/* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   http://lammps.sandia.gov, Sandia National Laboratories
   Steve Plimpton, sjplimp@sandia.gov

   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under 
   the GNU General Public License.

   See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */

/* ----------------------------------------------------------------------
   Contributing author: Pieter in 't Veld (SNL)
------------------------------------------------------------------------- */

#include "math.h"
#include "stdlib.h"
#include "string.h"
#include "region_prism.h"
#include "domain.h"
#include "force.h"
#include "error.h"

using namespace LAMMPS_NS;

#define BIG 1.0e20

#define MIN(A,B) ((A) < (B)) ? (A) : (B)
#define MAX(A,B) ((A) > (B)) ? (A) : (B)

/* ---------------------------------------------------------------------- */

RegPrism::RegPrism(LAMMPS *lmp, int narg, char **arg) : Region(lmp, narg, arg)
{
  options(narg-11,&arg[11]);

  if (strcmp(arg[2],"INF") == 0 || strcmp(arg[2],"EDGE") == 0) {
    if (domain->box_exist == 0) 
      error->all("Cannot use region INF or EDGE when box does not exist");
    if (strcmp(arg[2],"INF") == 0) xlo = -BIG;
    else xlo = domain->boxlo[0];
  } else xlo = xscale*atof(arg[2]);

  if (strcmp(arg[3],"INF") == 0 || strcmp(arg[3],"EDGE") == 0) {
    if (domain->box_exist == 0) 
      error->all("Cannot use region INF or EDGE when box does not exist");
    if (strcmp(arg[3],"INF") == 0) xhi = BIG;
    else xhi = domain->boxhi[0];
  } else xhi = xscale*atof(arg[3]);

  if (strcmp(arg[4],"INF") == 0 || strcmp(arg[4],"EDGE") == 0) {
    if (domain->box_exist == 0) 
      error->all("Cannot use region INF or EDGE when box does not exist");
    if (strcmp(arg[4],"INF") == 0) ylo = -BIG;
    else ylo = domain->boxlo[1];
  } else ylo = yscale*atof(arg[4]);

  if (strcmp(arg[5],"INF") == 0 || strcmp(arg[5],"EDGE") == 0) {
    if (domain->box_exist == 0) 
      error->all("Cannot use region INF or EDGE when box does not exist");
    if (strcmp(arg[5],"INF") == 0) yhi = BIG;
    else yhi = domain->boxhi[1];
  } else yhi = yscale*atof(arg[5]);

  if (strcmp(arg[6],"INF") == 0 || strcmp(arg[6],"EDGE") == 0) {
    if (domain->box_exist == 0) 
      error->all("Cannot use region INF or EDGE when box does not exist");
    if (strcmp(arg[6],"INF") == 0) zlo = -BIG;
    else zlo = domain->boxlo[2];
  } else zlo = zscale*atof(arg[6]);

  if (strcmp(arg[7],"INF") == 0 || strcmp(arg[7],"EDGE") == 0) {
    if (domain->box_exist == 0) 
      error->all("Cannot use region INF or EDGE when box does not exist");
    if (strcmp(arg[7],"INF") == 0) zhi = BIG;
    else zhi = domain->boxhi[2];
  } else zhi = zscale*atof(arg[7]);

  xy = xscale*atof(arg[8]);
  xz = xscale*atof(arg[9]);
  yz = yscale*atof(arg[10]);

  // error check
  // prism cannot be 0 thickness in any dim, else inverse blows up
  // non-zero tilt values cannot be used if either dim is INF on both ends

  if (xlo >= xhi || ylo >= yhi || zlo >= zhi)
    error->all("Illegal region prism command");

  if (xy != 0.0 && xlo == -BIG && xhi == BIG)
    error->all("Illegal region prism command");
  if (xy != 0.0 && ylo == -BIG && yhi == BIG)
    error->all("Illegal region prism command");

  if (xz != 0.0 && xlo == -BIG && xhi == BIG)
    error->all("Illegal region prism command");
  if (xz != 0.0 && zlo == -BIG && zhi == BIG)
    error->all("Illegal region prism command");

  if (yz != 0.0 && ylo == -BIG && yhi == BIG)
    error->all("Illegal region prism command");
  if (yz != 0.0 && zlo == -BIG && zhi == BIG)
    error->all("Illegal region prism command");

  // extent of prism
  
  if (interior) {
    bboxflag = 1;
    extent_xlo = MIN(xlo,xlo+xy);
    extent_xlo = MIN(extent_xlo,extent_xlo+xz);
    extent_ylo = MIN(ylo,ylo+yz);
    extent_zlo = zlo;
    
    extent_xhi = MAX(xhi,xhi+xy);
    extent_xhi = MAX(extent_xhi,extent_xhi+xz);
    extent_yhi = MAX(yhi,yhi+yz);
    extent_zhi = zhi;
  } else bboxflag = 0;

