nsc.c

/*
 *
 *  program NSC
 *  version 1.0  (April 1994)
 *
 *  Author: Frank Eisenhaber
 *
 *  For user notes see file nsc.h !!
 *
 *  Copyright Notice:
 *  All rights reserved, whether the whole or part of the program is
 *  concerned. The software may not be used without specific, prior 
 *  written permission of the author. 
 *
 *  An academic licence agreement for the package ASC/GM or its parts
 *  is granted if you make the following commitments:
 *  1) In using this software, the user will respect the interests of 
 *     the author.
 *  2) The use of the software in commercial activities is not allowed 
 *     without a prior written commercial licence agreement. The program
 *     will not be used in classified research.
 *  3) Other interested research groups will be redirected
 *     to the author. The user will not redistribute the code outside
 *     his immediate research group.
 *  4) The copyright messages will not be modified or suppressed.
 *  5) The reference given below will be cited in any publication
 *     of scientific results based in part or completely on use of the
 *     program.
 *  6) Bugs will be reported to the author.
 *
 *  Permission to use, copy, and modify this software and
 *  its documentation is hereby granted without fee for 
 *  academic use, provided
 *  that the above copyright notices and this permission notice appear in
 *  all copies of the software and related documentation.
 *
 *  THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF
 *  ANY KIND,
 *  EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
 *  WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
 *
 *  IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 *  ANY SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND,
 *  OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
 *  WHETHER OR NOT ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF
 *  LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
 *  OF THIS SOFTWARE.
 *
 * 
 *  contact address :    European Molecular Biology Laboratory
 *                       Biocomputing Unit
 *                       Meyerhofstr. 1
 *                       Postfach 10.2209
 *                       D-69012 Heidelberg
 *                       Federal Republic of Germany
 *
 *
 *
 *  E-mail : IN%"EISENHABER@EMBL-Heidelberg.DE"
 *  Please send your contact address to get information on updates and
 *  new features. Questions will be answered as soon as possible.
 *
 *
 *  references :
 *  1.F.Eisenhaber, P.Lijnzaad, P.Argos, M.Scharf
 *    "The Double Cubic Lattice Method: Efficient Approaches to
 *    Numerical Integration of Surface Area and Volume and to Dot
 *    Surface Contouring of Molecular Assemblies"
 *    Journal of Computational Chemistry (1994) submitted
 *  2.F.Eisenhaber, P.Argos
 *    "Improved Strategy in Analytic Surface Calculation for Molecular
 *    Systems: Handling of Singularities and Computational Efficiency"
 *    Journal of Computational Chemistry (1993) v.14, N11, pp-1272-1280
 *
 */

#include "stride.h"

#define TEST_NSC 0

#define TEST_ARC 0
#define TEST_DOD 0
#define TEST_CUBE 0

#define UNSP_ICO_DOD      9
#define UNSP_ICO_ARC     10

#define PI               3.14159265358979323846
#define HALFPI           1.57079632679489661923

typedef double * point_double;
typedef int    * point_int;
point_double xpunsp=NULL;
double       del_cube;
point_int    ico_wk=NULL, ico_pt=NULL;
int          n_dot, ico_cube, last_n_dot=0, last_densit=0, last_unsp=0;
int          last_cubus=0;

#define FOURPI (4.*PI)
#define TORAD(A)     ((A)*0.017453293)
#define DP_TOL     0.001
#define MAXIMUM(A, B)  (((A) > (B) ? (A) : (B)))
#define MINIMUM(A, B)  (((A) < (B) ? (A) : (B)))

#define UPDATE_FL  __file__=__FILE__,__line__=__LINE__
char * __file__;         /* declared versions of macros */
int  __line__;           /* __FILE__  and __LINE__ */

#define ERROR UPDATE_FL,error
void error(const char *fmt, ...) {
  va_list args;
  fprintf(stderr,
    "\n---> ERROR when executing line %i in file %s !\n",
    __line__,__file__);
  va_start(args,fmt);
  vfprintf(stderr, fmt, args);
  va_end(args);
  fprintf(stderr, "\n---> Execution stopped !\n\n");
  }

#define WARNING UPDATE_FL,warning
void warning(const char *fmt, ...) {
  va_list args;
  fprintf(stderr,
    "\n---> WARNING : line %i in file %s\n",
    __line__,__file__);
  va_start(args,fmt);
  vfprintf(stderr, fmt, args);
  va_end(args);
  fprintf(stderr, " ...!\n\n");
  fflush(stderr);
  fflush(stdout);
  }

#define ASIN safe_asin
double safe_asin(double f) {
  if ( (fabs(f) < 1.00) ) return( asin(f) );
  if ( (fabs(f) - 1.00)  < DP_TOL ) return(HALFPI);
  else ERROR("ASIN : invalid argument %f", f);
  return(0.0);
  }

