/* ----------------------------------------------------------------------
   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: Pim Schravendijk
------------------------------------------------------------------------- */

#include "region_cone.h"

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

#include <cmath>
#include <cstring>

using namespace LAMMPS_NS;

static constexpr double BIG = 1.0e20;

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

RegCone::RegCone(LAMMPS *lmp, int narg, char **arg) :
    Region(lmp, narg, arg), lo(0.0), hi(0.0), c1str(nullptr), c2str(nullptr), rlostr(nullptr),
    rhistr(nullptr), lostr(nullptr), histr(nullptr)
{
  options(narg - 9, &arg[9]);

  // check open face settings

  if (openflag)
    for (int i = 3; i < 6; i++)
      if (open_faces[i])
        error->all(FLERR, Error::NOPOINTER, "Illegal region cone open face: {}", i + 1);

  if (strcmp(arg[2], "x") != 0 && strcmp(arg[2], "y") != 0 && strcmp(arg[2], "z") != 0)
    error->all(FLERR, 2, "Illegal region cone axis: {}", arg[2]);
  axis = arg[2][0];

  if (axis == 'x') {
    if (utils::strmatch(arg[3], "^v_")) {
      c1str = utils::strdup(arg[3] + 2);
      c1 = 0.0;
      c1style = VARIABLE;
      varshape = 1;
    } else {
      c1 = yscale * utils::numeric(FLERR, arg[3], false, lmp);
      c1style = CONSTANT;
    }

    if (utils::strmatch(arg[4], "^v_")) {
      c2str = utils::strdup(arg[4] + 2);
      c2 = 0.0;
      c2style = VARIABLE;
      varshape = 1;
    } else {
      c2 = zscale * utils::numeric(FLERR, arg[4], false, lmp);
      c2style = CONSTANT;
    }

    if (utils::strmatch(arg[5], "^v_")) {
      rlostr = utils::strdup(arg[5] + 2);
      radiuslo = 0.0;
      rlostyle = VARIABLE;
      varshape = 1;
    } else {
      radiuslo = yscale * utils::numeric(FLERR, arg[5], false, lmp);
      rlostyle = CONSTANT;
    }

    if (utils::strmatch(arg[6], "^v_")) {
      rhistr = utils::strdup(arg[6] + 2);
      radiushi = 0.0;
      rhistyle = VARIABLE;
      varshape = 1;
    } else {
      radiushi = yscale * utils::numeric(FLERR, arg[6], false, lmp);
      rhistyle = CONSTANT;
    }

  } else if (axis == 'y') {

    if (utils::strmatch(arg[3], "^v_")) {
      c1str = utils::strdup(arg[3] + 2);
      c1 = 0.0;
      c1style = VARIABLE;
      varshape = 1;
    } else {
      c1 = xscale * utils::numeric(FLERR, arg[3], false, lmp);
      c1style = CONSTANT;
    }

    if (utils::strmatch(arg[4], "^v_")) {
      c2str = utils::strdup(arg[4] + 2);
      c2 = 0.0;
      c2style = VARIABLE;
      varshape = 1;
    } else {
      c2 = zscale * utils::numeric(FLERR, arg[4], false, lmp);
      c2style = CONSTANT;
    }

    if (utils::strmatch(arg[5], "^v_")) {
      rlostr = utils::strdup(arg[5] + 2);
      radiuslo = 0.0;
      rlostyle = VARIABLE;
      varshape = 1;
    } else {
      radiuslo = xscale * utils::numeric(FLERR, arg[5], false, lmp);
      rlostyle = CONSTANT;
    }

    if (utils::strmatch(arg[6], "^v_")) {
      rhistr = utils::strdup(arg[6] + 2);
      radiushi = 0.0;
      rhistyle = VARIABLE;
      varshape = 1;
    } else {
      radiushi = xscale * utils::numeric(FLERR, arg[6], false, lmp);
      rhistyle = CONSTANT;
    }