  // particle could contact all 6 planes

  cmax = 6;
  contact = new Contact[cmax];

  // h = transformation matrix from tilt coords (0-1) to box coords (xyz)
  // columns of h are edge vectors of tilted box
  // hinv = transformation matrix from box coords to tilt coords
  // both h and hinv are upper triangular
  //   since 1st edge of prism is along x-axis
  //   and bottom face of prism is in xy plane

  h[0][0] = xhi - xlo;
  h[0][1] = xy;
  h[0][2] = xz;
  h[1][1] = yhi - ylo;
  h[1][2] = yz;
  h[2][2] = zhi - zlo;

  hinv[0][0] = 1.0/h[0][0];
  hinv[0][1] = -h[0][1] / (h[0][0]*h[1][1]);
  hinv[0][2] = (h[0][1]*h[1][2] - h[0][2]*h[1][1]) / (h[0][0]*h[1][1]*h[2][2]);
  hinv[1][1] = 1.0/h[1][1];
  hinv[1][2] = -h[1][2] / (h[1][1]*h[2][2]);
  hinv[2][2] = 1.0/h[2][2];

  // corners = 8 corner points of prism
  // order = x varies fastest, then y, finally z
  // clo/chi = lo and hi corner pts of prism

  a[0] = xhi-xlo;
  a[1] = 0.0;
  a[2] = 0.0;
  b[0] = xy;
  b[1] = yhi-ylo;
  b[2] = 0.0;
  c[0] = xz;
  c[1] = yz;
  c[2] = zhi-zlo;

  clo[0] = corners[0][0] = xlo;
  clo[1] = corners[0][1] = ylo;
  clo[2] = corners[0][2] = zlo;

  corners[1][0] = xlo + a[0];
  corners[1][1] = ylo + a[1];
  corners[1][2] = zlo + a[2];

  corners[2][0] = xlo + b[0];
  corners[2][1] = ylo + b[1];
  corners[2][2] = zlo + b[2];

  corners[3][0] = xlo + a[0] + b[0];
  corners[3][1] = ylo + a[1] + b[1];
  corners[3][2] = zlo + a[2] + b[2];

  corners[4][0] = xlo + c[0];
  corners[4][1] = ylo + c[1];
  corners[4][2] = zlo + c[2];

  corners[5][0] = xlo + a[0] + c[0];
  corners[5][1] = ylo + a[1] + c[1];
  corners[5][2] = zlo + a[2] + c[2];

  corners[6][0] = xlo + b[0] + c[0];
  corners[6][1] = ylo + b[1] + c[1];
  corners[6][2] = zlo + b[2] + c[2];

  chi[0] = corners[7][0] = xlo + a[0] + b[0] + c[0];
  chi[1] = corners[7][1] = ylo + a[1] + b[1] + c[1];
  chi[2] = corners[7][2] = zlo + a[2] + b[2] + c[2];

  // face = 6 inward-facing unit normals to prism faces
  // order = xy plane, xz plane, yz plane

  cross(a,b,face[0]);
  cross(b,a,face[1]);
  cross(c,a,face[2]);
  cross(a,c,face[3]);
  cross(b,c,face[4]);
  cross(c,b,face[5]);

  for (int i = 0; i < 6; i++) normalize(face[i]);

  // tri = 3 vertices (0-7) in each of 12 triangles on 6 faces
  // verts in each tri are ordered so that right-hand rule gives inward norm
  // order = xy plane, xz plane, yz plane

  tri[0][0] =  0; tri[0][1] =  1; tri[0][2] =  3;
  tri[1][0] =  0; tri[1][1] =  3; tri[1][2] =  2;
  tri[2][0] =  4; tri[2][1] =  7; tri[2][2] =  5;
  tri[3][0] =  4; tri[3][1] =  6; tri[3][2] =  7;

  tri[4][0] =  0; tri[4][1] =  4; tri[4][2] =  5;
  tri[5][0] =  0; tri[5][1] =  5; tri[5][2] =  1;
  tri[6][0] =  2; tri[6][1] =  7; tri[6][2] =  6;
  tri[7][0] =  2; tri[7][1] =  3; tri[7][2] =  7;

  tri[8][0] =  2; tri[8][1] =  6; tri[8][2] =  4;
  tri[9][0] =  2; tri[9][1] =  4; tri[9][2] =  0;
  tri[10][0] = 1; tri[10][1] = 5; tri[10][2] = 7;
  tri[11][0] = 1; tri[11][1] = 7; tri[11][2] = 3;
}