#define CALLOC(n, size) mycalloc(__FILE__,__LINE__, n, size)
void * mycalloc(const char * filename, const int linenr,
                size_t nelem, size_t elsize) {
  int * ip;
  ip = (int *) calloc(nelem, elsize);
  if(ip) return(ip);
  else ERROR("CALLOC : failed in file %s at line %d", filename, linenr);
  return(void *)ip;
  }

#define REALLOC(ptr, size) myrealloc(__FILE__,__LINE__,  ptr, size)
void * myrealloc(const char * filename, const int linenr,
                 void * ptr, size_t size) {
  int * ip;
  ip = (int *) realloc(ptr, size);
  if(ip) return(ip);
  else ERROR("REALLOC : failed in file %s at line %d", filename, linenr);
  return(void*)ip;
  }


/* routines for dot distributions on the surface of the unit sphere */
double rg, rh;

void icosaeder_vertices(double *xus) {
  rh = sqrt(1.-2.*cos(TORAD(72.)))/(1.-cos(TORAD(72.)));
  rg = cos(TORAD(72.))/(1.-cos(TORAD(72.)));
/* icosaeder vertices */
  xus[ 0] = 0.;                  xus[ 1] = 0.;                  xus[ 2] = 1.;
  xus[ 3] = rh*cos(TORAD(72.));  xus[ 4] = rh*sin(TORAD(72.));  xus[ 5] = rg;
  xus[ 6] = rh*cos(TORAD(144.)); xus[ 7] = rh*sin(TORAD(144.)); xus[ 8] = rg;
  xus[ 9] = rh*cos(TORAD(216.)); xus[10] = rh*sin(TORAD(216.)); xus[11] = rg;
  xus[12] = rh*cos(TORAD(288.)); xus[13] = rh*sin(TORAD(288.)); xus[14] = rg;
  xus[15] = rh;                  xus[16] = 0;                   xus[17] = rg;
  xus[18] = rh*cos(TORAD(36.));  xus[19] = rh*sin(TORAD(36.));  xus[20] = -rg;
  xus[21] = rh*cos(TORAD(108.)); xus[22] = rh*sin(TORAD(108.)); xus[23] = -rg;
  xus[24] = -rh;                 xus[25] = 0;                   xus[26] = -rg;
  xus[27] = rh*cos(TORAD(252.)); xus[28] = rh*sin(TORAD(252.)); xus[29] = -rg;
  xus[30] = rh*cos(TORAD(324.)); xus[31] = rh*sin(TORAD(324.)); xus[32] = -rg;
  xus[33] = 0.;                  xus[34] = 0.;                  xus[35] = -1.;
  }


void divarc(double x1, double y1, double z1,
            double x2, double y2, double z2,
            int div1, int div2, double *xr, double *yr, double *zr) {

  double xd, yd, zd, dd, d1, d2, s, x, y, z;
  double phi, sphi, cphi;

  xd = y1*z2-y2*z1;
  yd = z1*x2-z2*x1;
  zd = x1*y2-x2*y1;
  dd = sqrt(xd*xd+yd*yd+zd*zd);
  if (dd < DP_TOL) ERROR("divarc: rotation axis of length %f", dd);

  d1 = x1*x1+y1*y1+z1*z1;
  if (d1 < 0.5) ERROR("divarc: vector 1 of sq.length %f", d1);
  d2 = x2*x2+y2*y2+z2*z2;
  if (d2 < 0.5) ERROR("divarc: vector 2 of sq.length %f", d2);

  phi = ASIN(dd/sqrt(d1*d2));
  phi = phi*((double)div1)/((double)div2);
  sphi = sin(phi); cphi = cos(phi);
  s  = (x1*xd+y1*yd+z1*zd)/dd;

  x = xd*s*(1.-cphi)/dd + x1 * cphi + (yd*z1-y1*zd)*sphi/dd;
  y = yd*s*(1.-cphi)/dd + y1 * cphi + (zd*x1-z1*xd)*sphi/dd;
  z = zd*s*(1.-cphi)/dd + z1 * cphi + (xd*y1-x1*yd)*sphi/dd;
  dd = sqrt(x*x+y*y+z*z);
  *xr = x/dd; *yr = y/dd; *zr = z/dd;
  }

int ico_dot_arc(int densit) { /* densit...required dots per unit sphere */
/* dot distribution on a unit sphere based on an icosaeder *
 * great circle average refining of icosahedral face       */

  int i, j, k, tl, tl2, tn, tess;
  double a, d, x, y, z, x2, y2, z2, x3, y3, z3;
  double xij, yij, zij, xji, yji, zji, xik, yik, zik, xki, yki, zki,
    xjk, yjk, zjk, xkj, ykj, zkj;
  point_double xus=NULL;