  } else if (axis == 'z') {

    if (utils::strmatch(arg[3], "^v_")) {
      c1str = utils::strdup(arg[3] + 2);
      c1 = 0.0;
      c1style = VARIABLE;
      varshape = 1;
    } else {
      c1 = xscale * utils::numeric(FLERR, arg[3], false, lmp);
      c1style = CONSTANT;
    }

    if (utils::strmatch(arg[4], "^v_")) {
      c2str = utils::strdup(arg[4] + 2);
      c2 = 0.0;
      c2style = VARIABLE;
      varshape = 1;
    } else {
      c2 = yscale * utils::numeric(FLERR, arg[4], false, lmp);
      c2style = CONSTANT;
    }

    if (utils::strmatch(arg[5], "^v_")) {
      rlostr = utils::strdup(arg[5] + 2);
      radiuslo = 0.0;
      rlostyle = VARIABLE;
      varshape = 1;
    } else {
      radiuslo = xscale * utils::numeric(FLERR, arg[5], false, lmp);
      rlostyle = CONSTANT;
    }

    if (utils::strmatch(arg[6], "^v_")) {
      rhistr = utils::strdup(arg[6] + 2);
      radiushi = 0.0;
      rhistyle = VARIABLE;
      varshape = 1;
    } else {
      radiushi = xscale * utils::numeric(FLERR, arg[6], false, lmp);
      rhistyle = CONSTANT;
    }
  }

  lostyle = 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 (axis == 'x') {
      if (strcmp(arg[7], "INF") == 0)
        lo = -BIG;
      else if (domain->triclinic == 0)
        lo = domain->boxlo[0];
      else
        lo = domain->boxlo_bound[0];
    }
    if (axis == 'y') {
      if (strcmp(arg[7], "INF") == 0)
        lo = -BIG;
      else if (domain->triclinic == 0)
        lo = domain->boxlo[1];
      else
        lo = domain->boxlo_bound[1];
    }
    if (axis == 'z') {
      if (strcmp(arg[7], "INF") == 0)
        lo = -BIG;
      else if (domain->triclinic == 0)
        lo = domain->boxlo[2];
      else
        lo = domain->boxlo_bound[2];
    }
  } else if (utils::strmatch(arg[7], "^v_")) {
    lostr = utils::strdup(arg[7] + 2);
    lo = 0.0;
    lostyle = VARIABLE;
    varshape = 1;
  } else {
    if (axis == 'x') lo = xscale * utils::numeric(FLERR, arg[7], false, lmp);
    if (axis == 'y') lo = yscale * utils::numeric(FLERR, arg[7], false, lmp);
    if (axis == 'z') lo = zscale * utils::numeric(FLERR, arg[7], false, lmp);
  }

  if (strcmp(arg[8], "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 (axis == 'x') {
      if (strcmp(arg[8], "INF") == 0)
        hi = BIG;
      else if (domain->triclinic == 0)
        hi = domain->boxhi[0];
      else
        hi = domain->boxhi_bound[0];
    }
    if (axis == 'y') {
      if (strcmp(arg[8], "INF") == 0) hi = BIG;
      if (domain->triclinic == 0)
        hi = domain->boxhi[1];
      else
        hi = domain->boxhi_bound[1];
    }
    if (axis == 'z') {
      if (strcmp(arg[8], "INF") == 0)
        hi = BIG;
      else if (domain->triclinic == 0)
        hi = domain->boxhi[2];
      else
        hi = domain->boxhi_bound[2];
    }
  } else if (utils::strmatch(arg[8], "^v_")) {
    histr = utils::strdup(arg[8] + 2);
    hi = 0.0;
    histyle = VARIABLE;
    varshape = 1;
  } else {
    if (axis == 'x') hi = xscale * utils::numeric(FLERR, arg[8], false, lmp);
    if (axis == 'y') hi = yscale * utils::numeric(FLERR, arg[8], false, lmp);
    if (axis == 'z') hi = zscale * utils::numeric(FLERR, arg[8], false, lmp);
  }

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

  // error check

  if (radiuslo < 0.0) error->all(FLERR, 5, "Illegal lower radius in region cone command");
  if (radiushi < 0.0) error->all(FLERR, 6, "Illegal upper radius in region cone command");
  if (radiuslo == 0.0 && radiushi == 0.0)
    error->all(FLERR, "Illegal radius in region cone command");
  if (hi <= lo) error->all(FLERR, "Illegal cone length in region cone command");

