
     off_struct data )
* ACTION: computes intersection of an xray trajectory with an object.
* INPUT:  x,y,z and kx,ky,kz, are spatial coordinates and wavevector of the x-ray
*         respectively. data points to the OFF data structure.
* RETURN: the number of polyhedra the trajectory intersects
*         l0 and l3 are the smallest incoming and outgoing intersection lengths
*         n0 and n3 are the corresponding normal vectors to the surface
*******************************************************************************/
int off_x_intersect(double *l0,double *l3,
     Coords *n0, Coords *n3,
     double x,  double y,  double z,
     double kx, double ky, double kz,
     off_struct data )
{
  /*This function simply reformats and calls off_intersect (as for neutrons)
   *by normalizing the wavevector - this will yield the intersection lengths
   *in m*/
  double jx,jy,jz,invk;
  int n;
  invk=1/sqrt(scalar_prod(kx,ky,kz,kx,ky,kz));
  jx=kx*invk;jy=ky*invk;jz=kz*invk;
  n=off_intersect(l0,l3,n0,n3,x,y,z,jx,jy,jz,0.0,0.0,0.0,data);
  return n;
}


/*******************************************************************************
* void off_display(off_struct data)
* ACTION: display up to N_VERTEX_DISPLAYED polygons from the object
*******************************************************************************/
void off_display(off_struct data)
{
    if(mcdotrace==2){
    // Estimate size of the JSON string
    const int VERTEX_OVERHEAD = 30;
    const int FACE_OVERHEAD_BASE = 20;
    const int FACE_INDEX_OVERHEAD = 15;
    int estimated_size = 256; // Base size
    estimated_size += data.vtxSize * VERTEX_OVERHEAD;

    for (int i = 0; i < data.faceSize;) {
        int num_indices = data.faceArray[i];
        estimated_size += FACE_OVERHEAD_BASE + num_indices * FACE_INDEX_OVERHEAD;
        i += num_indices + 1;
    }

    char *json_string = malloc(estimated_size);
    if (json_string == NULL) {
        fprintf(stderr, "Memory allocation failed.\n");
        return;
    }

    char *ptr = json_string;
    ptr += sprintf(ptr, "{ \"vertices\": [");

    for (int i = 0; i < data.vtxSize; i++) {
        ptr += sprintf(ptr, "[%g, %g, %g]", data.vtxArray[i].x, data.vtxArray[i].y, data.vtxArray[i].z);
        if (i < data.vtxSize - 1) {
            ptr += sprintf(ptr, ", ");
        }
    }

    ptr += sprintf(ptr, "], \"faces\": [");

    for (int i = 0; i < data.faceSize;) {
        int num = data.faceArray[i];
        ptr += sprintf(ptr, "{ \"face\": [");
        for (int j = 1; j <= num; j++) {
            ptr += sprintf(ptr, "%lu", data.faceArray[i + j]);
            if (j < num) {
                ptr += sprintf(ptr, ", ");
            }
        }
        ptr += sprintf(ptr, "]}");
        i += num + 1;
        if(i<data.faceSize){
          ptr += sprintf(ptr, ", ");
        }
    }

    ptr += sprintf(ptr, "]}");
    mcdis_polyhedron(json_string);

    free(json_string);
    }
    else {
      unsigned int i;
      double ratio=(double)(N_VERTEX_DISPLAYED)/(double)data.faceSize;
      unsigned int pixel=0;
      for (i=0; i<data.faceSize-1; i++) {
        int j;
        int nbVertex = data.faceArray[i];
        double x0,y0,z0;
        x0 = data.vtxArray[data.faceArray[i+1]].x;
        y0 = data.vtxArray[data.faceArray[i+1]].y;
        z0 = data.vtxArray[data.faceArray[i+1]].z;
        double x1=x0,y1=y0,z1=z0;
        double cmx=0,cmy=0,cmz=0;

        int drawthis = rand01() < ratio;
        // First pass, calculate center of mass location...
        for (j=1; j<=nbVertex; j++) {
          cmx = cmx+data.vtxArray[data.faceArray[i+j]].x;
          cmy = cmy+data.vtxArray[data.faceArray[i+j]].y;
          cmz = cmz+data.vtxArray[data.faceArray[i+j]].z;
        }
        cmx /= nbVertex;
        cmy /= nbVertex;
        cmz /= nbVertex;

        char pixelinfo[1024];
	char pixelinfotmp[1024];
        sprintf(pixelinfo, "%li,%li,%li,%i,%g,%g,%g,%g,%g,%g", data.mantidoffset+pixel, data.mantidoffset, data.mantidoffset+data.polySize-1, nbVertex, cmx, cmy, cmz, x1-cmx, y1-cmy, z1-cmz);
        for (j=2; j<=nbVertex; j++) {
          double x2,y2,z2;
          x2 = data.vtxArray[data.faceArray[i+j]].x;
          y2 = data.vtxArray[data.faceArray[i+j]].y;
          z2 = data.vtxArray[data.faceArray[i+j]].z;
          sprintf(pixelinfotmp, "%s,%g,%g,%g", pixelinfo, x2-cmx, y2-cmy, z2-cmz);
	  sprintf(pixelinfo,"%s",pixelinfotmp);
          if (ratio > 1 || drawthis) {
	    mcdis_line(x1,y1,z1,x2,y2,z2);
          }
          x1 = x2; y1 = y2; z1 = z2;
        }
        if (ratio > 1 || drawthis) {
	    mcdis_line(x1,y1,z1,x0,y0,z0);
          }
        if (data.mantidflag) {
          printf("MANTID_PIXEL: %s\n", pixelinfo);
          pixel++;
        }
        i += nbVertex;
      }
    }
} /* off_display */

/* end of interoff-lib.c */