/* calculate tessalation level */
  a = sqrt((((double) densit)-2.)/10.);
  tess = (int) ceil(a);
  n_dot = 10*tess*tess+2;
  if (n_dot < densit) {
    ERROR("ico_dot_arc: error in formula for tessalation level (%d->%d, %d)",
      tess, n_dot, densit);
    }

  xus = (double *) CALLOC(3*n_dot, sizeof(double));
  xpunsp = xus;
  icosaeder_vertices(xus);

  if (tess > 1) {
    tn = 12;
    a = rh*rh*2.*(1.-cos(TORAD(72.)));
/* calculate tessalation of icosaeder edges */
    for (i=0; i<11; i++) {
      for (j=i+1; j<12; j++) {
        x = xus[3*i]-xus[3*j];
        y = xus[1+3*i]-xus[1+3*j]; z = xus[2+3*i]-xus[2+3*j];
        d = x*x+y*y+z*z;
        if (fabs(a-d) > DP_TOL) continue;
        for (tl=1; tl<tess; tl++) {
          if (tn >= n_dot) { ERROR("ico_dot: tn exceeds dimension of xus"); }
          divarc(xus[3*i], xus[1+3*i], xus[2+3*i],
                 xus[3*j], xus[1+3*j], xus[2+3*j],
            tl, tess, &xus[3*tn], &xus[1+3*tn], &xus[2+3*tn]);
          tn++;
          }
        }
      }
/* calculate tessalation of icosaeder faces */
    for (i=0; i<10; i++) {
      for (j=i+1; j<11; j++) {
        x = xus[3*i]-xus[3*j];
        y = xus[1+3*i]-xus[1+3*j]; z = xus[2+3*i]-xus[2+3*j];
        d = x*x+y*y+z*z;
        if (fabs(a-d) > DP_TOL) continue;

        for (k=j+1; k<12; k++) {
          x = xus[3*i]-xus[3*k];
          y = xus[1+3*i]-xus[1+3*k]; z = xus[2+3*i]-xus[2+3*k];
          d = x*x+y*y+z*z;
          if (fabs(a-d) > DP_TOL) continue;
          x = xus[3*j]-xus[3*k];
          y = xus[1+3*j]-xus[1+3*k]; z = xus[2+3*j]-xus[2+3*k];
          d = x*x+y*y+z*z;
          if (fabs(a-d) > DP_TOL) continue;
          for (tl=1; tl<tess-1; tl++) {
            divarc(xus[3*j], xus[1+3*j], xus[2+3*j],
                   xus[3*i], xus[1+3*i], xus[2+3*i],
              tl, tess, &xji, &yji, &zji);
            divarc(xus[3*k], xus[1+3*k], xus[2+3*k],
                   xus[3*i], xus[1+3*i], xus[2+3*i],
              tl, tess, &xki, &yki, &zki);

            for (tl2=1; tl2<tess-tl; tl2++) {
              divarc(xus[3*i], xus[1+3*i], xus[2+3*i],
                     xus[3*j], xus[1+3*j], xus[2+3*j],
                tl2, tess, &xij, &yij, &zij);
              divarc(xus[3*k], xus[1+3*k], xus[2+3*k],
                     xus[3*j], xus[1+3*j], xus[2+3*j],
                tl2, tess, &xkj, &ykj, &zkj);
              divarc(xus[3*i], xus[1+3*i], xus[2+3*i],
                     xus[3*k], xus[1+3*k], xus[2+3*k],
                tess-tl-tl2, tess, &xik, &yik, &zik);
              divarc(xus[3*j], xus[1+3*j], xus[2+3*j],
                     xus[3*k], xus[1+3*k], xus[2+3*k],
                tess-tl-tl2, tess, &xjk, &yjk, &zjk);
              if (tn >= n_dot) ERROR("ico_dot: tn exceeds dimension of xus");
              divarc(xki, yki, zki, xji, yji, zji, tl2, tess-tl,
                &x, &y, &z);
              divarc(xkj, ykj, zkj, xij, yij, zij, tl, tess-tl2,
                &x2, &y2, &z2);
              divarc(xjk, yjk, zjk, xik, yik, zik, tl, tl+tl2,
                &x3, &y3, &z3);
              x = x+x2+x3; y = y+y2+y3; z = z+z2+z3;
              d = sqrt(x*x+y*y+z*z);
              xus[3*tn] = x/d;
              xus[1+3*tn] = y/d;
              xus[2+3*tn] = z/d;
              tn++;
              }		/* cycle tl2 */
            }		/* cycle tl */
          }		/* cycle k */
        }		/* cycle j */
      }			/* cycle i */
    if (n_dot != tn) {
      ERROR("ico_dot: n_dot(%d) and tn(%d) differ", n_dot, tn);
      }
    }		/* end of if (tess > 1) */
  return n_dot;
  }		/* end of routine ico_dot_arc */

int ico_dot_dod(int densit) { /* densit...required dots per unit sphere */
/* dot distribution on a unit sphere based on an icosaeder *
 * great circle average refining of icosahedral face       */