  // extent of cone
  maxradius = ((radiuslo > radiushi) ? radiuslo : radiushi);

  if (interior) {
    bboxflag = 1;
    if (axis == 'x') {
      extent_xlo = lo;
      extent_xhi = hi;
      extent_ylo = c1 - maxradius;
      extent_yhi = c1 + maxradius;
      extent_zlo = c2 - maxradius;
      extent_zhi = c2 + maxradius;
    }
    if (axis == 'y') {
      extent_xlo = c1 - maxradius;
      extent_xhi = c1 + maxradius;
      extent_ylo = lo;
      extent_yhi = hi;
      extent_zlo = c2 - maxradius;
      extent_zhi = c2 + maxradius;
    }
    if (axis == 'z') {
      extent_xlo = c1 - maxradius;
      extent_xhi = c1 + maxradius;
      extent_ylo = c2 - maxradius;
      extent_yhi = c2 + maxradius;
      extent_zlo = lo;
      extent_zhi = hi;
    }
  } else
    bboxflag = 0;

  // particle could be close to cone surface and 2 ends
  // particle can only touch surface and 1 end

  cmax = 3;
  contact = new Contact[cmax];
  tmax = (interior ? 2 : 1);
}

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

RegCone::~RegCone()
{
  delete[] c1str;
  delete[] c2str;
  delete[] rlostr;
  delete[] rhistr;
  delete[] lostr;
  delete[] histr;
  delete[] contact;
}

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

void RegCone::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
------------------------------------------------------------------------- */

int RegCone::inside(double x, double y, double z)
{
  double del1, del2, dist;
  double currentradius;

  if (axis == 'x') {
    del1 = y - c1;
    del2 = z - c2;
    dist = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x - lo) * (radiushi - radiuslo) / (hi - lo);
    if (dist <= currentradius && x >= lo && x <= hi)
      return 1;
    else
      return 0;
  } else if (axis == 'y') {
    del1 = x - c1;
    del2 = z - c2;
    dist = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (y - lo) * (radiushi - radiuslo) / (hi - lo);
    if (dist <= currentradius && y >= lo && y <= hi)
      return 1;
    else
      return 0;
  } else if (axis == 'z') {
    del1 = x - c1;
    del2 = y - c2;
    dist = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (z - lo) * (radiushi - radiuslo) / (hi - lo);
    if (dist <= currentradius && z >= lo && z <= hi)
      return 1;
    else
      return 0;
  }

  return 0;
}

/* ----------------------------------------------------------------------
   contact if 0 <= x < cutoff from one or more inner surfaces of cone
   can be one contact for each of 3 cone surfaces
   no contact if outside (possible if called from union/intersect)
   delxyz = vector from nearest point on cone to x
   special case: no contact with curved surf if x is on center axis
------------------------------------------------------------------------- */

int RegCone::surface_interior(double *x, double cutoff)
{
  double del1, del2, r, currentradius, delx, dely, delz, dist, delta;
  double surflo[3], surfhi[3], xs[3];

  int n = 0;

  if (axis == 'x') {
    del1 = x[1] - c1;
    del2 = x[2] - c2;
    r = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x[0] - lo) * (radiushi - radiuslo) / (hi - lo);

    // x is exterior to cone

    if (r > currentradius || x[0] < lo || x[0] > hi) return 0;

    // x is interior to cone or on its surface
    // surflo = pt on outer circle of bottom end plane, same dir as x vs axis
    // surfhi = pt on outer circle of top end plane, same dir as x vs axis

    if (r > 0.0 && !open_faces[2]) {
      surflo[0] = lo;
      surflo[1] = c1 + del1 * radiuslo / r;
      surflo[2] = c2 + del2 * radiuslo / r;
      surfhi[0] = hi;
      surfhi[1] = c1 + del1 * radiushi / r;
      surfhi[2] = c2 + del2 * radiushi / r;
      point_on_line_segment(surflo, surfhi, x, xs);
      delx = x[0] - xs[0];
      dely = x[1] - xs[1];
      delz = x[2] - xs[2];
      dist = sqrt(delx * delx + dely * dely + delz * delz);
      if (dist < cutoff) {
        contact[n].r = dist;
        contact[n].delx = delx;
        contact[n].dely = dely;
        contact[n].delz = delz;
        contact[n].radius = -2.0 * (radiuslo + (xs[0] - lo) * (radiushi - radiuslo) / (hi - lo));
        contact[n].iwall = 2;
        n++;
      }
    }

