/* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org

   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 "region_prism.h"

#include "domain.h"
#include "error.h"
#include "input.h"
#include "math_extra.h"
#include "update.h"
#include "variable.h"

#include <cstring>

using namespace LAMMPS_NS;

static constexpr double BIG = 1.0e20;

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

RegPrism::RegPrism(LAMMPS *lmp, int narg, char **arg) : Region(lmp, narg, arg),
   xlostr(nullptr), ylostr(nullptr), zlostr(nullptr), xhistr(nullptr),
   yhistr(nullptr), zhistr(nullptr), xystr(nullptr), xzstr(nullptr), yzstr(nullptr)
{
  options(narg - 11, &arg[11]);

  xlostyle = CONSTANT;
  if (strcmp(arg[2], "INF") == 0 || strcmp(arg[2], "EDGE") == 0) {
    if (domain->box_exist == 0)
      error->all(FLERR, "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 if (utils::strmatch(arg[2], "^v_")) {
    xlostr = utils::strdup(arg[2] + 2);
    xlo = 0.0;
    xlostyle = VARIABLE;
    varshape = 1;
  } else
    xlo = xscale * utils::numeric(FLERR, arg[2], false, lmp);

  xhistyle = CONSTANT;
  if (strcmp(arg[3], "INF") == 0 || strcmp(arg[3], "EDGE") == 0) {
    if (domain->box_exist == 0)
      error->all(FLERR, "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 if (utils::strmatch(arg[3], "^v_")) {
    xhistr = utils::strdup(arg[3] + 2);
    xhi = 0.0;
    xhistyle = VARIABLE;
    varshape = 1;
  } else
    xhi = xscale * utils::numeric(FLERR, arg[3], false, lmp);

  ylostyle = CONSTANT;
  if (strcmp(arg[4], "INF") == 0 || strcmp(arg[4], "EDGE") == 0) {
    if (domain->box_exist == 0)
      error->all(FLERR, "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 if (utils::strmatch(arg[4], "^v_")) {
    ylostr = utils::strdup(arg[4] + 2);
    ylo = 0.0;
    ylostyle = VARIABLE;
    varshape = 1;
  } else
    ylo = yscale * utils::numeric(FLERR, arg[4], false, lmp);

  yhistyle = CONSTANT;
  if (strcmp(arg[5], "INF") == 0 || strcmp(arg[5], "EDGE") == 0) {
    if (domain->box_exist == 0)
      error->all(FLERR, "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 if (utils::strmatch(arg[5], "^v_")) {
    yhistr = utils::strdup(arg[5] + 2);
    yhi = 0.0;
    yhistyle = VARIABLE;
    varshape = 1;
  } else
    yhi = yscale * utils::numeric(FLERR, arg[5], false, lmp);

  zlostyle = CONSTANT;
  if (strcmp(arg[6], "INF") == 0 || strcmp(arg[6], "EDGE") == 0) {
    if (domain->box_exist == 0)
      error->all(FLERR, "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 if (utils::strmatch(arg[6], "^v_")) {
    zlostr = utils::strdup(arg[6] + 2);
    zlo = 0.0;
    zlostyle = VARIABLE;
    varshape = 1;
  } else
    zlo = zscale * utils::numeric(FLERR, arg[6], false, lmp);

  zhistyle = CONSTANT;
  if (strcmp(arg[7], "INF") == 0 || strcmp(arg[7], "EDGE") == 0) {
    if (domain->box_exist == 0)
      error->all(FLERR, "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 if (utils::strmatch(arg[7], "^v_")) {
    zhistr = utils::strdup(arg[7] + 2);
    zhi = 0.0;
    zhistyle = VARIABLE;
    varshape = 1;
  } else
    zhi = zscale * utils::numeric(FLERR, arg[7], false, lmp);

  if (utils::strmatch(arg[8], "^v_")) {
    xystr = utils::strdup(arg[8] + 2);
    xy = 0.0;
    xystyle = VARIABLE;
    varshape = 1;
  } else {
    xy = xscale * utils::numeric(FLERR, arg[8], false, lmp);
    xystyle = CONSTANT;
  }

  if (utils::strmatch(arg[9], "^v_")) {
    xzstr = utils::strdup(arg[9] + 2);
    xz = 0.0;
    xzstyle = VARIABLE;
    varshape = 1;
  } else {
    xz = xscale * utils::numeric(FLERR, arg[9], false, lmp);
    xzstyle = CONSTANT;
  }

  if (utils::strmatch(arg[10], "^v_")) {
    yzstr = utils::strdup(arg[10] + 2);
    yz = 0.0;
    yzstyle = VARIABLE;
    varshape = 1;
  } else {
    yz = yscale * utils::numeric(FLERR, arg[10], false, lmp);
    yzstyle = CONSTANT;
  }