  int i, j, k, tl, tl2, tn, tess, j1, j2;
  double a, d, x, y, z, x2, y2, z2, x3, y3, z3, ai_d, adod;
  double xij, yij, zij, xji, yji, zji, xik, yik, zik, xki, yki, zki,
    xjk, yjk, zjk, xkj, ykj, zkj;
  point_double xus=NULL;
/* calculate tesselation level */
  a = sqrt((((double) densit)-2.)/30.);
  tess = MAXIMUM((int) ceil(a), 1);
  n_dot = 30*tess*tess+2;
  if (n_dot < densit) {
    ERROR("ico_dot_dod: error in formula for tessalation level (%d->%d, %d)",
      tess, n_dot, densit);
    }

  xus = (double *) CALLOC(3*n_dot, sizeof(double));
  xpunsp = xus;
  icosaeder_vertices(xus);

  tn=12;
/* square of the edge of an icosaeder */
    a = rh*rh*2.*(1.-cos(TORAD(72.)));
/* dodecaeder vertices */
  for (i=0; i<10; i++) {
    for (j=i+1; j<11; j++) {
      x = xus[3*i]-xus[3*j];
      y = xus[1+3*i]-xus[1+3*j]; z = xus[2+3*i]-xus[2+3*j];
      d = x*x+y*y+z*z;
      if (fabs(a-d) > DP_TOL) continue;
      for (k=j+1; k<12; k++) {
        x = xus[3*i]-xus[3*k];
        y = xus[1+3*i]-xus[1+3*k]; z = xus[2+3*i]-xus[2+3*k];
        d = x*x+y*y+z*z;
        if (fabs(a-d) > DP_TOL) continue;
        x = xus[3*j]-xus[3*k];
        y = xus[1+3*j]-xus[1+3*k]; z = xus[2+3*j]-xus[2+3*k];
        d = x*x+y*y+z*z;
        if (fabs(a-d) > DP_TOL) continue;
        x = xus[  3*i]+xus[  3*j]+xus[  3*k];
        y = xus[1+3*i]+xus[1+3*j]+xus[1+3*k];
        z = xus[2+3*i]+xus[2+3*j]+xus[2+3*k];
        d = sqrt(x*x+y*y+z*z);
        xus[3*tn]=x/d; xus[1+3*tn]=y/d; xus[2+3*tn]=z/d;
        tn++;
        }
      }
    }

  if (tess > 1) {
    tn = 32;
/* square of the edge of an dodecaeder */
    adod = 4.*(cos(TORAD(108.))-cos(TORAD(120.)))/(1.-cos(TORAD(120.)));
/* square of the distance of two adjacent vertices of ico- and dodecaeder */
    ai_d = 2.*(1.-sqrt(1.-a/3.));

/* calculate tessalation of mixed edges */
    for (i=0; i<31; i++) {
      j1 = 12; j2 = 32; a = ai_d;
      if (i>=12) { j1=i+1; a = adod; }
      for (j=j1; j<j2; j++) {
        x = xus[3*i]-xus[3*j];
        y = xus[1+3*i]-xus[1+3*j]; z = xus[2+3*i]-xus[2+3*j];
        d = x*x+y*y+z*z;
        if (fabs(a-d) > DP_TOL) continue;
        for (tl=1; tl<tess; tl++) {
          if (tn >= n_dot) {
            ERROR("ico_dot: tn exceeds dimension of xus");
            }
          divarc(xus[3*i], xus[1+3*i], xus[2+3*i],
                 xus[3*j], xus[1+3*j], xus[2+3*j],
            tl, tess, &xus[3*tn], &xus[1+3*tn], &xus[2+3*tn]);
          tn++;
          }
        }
      }
/* calculate tessalation of pentakisdodecahedron faces */
    for (i=0; i<12; i++) {
      for (j=12; j<31; j++) {
        x = xus[3*i]-xus[3*j];
        y = xus[1+3*i]-xus[1+3*j]; z = xus[2+3*i]-xus[2+3*j];
        d = x*x+y*y+z*z;
        if (fabs(ai_d-d) > DP_TOL) continue;

        for (k=j+1; k<32; k++) {
          x = xus[3*i]-xus[3*k];
          y = xus[1+3*i]-xus[1+3*k]; z = xus[2+3*i]-xus[2+3*k];
          d = x*x+y*y+z*z;
          if (fabs(ai_d-d) > DP_TOL) continue;
          x = xus[3*j]-xus[3*k];
          y = xus[1+3*j]-xus[1+3*k]; z = xus[2+3*j]-xus[2+3*k];
          d = x*x+y*y+z*z;
          if (fabs(adod-d) > DP_TOL) continue;
          for (tl=1; tl<tess-1; tl++) {
            divarc(xus[3*j], xus[1+3*j], xus[2+3*j],
                   xus[3*i], xus[1+3*i], xus[2+3*i],
              tl, tess, &xji, &yji, &zji);
            divarc(xus[3*k], xus[1+3*k], xus[2+3*k],
                   xus[3*i], xus[1+3*i], xus[2+3*i],
              tl, tess, &xki, &yki, &zki);