    delta = x[0] - lo;
    if (delta < cutoff && !open_faces[0]) {
      contact[n].r = delta;
      contact[n].delx = delta;
      contact[n].dely = contact[n].delz = 0.0;
      contact[n].radius = 0;
      contact[n].iwall = 0;
      n++;
    }
    delta = hi - x[0];
    if (delta < cutoff && !open_faces[1]) {
      contact[n].r = delta;
      contact[n].delx = -delta;
      contact[n].dely = contact[n].delz = 0.0;
      contact[n].radius = 0;
      contact[n].iwall = 1;
      n++;
    }

  } else if (axis == 'y') {
    del1 = x[0] - c1;
    del2 = x[2] - c2;
    r = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x[1] - lo) * (radiushi - radiuslo) / (hi - lo);

    // y is exterior to cone

    if (r > currentradius || x[1] < lo || x[1] > hi) return 0;

    // y is interior to cone or on its surface
    // surflo = pt on outer circle of bottom end plane, same dir as y vs axis
    // surfhi = pt on outer circle of top end plane, same dir as y vs axis

    if (r > 0.0 && !open_faces[2]) {
      surflo[0] = c1 + del1 * radiuslo / r;
      surflo[1] = lo;
      surflo[2] = c2 + del2 * radiuslo / r;
      surfhi[0] = c1 + del1 * radiushi / r;
      surfhi[1] = hi;
      surfhi[2] = c2 + del2 * radiushi / r;
      point_on_line_segment(surflo, surfhi, x, xs);
      delx = x[0] - xs[0];
      dely = x[1] - xs[1];
      delz = x[2] - xs[2];
      dist = sqrt(delx * delx + dely * dely + delz * delz);
      if (dist < cutoff) {
        contact[n].r = dist;
        contact[n].delx = delx;
        contact[n].dely = dely;
        contact[n].delz = delz;
        contact[n].iwall = 2;
        contact[n].radius = -2.0 * (radiuslo + (xs[1] - lo) * (radiushi - radiuslo) / (hi - lo));
        n++;
      }
    }

    delta = x[1] - lo;
    if (delta < cutoff && !open_faces[0]) {
      contact[n].r = delta;
      contact[n].delz = delta;
      contact[n].delx = contact[n].dely = 0.0;
      contact[n].iwall = 0;
      contact[n].radius = 0;
      n++;
    }
    delta = hi - x[1];
    if (delta < cutoff && !open_faces[1]) {
      contact[n].r = delta;
      contact[n].delz = -delta;
      contact[n].delx = contact[n].dely = 0.0;
      contact[n].iwall = 1;
      contact[n].radius = 0;
      n++;
    }

  } else {
    del1 = x[0] - c1;
    del2 = x[1] - c2;
    r = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x[2] - lo) * (radiushi - radiuslo) / (hi - lo);

    // z is exterior to cone

    if (r > currentradius || x[2] < lo || x[2] > hi) return 0;

    // z is interior to cone or on its surface
    // surflo = pt on outer circle of bottom end plane, same dir as z vs axis
    // surfhi = pt on outer circle of top end plane, same dir as z vs axis

    if (r > 0.0 && !open_faces[2]) {
      surflo[0] = c1 + del1 * radiuslo / r;
      surflo[1] = c2 + del2 * radiuslo / r;
      surflo[2] = lo;
      surfhi[0] = c1 + del1 * radiushi / r;
      surfhi[1] = c2 + del2 * radiushi / r;
      surfhi[2] = hi;
      point_on_line_segment(surflo, surfhi, x, xs);
      delx = x[0] - xs[0];
      dely = x[1] - xs[1];
      delz = x[2] - xs[2];
      dist = sqrt(delx * delx + dely * dely + delz * delz);
      if (dist < cutoff) {
        contact[n].r = dist;
        contact[n].delx = delx;
        contact[n].dely = dely;
        contact[n].delz = delz;
        contact[n].iwall = 2;
        contact[n].radius = -2.0 * (radiuslo + (xs[2] - lo) * (radiushi - radiuslo) / (hi - lo));
        n++;
      }
    }