  if (varshape) {
    variable_check();
    RegPrism::shape_update();
  }

  // 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) error->all(FLERR, "Illegal region prism xlo: {} >= xhi: {}", xlo, xhi);
  if (ylo >= yhi) error->all(FLERR, "Illegal region prism ylo: {} >= yhi: {}", ylo, yhi);
  if (zlo >= zhi) error->all(FLERR, "Illegal region prism zlo: {} >= zhi: {}", zlo, zhi);

  if (xy != 0.0 && xlo == -BIG && xhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xy tilt with infinite x size");
  if (xy != 0.0 && ylo == -BIG && yhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xy tilt with infinite y size");

  if (xz != 0.0 && xlo == -BIG && xhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xz tilt with infinite x size");
  if (xz != 0.0 && zlo == -BIG && zhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xz tilt with infinite z size");

  if (yz != 0.0 && ylo == -BIG && yhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero yz tilt with infinite y size");
  if (yz != 0.0 && zlo == -BIG && zhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero yz tilt with infinite z size");

  // 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 be close to all 6 planes
  // particle can only touch 3 planes

  cmax = 6;
  contact = new Contact[cmax];
  if (interior)
    tmax = 3;
  else
    tmax = 1;

  // 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

  MathExtra::cross3(a, b, face[0]);
  MathExtra::cross3(b, a, face[1]);
  MathExtra::cross3(c, a, face[2]);
  MathExtra::cross3(a, c, face[3]);
  MathExtra::cross3(b, c, face[4]);
  MathExtra::cross3(c, b, face[5]);

  // remap open face indices to be consistent

  if (openflag) {
    int temp[6];
    for (int i = 0; i < 6; i++) temp[i] = open_faces[i];
    open_faces[0] = temp[4];
    open_faces[1] = temp[5];
    open_faces[2] = temp[2];
    open_faces[3] = temp[3];
    open_faces[4] = temp[0];
    open_faces[5] = temp[1];
  }

  for (int i = 0; i < 6; i++) MathExtra::norm3(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[] xlostr;
  delete[] ylostr;
  delete[] zlostr;
  delete[] xhistr;
  delete[] yhistr;
  delete[] zhistr;
  delete[] xystr;
  delete[] xzstr;
  delete[] yzstr;
  delete[] contact;
}

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

void RegPrism::init()
{
  Region::init();
  if (varshape) variable_check();
}

/* ----------------------------------------------------------------------
   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 (i = 0; i < 6; i++) {
    if (open_faces[i]) continue;
    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];
      contact[n].radius = 0;
      contact[n].iwall = i;
      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);
  contact[0].radius = 0;
  contact[0].iwall = 0;
  if (contact[0].r < cutoff) return 1;
  return 0;
}

/* ----------------------------------------------------------------------
   change region shape via variable evaluation
------------------------------------------------------------------------- */

void RegPrism::shape_update()
{
  if (xlostyle == VARIABLE) xlo = xscale * input->variable->compute_equal(xlovar);

  if (xhistyle == VARIABLE) xhi = xscale * input->variable->compute_equal(xhivar);

  if (ylostyle == VARIABLE) ylo = yscale * input->variable->compute_equal(ylovar);

  if (yhistyle == VARIABLE) yhi = yscale * input->variable->compute_equal(yhivar);

  if (zlostyle == VARIABLE) zlo = zscale * input->variable->compute_equal(zlovar);

  if (zhistyle == VARIABLE) zhi = zscale * input->variable->compute_equal(zhivar);

  if (xystyle == VARIABLE) xy = xscale * input->variable->compute_equal(xyvar);

  if (xzstyle == VARIABLE) xz = xscale * input->variable->compute_equal(xzvar);

  if (yzstyle == VARIABLE) yz = yscale * input->variable->compute_equal(yzvar);

  // 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) error->all(FLERR, "Illegal region prism xlo: {} >= xhi: {}", xlo, xhi);
  if (ylo >= yhi) error->all(FLERR, "Illegal region prism ylo: {} >= yhi: {}", ylo, yhi);
  if (zlo >= zhi) error->all(FLERR, "Illegal region prism zlo: {} >= zhi: {}", zlo, zhi);

  if (xy != 0.0 && xlo == -BIG && xhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xy tilt with infinite x size");
  if (xy != 0.0 && ylo == -BIG && yhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xy tilt with infinite y size");

  if (xz != 0.0 && xlo == -BIG && xhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xz tilt with infinite x size");
  if (xz != 0.0 && zlo == -BIG && zhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero xz tilt with infinite z size");

  if (yz != 0.0 && ylo == -BIG && yhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero yz tilt with infinite y size");
  if (yz != 0.0 && zlo == -BIG && zhi == BIG)
    error->all(FLERR, "Illegal region prism non-zero yz tilt with infinite z size");