            for (tl2=1; tl2<tess-tl; tl2++) {
              divarc(xus[3*i], xus[1+3*i], xus[2+3*i],
                     xus[3*j], xus[1+3*j], xus[2+3*j],
                tl2, tess, &xij, &yij, &zij);
              divarc(xus[3*k], xus[1+3*k], xus[2+3*k],
                     xus[3*j], xus[1+3*j], xus[2+3*j],
                tl2, tess, &xkj, &ykj, &zkj);
              divarc(xus[3*i], xus[1+3*i], xus[2+3*i],
                     xus[3*k], xus[1+3*k], xus[2+3*k],
                tess-tl-tl2, tess, &xik, &yik, &zik);
              divarc(xus[3*j], xus[1+3*j], xus[2+3*j],
                     xus[3*k], xus[1+3*k], xus[2+3*k],
                tess-tl-tl2, tess, &xjk, &yjk, &zjk);
              if (tn >= n_dot) {
                ERROR("ico_dot: tn exceeds dimension of xus");
                }
              divarc(xki, yki, zki, xji, yji, zji, tl2, tess-tl,
                &x, &y, &z);
              divarc(xkj, ykj, zkj, xij, yij, zij, tl, tess-tl2,
                &x2, &y2, &z2);
              divarc(xjk, yjk, zjk, xik, yik, zik, tl, tl+tl2,
                &x3, &y3, &z3);
              x = x+x2+x3; y = y+y2+y3; z = z+z2+z3;
              d = sqrt(x*x+y*y+z*z);
              xus[3*tn] = x/d;
              xus[1+3*tn] = y/d;
              xus[2+3*tn] = z/d;
              tn++;
              }		/* cycle tl2 */
            }		/* cycle tl */
          }		/* cycle k */
        }		/* cycle j */
      }			/* cycle i */
    if (n_dot != tn) {
      ERROR("ico_dot: n_dot(%d) and tn(%d) differ", n_dot, tn);
      }
    }		/* end of if (tess > 1) */
  return n_dot;
  }		/* end of routine ico_dot_dod */

int unsp_type(int densit) {
  int i1, i2;
  i1 = 1;
  while (10*i1*i1+2 < densit) i1++;
  i2 = 1;
  while (30*i2*i2+2 < densit) i2++;
  if (10*i1*i1-2 < 30*i2*i2-2) return UNSP_ICO_ARC;
  else return UNSP_ICO_DOD;
  }

int make_unsp(int densit, int mode, int * num_dot, int cubus) {
  int ndot, ico_cube_cb, i, j, k, l, ijk, tn, tl, tl2;
  point_double xus;
  point_int    work;
  double x, y, z;

  if (xpunsp) free(xpunsp); if (ico_wk) free(ico_wk);

  k=1; if (mode < 0) { k=0; mode = -mode; }
  if (mode == UNSP_ICO_ARC)      { ndot = ico_dot_arc(densit); }
  else if (mode == UNSP_ICO_DOD)      { ndot = ico_dot_dod(densit); }
  else {
    WARNING("make_unsp: mode %c%d not allowed", (k) ? '+':'-',mode);
    return 1;
    }

  last_n_dot = ndot; last_densit = densit; last_unsp = mode;
  *num_dot=ndot; if (k) return 0;

/* in the following the dots of the unit sphere may be resorted */
  last_unsp = -last_unsp;

/* determine distribution of points in elementary cubes */
  if (cubus) {
    ico_cube = cubus;
    }
  else {
    last_cubus = 0;
    i=1;
    while (i*i*i*2 < ndot) i++;
    ico_cube = MAXIMUM(i-1, 0);
    }
  ico_cube_cb = ico_cube*ico_cube*ico_cube;
  del_cube=2./((double)ico_cube);
  work = (int *) CALLOC(ndot, sizeof(int));
  xus = xpunsp;
  for (l=0; l<ndot; l++) {
    i = MAXIMUM((int) floor((1.+xus[3*l])/del_cube), 0);
    if (i>=ico_cube) i = ico_cube-1;
    j = MAXIMUM((int) floor((1.+xus[1+3*l])/del_cube), 0);
    if (j>=ico_cube) j = ico_cube-1;
    k = MAXIMUM((int) floor((1.+xus[2+3*l])/del_cube), 0);
    if (k>=ico_cube) k = ico_cube-1;
    ijk = i+j*ico_cube+k*ico_cube*ico_cube;
    work[l] = ijk;
    }

  ico_wk = (int *) CALLOC(2*ico_cube_cb+1, sizeof(int));
  ico_pt = ico_wk+ico_cube_cb;
  for (l=0; l<ndot; l++) {
    ico_wk[work[l]]++;   /* dots per elementary cube */
    }