    delta = x[2] - lo;
    if (delta < cutoff && !open_faces[0]) {
      contact[n].r = delta;
      contact[n].delz = delta;
      contact[n].delx = contact[n].dely = 0.0;
      contact[n].iwall = 0;
      contact[n].radius = 0;
      n++;
    }
    delta = hi - x[2];
    if (delta < cutoff && !open_faces[1]) {
      contact[n].r = delta;
      contact[n].delz = -delta;
      contact[n].delx = contact[n].dely = 0.0;
      contact[n].iwall = 1;
      contact[n].radius = 0;
      n++;
    }
  }

  return n;
}

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

int RegCone::surface_exterior(double *x, double cutoff)
{
  double del1, del2, r, currentradius, distsq, distsqprev, crad;
  double corner1[3], corner2[3], corner3[3], corner4[3], xp[3], nearest[3];

  if (axis == 'x') {
    del1 = x[1] - c1;
    del2 = x[2] - c2;
    r = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x[0] - lo) * (radiushi - radiuslo) / (hi - lo);

    // radius of curvature, only used for granular walls

    crad = 0.0;

    // x is far enough from cone that there is no contact
    // x is interior to cone

    if (r >= maxradius + cutoff || x[0] <= lo - cutoff || x[0] >= hi + cutoff) return 0;
    if (r < currentradius && x[0] > lo && x[0] < hi) return 0;

    // x is exterior to cone or on its surface
    // corner1234 = 4 corner pts of half trapezoid = cone surf in plane of x
    // project x to 3 line segments in half trapezoid (4th is axis of cone)
    // nearest = point on surface of cone that x is closest to
    //           could be edge of cone
    // do not add contact point if r >= cutoff

    corner1[0] = lo;
    corner1[1] = c1 + del1 * radiuslo / r;
    corner1[2] = c2 + del2 * radiuslo / r;
    corner2[0] = hi;
    corner2[1] = c1 + del1 * radiushi / r;
    corner2[2] = c2 + del2 * radiushi / r;
    corner3[0] = lo;
    corner3[1] = c1;
    corner3[2] = c2;
    corner4[0] = hi;
    corner4[1] = c1;
    corner4[2] = c2;

    distsq = BIG;

    if (!open_faces[2]) {
      point_on_line_segment(corner1, corner2, x, xp);
      distsq = closest(x, xp, nearest, distsq);
      crad = -2.0 * (radiuslo + (nearest[0] - lo) * (radiushi - radiuslo) / (hi - lo));
    }

    if (!open_faces[0]) {
      point_on_line_segment(corner1, corner3, x, xp);
      distsqprev = distsq;
      distsq = closest(x, xp, nearest, distsq);
      if (distsq < distsqprev) crad = 0.0;
    }

    if (!open_faces[1]) {
      point_on_line_segment(corner2, corner4, x, xp);
      distsqprev = distsq;
      distsq = closest(x, xp, nearest, distsq);
      if (distsq < distsqprev) crad = 0.0;
    }

    if (distsq == BIG) return 0;
    add_contact(0, x, nearest[0], nearest[1], nearest[2]);
    contact[0].radius = crad;
    contact[0].iwall = 0;
    if (contact[0].r < cutoff) return 1;
    return 0;

  } else if (axis == 'y') {
    del1 = x[0] - c1;
    del2 = x[2] - c2;
    r = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x[1] - lo) * (radiushi - radiuslo) / (hi - lo);

    // radius of curvature, only used for granular walls

    crad = 0.0;

    // y is far enough from cone that there is no contact
    // y is interior to cone

    if (r >= maxradius + cutoff || x[1] <= lo - cutoff || x[1] >= hi + cutoff) return 0;
    if (r < currentradius && x[1] > lo && x[1] < hi) return 0;