/* ---------------------------------------------------------------------- */

RegPrism::~RegPrism()
{
  delete [] contact;
}

/* ----------------------------------------------------------------------
   inside = 1 if x,y,z is inside or on surface
   inside = 0 if x,y,z is outside and not on surface
   abc = Hinv * (xyz - xyz/lo)
   abc = tilt coords (0-1)
   Hinv = transformation matrix from box coords to tilt coords
   xyz = box coords
   xyz/lo = lower-left corner of prism
------------------------------------------------------------------------- */

int RegPrism::inside(double x, double y, double z)
{
  double a = hinv[0][0]*(x-xlo) + hinv[0][1]*(y-ylo) + hinv[0][2]*(z-zlo);
  double b = hinv[1][1]*(y-ylo) + hinv[1][2]*(z-zlo);
  double c = hinv[2][2]*(z-zlo);

  if (a >= 0.0 && a <= 1.0 && b >= 0.0 && b <= 1.0 && c >= 0.0 && c <= 1.0)
    return 1;
  return 0;
}

/* ----------------------------------------------------------------------
   contact if 0 <= x < cutoff from one or more inner surfaces of prism
   can be one contact for each of 6 faces
   no contact if outside (possible if called from union/intersect)
   delxyz = vector from nearest point on prism to x
------------------------------------------------------------------------- */

int RegPrism::surface_interior(double *x, double cutoff)
{
  int i;
  double dot;
  double *corner;

  // x is exterior to prism

  for (i = 0; i < 6; i++) {
    if (i % 2) corner = chi;
    else corner = clo;
    dot = (x[0]-corner[0])*face[i][0] + (x[1]-corner[1])*face[i][1] + 
      (x[2]-corner[2])*face[i][2];
    if (dot < 0.0) return 0;
  }

  // x is interior to prism or on its surface

  int n = 0;

  for (int i = 0; i < 6; i++) {
    if (i % 2) corner = chi;
    else corner = clo;
    dot = (x[0]-corner[0])*face[i][0] + (x[1]-corner[1])*face[i][1] + 
      (x[2]-corner[2])*face[i][2];
    if (dot < cutoff) {
      contact[n].r = dot;
      contact[n].delx = dot*face[i][0];
      contact[n].dely = dot*face[i][1];
      contact[n].delz = dot*face[i][2];
      n++;
    }
  }

  return n;
}

/* ----------------------------------------------------------------------
   one contact if 0 <= x < cutoff from outer surface of prism
   no contact if inside (possible if called from union/intersect)
   delxyz = vector from nearest point on prism to x
------------------------------------------------------------------------- */

int RegPrism::surface_exterior(double *x, double cutoff)
{
  int i;
  double dot;
  double *corner;
  double xp,yp,zp;

  // x is far enough from prism that there is no contact

  for (i = 0; i < 6; i++) {
    if (i % 2) corner = chi;
    else corner = clo;
    dot = (x[0]-corner[0])*face[i][0] + (x[1]-corner[1])*face[i][1] + 
      (x[2]-corner[2])*face[i][2];
    if (dot <= -cutoff) return 0;
  }

  // x is interior to prism

  for (i = 0; i < 6; i++) {
    if (i % 2) corner = chi;
    else corner = clo;
    dot = (x[0]-corner[0])*face[i][0] + (x[1]-corner[1])*face[i][1] + 
      (x[2]-corner[2])*face[i][2];
    if (dot <= 0.0) break;
  }

  if (i == 6) return 0;

  // x is exterior to prism or on its surface
  // xp,yp,zp = point on surface of prism that x is closest to
  //            could be edge or corner pt of prism
  // do not add contact point if r >= cutoff

  find_nearest(x,xp,yp,zp);
  add_contact(0,x,xp,yp,zp);
  if (contact[0].r < cutoff) return 1;
  return 0;
}

/* ----------------------------------------------------------------------
   x is exterior to prism or on its surface
   return (xp,yp,zp) = nearest pt to x that is on surface of prism
------------------------------------------------------------------------- */

void RegPrism::find_nearest(double *x, double &xp, double &yp, double &zp)
{
  int i,j,k,iface;
  double xproj[3],xline[3],nearest[3];
  double dot;