/* reordering of the coordinate array in accordance with box number */
  tn=0;
  for (i=0; i<ico_cube; i++) {
    for (j=0; j<ico_cube; j++) {
      for (k=0; k<ico_cube; k++) {
        tl=0;
        tl2 = tn;
        ijk = i+ico_cube*j+ico_cube*ico_cube*k;
        *(ico_pt+ijk) = tn;
        for (l=tl2; l<ndot; l++) {
          if (ijk == work[l]) {
            x = xus[3*l]; y = xus[1+3*l]; z = xus[2+3*l];
            xus[3*l] = xus[3*tn];
            xus[1+3*l] = xus[1+3*tn]; xus[2+3*l] = xus[2+3*tn];
            xus[3*tn] = x; xus[1+3*tn] = y; xus[2+3*tn] = z;
            ijk = work[l]; work[l]=work[tn]; work[tn]=ijk;
            tn++; tl++;
            }
          }
        *(ico_wk+ijk) = tl;
        }		/* cycle k */
      }			/* cycle j */
    }			/* cycle i */
  free(work); return 0;
  }


typedef struct _stwknb {
  double x;
  double y;
  double z;
  double dot;
  } Neighb;

int nsc_dclm(
  double *co, double *radius, int nat,
  int densit, int mode,
  double *value_of_area, double **at_area,
  double *value_of_vol,
  double **lidots, int *nu_dots) {

  int iat, i, ii, iii, ix, iy, iz, ixe, ixs, iye, iys, ize, izs, i_ac;
  int jat, j, jj, jjj, jx, jy, jz;
  int distribution;
  int l;
  int maxnei, nnei, last, maxdots;
  point_int wkdot=NULL, wkbox=NULL, wkat1=NULL, wkatm=NULL;
  Neighb  *wknb, *ctnb;
  int iii1, iii2, iiat, lfnr, i_at, j_at;
  double dx, dy, dz, dd, ai, aisq, ajsq, aj, as, a;
  double xi, yi, zi, xs=0., ys=0., zs=0.;
  double dotarea, area, vol=0.;
  point_double xus, dots=NULL, atom_area=NULL;

  int    nxbox, nybox, nzbox, nxy, nxyz;
  double xmin, ymin, zmin, xmax, ymax, zmax, ra2max, d, *pco;

  distribution = unsp_type(densit);
  if (distribution != -last_unsp || last_cubus != 4 ||
     (densit != last_densit && densit != last_n_dot)) {
    if (make_unsp(densit, (-distribution), &n_dot, 4)) return 1;
    }
  xus = xpunsp;

  dotarea = FOURPI/(double) n_dot;
  area = 0.;

#if TEST_CUBE 
  printf("nsc_dclm: n_dot=%5d %9.3f\n", n_dot, dotarea);
#endif

/* start with neighbour list */
/* calculate neighbour list with the box algorithm */
  if (nat==0) {
    WARNING("nsc_dclm: no surface atoms selected");
    return 1;
    }
  if (mode & FLAG_VOLUME) vol=0.;
  if (mode & FLAG_DOTS) {
    maxdots = 3*n_dot*nat/10;
    dots = (double *) CALLOC(maxdots, sizeof(double));
    lfnr=0;
    }
  if (mode & FLAG_ATOM_AREA) {
    atom_area = (double *) CALLOC(nat, sizeof(double));
    }

/* dimensions of atomic set, cell edge is 2*ra_max */
  xmin = co[0]; xmax = xmin; xs=xmin;
  ymin = co[1]; ymax = ymin; ys=ymin;
  zmin = co[2]; zmax = zmin; zs=zmin;
  ra2max = radius[0];

  for (iat=1; iat<nat; iat++) {
    pco = co+3*iat;
    xmin = MINIMUM(xmin, *pco);     xmax = MAXIMUM(xmax, *pco);
    ymin = MINIMUM(ymin, *(pco+1)); ymax = MAXIMUM(ymax, *(pco+1));
    zmin = MINIMUM(zmin, *(pco+2)); zmax = MAXIMUM(zmax, *(pco+2));
    xs= xs+ *pco; ys = ys+ *(pco+1); zs= zs+ *(pco+2);
    ra2max = MAXIMUM(ra2max, radius[iat]);
    }
  xs = xs/ (double) nat;
  ys = ys/ (double) nat;
  zs = zs/ (double) nat;
  ra2max = 2.*ra2max;
#if TEST_CUBE
  printf("nsc_dclm: n_dot=%5d ra2max=%9.3f %9.3f\n", n_dot, ra2max, dotarea);
#endif

  d = xmax-xmin; nxbox = (int) MAXIMUM(ceil(d/ra2max), 1.);
  d = (((double)nxbox)*ra2max-d)/2.;
  xmin = xmin-d; xmax = xmax+d;
  d = ymax-ymin; nybox = (int) MAXIMUM(ceil(d/ra2max), 1.);
  d = (((double)nybox)*ra2max-d)/2.;
  ymin = ymin-d; ymax = ymax+d;
  d = zmax-zmin; nzbox = (int) MAXIMUM(ceil(d/ra2max), 1.);
  d = (((double)nzbox)*ra2max-d)/2.;
  zmin = zmin-d; zmax = zmax+d;
  nxy = nxbox*nybox;
  nxyz = nxy*nzbox;