    // y is exterior to cone or on its surface
    // corner1234 = 4 corner pts of half trapezoid = cone surf in plane of y
    // project x to 3 line segments in half trapezoid (4th is axis of cone)
    // nearest = point on surface of cone that y is closest to
    //           could be edge of cone
    // do not add contact point if r >= cutoff

    corner1[0] = c1 + del1 * radiuslo / r;
    corner1[1] = lo;
    corner1[2] = c2 + del2 * radiuslo / r;
    corner2[0] = c1 + del1 * radiushi / r;
    corner2[1] = hi;
    corner2[2] = c2 + del2 * radiushi / r;
    corner3[0] = c1;
    corner3[1] = lo;
    corner3[2] = c2;
    corner4[0] = c1;
    corner4[1] = hi;
    corner4[2] = c2;

    distsq = BIG;

    if (!open_faces[2]) {
      point_on_line_segment(corner1, corner2, x, xp);
      distsq = closest(x, xp, nearest, distsq);
      crad = -2.0 * (radiuslo + (nearest[1] - lo) * (radiushi - radiuslo) / (hi - lo));
    }

    if (!open_faces[0]) {
      point_on_line_segment(corner1, corner3, x, xp);
      distsqprev = distsq;
      distsq = closest(x, xp, nearest, distsq);
      if (distsq < distsqprev) crad = 0;
    }

    if (!open_faces[1]) {
      point_on_line_segment(corner2, corner4, x, xp);
      distsqprev = distsq;
      distsq = closest(x, xp, nearest, distsq);
      if (distsq < distsqprev) crad = 0;
    }

    add_contact(0, x, nearest[0], nearest[1], nearest[2]);
    contact[0].radius = crad;
    contact[0].iwall = 0;
    if (contact[0].r < cutoff) return 1;
    return 0;

  } else {
    del1 = x[0] - c1;
    del2 = x[1] - c2;
    r = sqrt(del1 * del1 + del2 * del2);
    currentradius = radiuslo + (x[2] - lo) * (radiushi - radiuslo) / (hi - lo);

    // radius of curvature, only used for granular walls

    crad = 0.0;

    // z is far enough from cone that there is no contact
    // z is interior to cone

    if (r >= maxradius + cutoff || x[2] <= lo - cutoff || x[2] >= hi + cutoff) return 0;
    if (r < currentradius && x[2] > lo && x[2] < hi) return 0;

    // z is exterior to cone or on its surface
    // corner1234 = 4 corner pts of half trapezoid = cone surf in plane of z
    // project x to 3 line segments in half trapezoid (4th is axis of cone)
    // nearest = point on surface of cone that z is closest to
    //           could be edge of cone
    // do not add contact point if r >= cutoff

    corner1[0] = c1 + del1 * radiuslo / r;
    corner1[1] = c2 + del2 * radiuslo / r;
    corner1[2] = lo;
    corner2[0] = c1 + del1 * radiushi / r;
    corner2[1] = c2 + del2 * radiushi / r;
    corner2[2] = hi;
    corner3[0] = c1;
    corner3[1] = c2;
    corner3[2] = lo;
    corner4[0] = c1;
    corner4[1] = c2;
    corner4[2] = hi;

    distsq = BIG;

    if (!open_faces[2]) {
      point_on_line_segment(corner1, corner2, x, xp);
      distsq = closest(x, xp, nearest, distsq);
      crad = -2.0 * (radiuslo + (nearest[2] - lo) * (radiushi - radiuslo) / (hi - lo));
    }

    if (!open_faces[0]) {
      point_on_line_segment(corner1, corner3, x, xp);
      distsqprev = distsq;
      distsq = closest(x, xp, nearest, distsq);
      if (distsq < distsqprev) crad = 0;
    }

    if (!open_faces[1]) {
      point_on_line_segment(corner2, corner4, x, xp);
      distsqprev = distsq;
      distsq = closest(x, xp, nearest, distsq);
      if (distsq < distsqprev) crad = 0;
    }

    add_contact(0, x, nearest[0], nearest[1], nearest[2]);
    contact[0].radius = crad;
    contact[0].iwall = 0;
    if (contact[0].r < cutoff) return 1;
    return 0;
  }
}