  // extent of prism

  if (interior) {
    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;
  }

  // h = transformation matrix from tilt coords (0-1) to box coords (xyz)

  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

  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

  MathExtra::cross3(a, b, face[0]);
  MathExtra::cross3(b, a, face[1]);
  MathExtra::cross3(c, a, face[2]);
  MathExtra::cross3(a, c, face[3]);
  MathExtra::cross3(b, c, face[4]);
  MathExtra::cross3(c, b, face[5]);

  for (int i = 0; i < 6; i++) MathExtra::norm3(face[i]);
}

/* ----------------------------------------------------------------------
   error check on existence of variable
------------------------------------------------------------------------- */

void RegPrism::variable_check()
{
  if (xlostyle == VARIABLE) {
    xlovar = input->variable->find(xlostr);
    if (xlovar < 0) error->all(FLERR, "Variable {} for region prism does not exist", xlostr);
    if (!input->variable->equalstyle(xlovar))
      error->all(FLERR, "Variable {} for region prism is invalid style", xlostr);
  }

  if (xhistyle == VARIABLE) {
    xhivar = input->variable->find(xhistr);
    if (xhivar < 0) error->all(FLERR, "Variable {} for region prism does not exist", xhistr);
    if (!input->variable->equalstyle(xhivar))
      error->all(FLERR, "Variable {} for region prism is invalid style", xhistr);
  }

  if (ylostyle == VARIABLE) {
    ylovar = input->variable->find(ylostr);
    if (ylovar < 0) error->all(FLERR, "Variable {} for region prism does not exist", ylostr);
    if (!input->variable->equalstyle(ylovar))
      error->all(FLERR, "Variable {} for region prism is invalid style", ylostr);
    }

  if (yhistyle == VARIABLE) {
    yhivar = input->variable->find(yhistr);
    if (yhivar < 0) error->all(FLERR, "Variable {} for region prism does not exist", yhistr);
    if (!input->variable->equalstyle(yhivar))
      error->all(FLERR, "Variable {} for region prism is invalid style", yhistr);
    }

   if (zlostyle == VARIABLE) {
     zlovar = input->variable->find(zlostr);
     if (zlovar < 0) error->all(FLERR, "Variable {} for region prism does not exist", zlostr);
     if (!input->variable->equalstyle(zlovar))
       error->all(FLERR, "Variable {} for region prism is invalid style", zlostr);
   }

   if (zhistyle == VARIABLE) {
     zhivar = input->variable->find(zhistr);
     if (zhivar < 0) error->all(FLERR, "Variable {} for region prism does not exist", zhistr);
     if (!input->variable->equalstyle(zhivar))
       error->all(FLERR, "Variable {} for region prism is invalid style", zhistr);
   }

   if (xystyle == VARIABLE) {
     xyvar = input->variable->find(xystr);
     if (xyvar < 0) error->all(FLERR, "Variable {} for region prism does not exist", xystr);
     if (!input->variable->equalstyle(xyvar))
       error->all(FLERR, "Variable {} for region prism is invalid style", xystr);
   }

   if (xzstyle == VARIABLE) {
     xzvar = input->variable->find(xzstr);
     if (xzvar < 0) error->all(FLERR, "Variable {} for region prism does not exist", xzstr);
     if (!input->variable->equalstyle(xzvar))
       error->all(FLERR, "Variable {} for region prism is invalid style", xzstr);
   }

   if (yzstyle == VARIABLE) {
     yzvar = input->variable->find(yzstr);
     if (yzvar < 0) error->all(FLERR, "Variable {} for region prism does not exist", yzstr);
     if (!input->variable->equalstyle(yzvar))
       error->all(FLERR, "Variable {} for region prism is invalid style", yzstr);
   }
}

/* ----------------------------------------------------------------------
   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;
    if (open_faces[iface]) continue;
    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];

  MathExtra::sub3(v2, v1, edge);
  MathExtra::sub3(x, v1, pvec);
  MathExtra::cross3(edge, pvec, xproduct);
  if (MathExtra::dot3(xproduct, norm) < 0.0) return 0;

  MathExtra::sub3(v3, v2, edge);
  MathExtra::sub3(x, v2, pvec);
  MathExtra::cross3(edge, pvec, xproduct);
  if (MathExtra::dot3(xproduct, norm) < 0.0) return 0;

  MathExtra::sub3(v1, v3, edge);
  MathExtra::sub3(x, v3, pvec);
  MathExtra::cross3(edge, pvec, xproduct);
  if (MathExtra::dot3(xproduct, norm) < 0.0) return 0;

  return 1;
}

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

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;
}