/* box number of atoms */
  wkatm = (int *) CALLOC(3*nat, sizeof(int));
  wkat1 = wkatm+nat;
  wkdot = (int *) CALLOC(n_dot+nxyz+1, sizeof(int));
  wkbox = wkdot+n_dot;

  for (iat=0; iat<nat; iat++) {
    pco = co+3*iat;
    i = (int) MAXIMUM(floor((  *pco  -xmin)/ra2max), 0); i = MINIMUM(i,nxbox-1);
    j = (int) MAXIMUM(floor((*(pco+1)-ymin)/ra2max), 0); j = MINIMUM(j,nybox-1);
    l = (int) MAXIMUM(floor((*(pco+2)-zmin)/ra2max), 0); l = MINIMUM(l,nzbox-1);
    i = i+j*nxbox+l*nxy;
    wkat1[iat] = i; wkbox[i]++;
    }

/* sorting of atoms in accordance with box numbers */
  j = wkbox[0]; for (i=1; i<nxyz; i++) j= MAXIMUM(wkbox[i], j);
  for (i=1; i<=nxyz; i++) wkbox[i] += wkbox[i-1];
/*
  maxnei = (int) floor(ra2max*ra2max*ra2max*0.5);
*/
  maxnei = MINIMUM(nat, 27*j);
  wknb = (Neighb *) CALLOC(maxnei, sizeof(Neighb));
  for (iat=0; iat<nat; iat++) {
    wkatm[--wkbox[wkat1[iat]]] = iat;
#if TEST_CUBE
    printf("atom %5d on place %5d\n", iat, wkbox[wkat1[iat]]);
#endif
    }
#if TEST_CUBE
  printf("nsc_dclm: n_dot=%5d ra2max=%9.3f %9.3f\n", n_dot, ra2max, dotarea);
  printf("neighbour list calculated/box(xyz):%d %d %d\n", nxbox, nybox, nzbox);
  for (i=0; i<nxyz; i++) printf("box %6d : atoms %4d-%4d    %5d\n",
    i, wkbox[i], wkbox[i+1]-1, wkbox[i+1]-wkbox[i]);
  for (i=0; i<nat; i++) {
    printf("list place %5d by atom %7d\n", i, wkatm[i]);
    }
#endif

/* calculate surface for all atoms, step cube-wise */
  for (iz=0; iz<nzbox; iz++) {
    iii = iz*nxy;
    izs = MAXIMUM(iz-1,0); ize = MINIMUM(iz+2, nzbox);
  for (iy=0; iy<nybox; iy++) {
    ii = iy*nxbox+iii;
    iys = MAXIMUM(iy-1,0); iye = MINIMUM(iy+2, nybox);
  for (ix=0; ix<nxbox; ix++) {
    i = ii+ix;
    iii1=wkbox[i]; iii2=wkbox[i+1];
    if (iii1 >= iii2) continue;
    ixs = MAXIMUM(ix-1,0); ixe = MINIMUM(ix+2, nxbox);

    iiat = 0;
/* make intermediate atom list */
    for (jz=izs; jz<ize; jz++) {
      jjj = jz*nxy;
    for (jy=iys; jy<iye; jy++) {
      jj = jy*nxbox+jjj;
    for (jx=ixs; jx<ixe; jx++) {
      j = jj+jx;
      for (jat=wkbox[j]; jat<wkbox[j+1]; jat++) {
        wkat1[iiat] = wkatm[jat]; iiat++;
        }     /* end of cycle "jat" */
      }       /* end of cycle "jx" */
      }       /* end of cycle "jy" */
      }       /* end of cycle "jz" */
    for (iat=iii1; iat<iii2; iat++) {
      i_at = wkatm[iat];
      ai = radius[i_at]; aisq = ai*ai;
      pco = co+3*i_at;
      xi = *pco; yi = *(pco+1); zi = *(pco+2);
      for (i=0; i<n_dot; i++) *(wkdot+i)=0;

      ctnb = wknb; nnei = 0;
      for (j=0; j<iiat; j++) {
        j_at = *(wkat1+j);
        if (j_at == i_at) continue;

        aj = radius[j_at]; ajsq = aj*aj;
        pco = co+3*j_at;
        dx = *pco-xi; dy = *(pco+1)-yi; dz = *(pco+2)-zi;
        dd = dx*dx+dy*dy+dz*dz;

        as = ai+aj; if (dd > as*as) continue;
        nnei++;
        ctnb->x = dx; ctnb->y = dy; ctnb->z = dz;
        ctnb->dot = (dd+aisq-ajsq)/(2.*ai); /* reference dot product */
        ctnb++;
        }