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

void RegCone::shape_update()
{
  if (c1style == VARIABLE) c1 = input->variable->compute_equal(c1var);
  if (c2style == VARIABLE) c2 = input->variable->compute_equal(c2var);
  if (rlostyle == VARIABLE) {
    radiuslo = input->variable->compute_equal(rlovar);
    if (radiuslo < 0.0) error->one(FLERR, "Variable evaluation in region gave bad value");
  }
  if (rhistyle == VARIABLE) {
    radiushi = input->variable->compute_equal(rhivar);
    if (radiushi < 0.0) error->one(FLERR, "Variable evaluation in region gave bad value");
  }
  if (lostyle == VARIABLE) lo = input->variable->compute_equal(lovar);
  if (histyle == VARIABLE) hi = input->variable->compute_equal(hivar);

  if (radiuslo == 0.0 && radiushi == 0.0) error->all(FLERR, "dtion in region gave bad value");

  if (axis == 'x') {
    if (c1style == VARIABLE) c1 *= yscale;
    if (c2style == VARIABLE) c2 *= zscale;
    if (rlostyle == VARIABLE) radiuslo *= yscale;
    if (rhistyle == VARIABLE) radiushi *= yscale;
    if (lostyle == VARIABLE) lo *= xscale;
    if (histyle == VARIABLE) hi *= xscale;
  } else if (axis == 'y') {
    if (c1style == VARIABLE) c1 *= xscale;
    if (c2style == VARIABLE) c2 *= zscale;
    if (rlostyle == VARIABLE) radiuslo *= xscale;
    if (rhistyle == VARIABLE) radiushi *= xscale;
    if (lostyle == VARIABLE) lo *= yscale;
    if (histyle == VARIABLE) hi *= yscale;
  } else {
    if (c1style == VARIABLE) c1 *= xscale;
    if (c2style == VARIABLE) c2 *= yscale;
    if (rlostyle == VARIABLE) radiuslo *= xscale;
    if (rhistyle == VARIABLE) radiushi *= xscale;
    if (lostyle == VARIABLE) lo *= zscale;
    if (histyle == VARIABLE) hi *= zscale;
  }
}

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

void RegCone::variable_check()
{
  if (c1style == VARIABLE) {
    c1var = input->variable->find(c1str);
    if (c1var < 0) error->all(FLERR, "Variable {} for region cone does not exist", c1str);
    if (!input->variable->equalstyle(c1var))
      error->all(FLERR, "Variable {} for region cone is invalid style", c1str);
  }

  if (c2style == VARIABLE) {
    c2var = input->variable->find(c2str);
    if (c2var < 0) error->all(FLERR, "Variable {} for region cone does not exist", c2str);
    if (!input->variable->equalstyle(c2var))
      error->all(FLERR, "Variable {} for region cone is invalid style", c2str);
  }

  if (rlostyle == VARIABLE) {
    rlovar = input->variable->find(rlostr);
    if (rlovar < 0) error->all(FLERR, "Variable {} for region cone does not exist", rlostr);
    if (!input->variable->equalstyle(rlovar))
      error->all(FLERR, "Variable {} for region cone is invalid style", rlostr);
  }

  if (rhistyle == VARIABLE) {
    rhivar = input->variable->find(rhistr);
    if (rhivar < 0) error->all(FLERR, "Variable {} for region cone does not exist", rhistr);
    if (!input->variable->equalstyle(rhivar))
      error->all(FLERR, "Variable {} for region cone is invalid style", rhistr);
  }

  if (lostyle == VARIABLE) {
    lovar = input->variable->find(lostr);
    if (lovar < 0) error->all(FLERR, "Variable {} for region cone does not exist", lostr);
    if (!input->variable->equalstyle(lovar))
      error->all(FLERR, "Variable {} for region cone is invalid style", lostr);
  }

  if (histyle == VARIABLE) {
    hivar = input->variable->find(histr);
    if (hivar < 0) error->all(FLERR, "Variable {} for region cone does not exist", histr);
    if (!input->variable->equalstyle(hivar))
      error->all(FLERR, "Variable {} for region cone is invalid style", histr);
  }
}

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

double RegCone::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;
}