  // generate successive xnear points, one nearest to x is (xp,yp,zp)
  // loop over 6 faces and 2 triangles in each face
  // xproj = x projected to plane of triangle
  // if xproj is inside or on triangle boundary, that is xnear
  // else: loop over 3 edges of triangle
  //       compute distance to edge line
  //       xnear = nearest point on line to xproj, bounded by segment end pts

  double distsq = BIG;

  for (int itri = 0; itri < 12; itri++) {
    iface = itri/2;
    i = tri[itri][0];
    j = tri[itri][1];
    k = tri[itri][2];
    dot = (x[0]-corners[i][0])*face[iface][0] + 
      (x[1]-corners[i][1])*face[iface][1] + 
      (x[2]-corners[i][2])*face[iface][2];
    xproj[0] = x[0] - dot*face[iface][0];
    xproj[1] = x[1] - dot*face[iface][1];
    xproj[2] = x[2] - dot*face[iface][2];
    if (inside_tri(xproj,corners[i],corners[j],corners[k],face[iface]))
      distsq = closest(x,xproj,nearest,distsq);
    else {
      point_on_line_segment(corners[i],corners[j],xproj,xline);
      distsq = closest(x,xline,nearest,distsq);
      point_on_line_segment(corners[j],corners[k],xproj,xline);
      distsq = closest(x,xline,nearest,distsq);
      point_on_line_segment(corners[i],corners[k],xproj,xline);
      distsq = closest(x,xline,nearest,distsq);
    }
  }
  
  xp = nearest[0];
  yp = nearest[1];
  zp = nearest[2];
}

/* ----------------------------------------------------------------------
   test if x is inside triangle with vertices v1,v2,v3
   norm = normal to triangle, defined by right-hand rule for v1,v2,v3 ordering
   edge = edge vector of triangle
   pvec = vector from vertex to x
   xproduct = cross product of edge with pvec
   if xproduct dot norm < 0.0 for any of 3 edges, then x is outside triangle
------------------------------------------------------------------------- */

int RegPrism::inside_tri(double *x, double *v1, double *v2, double *v3,
			 double *norm)
{
  double edge[3],pvec[3],xproduct[3];

  subtract(v1,v2,edge);
  subtract(v1,x,pvec);
  cross(edge,pvec,xproduct);
  if (dotproduct(xproduct,norm) < 0.0) return 0;

  subtract(v2,v3,edge);
  subtract(v2,x,pvec);
  cross(edge,pvec,xproduct);
  if (dotproduct(xproduct,norm) < 0.0) return 0;

  subtract(v3,v1,edge);
  subtract(v3,x,pvec);
  cross(edge,pvec,xproduct);
  if (dotproduct(xproduct,norm) < 0.0) return 0;

  return 1;
}

/* ----------------------------------------------------------------------
   find nearest point to C on line segment A,B and return it as D
   project (C-A) onto (B-A)
   t = length of that projection, normalized by length of (B-A)
   t <= 0, C is closest to A
   t >= 1, C is closest to B
   else closest point is between A and B
------------------------------------------------------------------------- */

void RegPrism::point_on_line_segment(double *a, double *b, 
				     double *c, double *d)
{
  double ba[3],ca[3];

  subtract(a,b,ba);
  subtract(a,c,ca);
  double t = dotproduct(ca,ba) / dotproduct(ba,ba);

  if (t <= 0.0) {
    d[0] = a[0];
    d[1] = a[1];
    d[2] = a[2];
  } else if (t >= 1.0) {
    d[0] = b[0];
    d[1] = b[1];
    d[2] = b[2];
  } else {
    d[0] = a[0] + t*ba[0];
    d[1] = a[1] + t*ba[1];
    d[2] = a[2] + t*ba[2];
  }
}

/* ---------------------------------------------------------------------- */

double RegPrism::closest(double *x, double *near, double *nearest, double dsq)
{
  double delx = x[0] - near[0];
  double dely = x[1] - near[1];
  double delz = x[2] - near[2];
  double rsq = delx*delx + dely*dely + delz*delz;
  if (rsq >= dsq) return dsq;

  nearest[0] = near[0];
  nearest[1] = near[1];
  nearest[2] = near[2];
  return rsq;
}

/* ----------------------------------------------------------------------
   v3 = v2 - v1
------------------------------------------------------------------------- */

void RegPrism::subtract(double *v1, double *v2, double *v3)
{
  v3[0] = v2[0] - v1[0];
  v3[1] = v2[1] - v1[1];
  v3[2] = v2[2] - v1[2];
}

/* ----------------------------------------------------------------------
   v3 = v1 x v2
------------------------------------------------------------------------- */

void RegPrism::cross(double *v1, double *v2, double *v3)
{
  v3[0] = v1[1]*v2[2] - v1[2]*v2[1];
  v3[1] = v1[2]*v2[0] - v1[0]*v2[2];
  v3[2] = v1[0]*v2[1] - v1[1]*v2[0];
}

/* ----------------------------------------------------------------------
   return dotproduct = v1 dot v2
------------------------------------------------------------------------- */

double RegPrism::dotproduct(double *v1, double *v2)
{
  return (v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]);
}

/* ---------------------------------------------------------------------- */

void RegPrism::normalize(double *x)
{
  double invlen = 1.0/sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
  x[0] *= invlen;
  x[1] *= invlen;
  x[2] *= invlen;
}