/* check points on accessibility */
      if (nnei) {
        last = 0; i_ac = 0;
        for (l=0; l<n_dot; l++) {
          if (xus[3*l]*(wknb+last)->x+
              xus[1+3*l]*(wknb+last)->y+
              xus[2+3*l]*(wknb+last)->z <= (wknb+last)->dot) {
            for (j=0; j<nnei; j++) {
              if (xus[3*l]*(wknb+j)->x+xus[1+3*l]*(wknb+j)->y+
                  xus[2+3*l]*(wknb+j)->z > (wknb+j)->dot) {
                last = j; break;
                }
              }
            if (j >= nnei) { i_ac++; wkdot[l] = 1; }
            }     /* end of cycle j */
          }       /* end of cycle l */
        }
      else {
        i_ac  = n_dot;
        for (l=0; l < n_dot; l++) wkdot[l] = 1;
        }

#if TEST_CUBE
      printf("i_ac=%d, dotarea=%8.3f, aisq=%8.3f\n", i_ac, dotarea, aisq);
#endif
      a = aisq*dotarea* (double) i_ac;
      area = area + a;
      if (mode & FLAG_ATOM_AREA) {
        atom_area[i_at] = a;
        }
      if (mode & FLAG_DOTS) {
        for (l=0; l<n_dot; l++) {
          if (wkdot[l]) {
            lfnr++;
            if (maxdots <= 3*lfnr+1) {
              maxdots = maxdots+n_dot*3;
              dots = (double *) REALLOC(dots, maxdots*sizeof(double));
              }
            dots[3*lfnr-3] = ai*xus[3*l]+xi;
            dots[3*lfnr-2] = ai*xus[1+3*l]+yi;
            dots[3*lfnr-1] = ai*xus[2+3*l]+zi;
            }
          }
        }
      if (mode & FLAG_VOLUME) {
        dx=0.; dy=0.; dz=0.;
        for (l=0; l<n_dot; l++) {
          if (wkdot[l]) {
            dx=dx+xus[3*l];
            dy=dy+xus[1+3*l];
            dz=dz+xus[2+3*l];
            }
          }
        vol = vol+aisq*(dx*(xi-xs)+dy*(yi-ys)+dz*(zi-zs)+ai* (double) i_ac);
        }

      }         /* end of cycle "iat" */
    }           /* end of cycle "ix" */
    }           /* end of cycle "iy" */
    }           /* end of cycle "iz" */

  free(wkatm); free(wkdot); free(wknb);

  if (mode & FLAG_VOLUME) {
    vol = vol*FOURPI/(3.* (double) n_dot);
    *value_of_vol = vol;
    }
  if (mode & FLAG_DOTS) {
    *nu_dots = lfnr;
    *lidots = dots;
    }
  if (mode & FLAG_ATOM_AREA) {
    *at_area = atom_area;
    }
  *value_of_area = area;

#if TEST_CUBE
  printf("area=%8.3f\n", area);
#endif
  return 0;
  }

#if TEST_NSC > 0
#define NAT 2
main () {

  int i, j, ndots;
  double co[3*NAT], ra[NAT], area, volume, a, b, c;
  double * dots;
  double * at_area;
  FILE *fp;


  a = 1.; c= 0.1;
  fp = fopen("nsc.txt", "w+");
  for (i=1; i<=NAT; i++) {
    j = i-1;
    co[3*i-3] = j*1*c;
    co[3*i-2] = j*1*c;
    co[3*i-1] = j*1*c;
/*
    co[3*i-3] = i*1.4;
    co[3*i-2] = 0.;
    co[3*i-1] = 0.;
*/
/*
    co[3*i-2] = a*0.3;
    a = -a; b=0;
    if (i%3 == 0) b=0.5;
    co[3*i-1] = b;
    ra[i-1] = 2.0;
*/
    ra[i-1] = (1.+j*0.5)*c;
    }
/*
  if (NSC(co, ra, NAT, 42, NULL, &area,
*/

  if (NSC(co, ra, NAT, 42,FLAG_VOLUME | FLAG_ATOM_AREA | FLAG_DOTS, &area,
      &at_area, &volume,
      &dots, &ndots)) ERROR("error in NSC");

  fprintf(fp, "\n");
  fprintf(fp, "area     : %8.3f\n", area);
  printf("area     : %8.3f\n", area);
  fprintf(fp, "volume   : %8.3f\n", volume);
  printf("volume   : %8.3f\n", volume);
  fprintf(fp, "ndots    : %8d\n", ndots);
  printf("ndots    : %8d\n", ndots);
  fprintf(fp, "\n");
  for (i=1; i<=NAT; i++) {
    fprintf(fp, "%4d ATOM %7.2f %7.2f %7.2f  ra=%4.1f  area=%8.3f\n",
      i, co[3*i-3], co[3*i-2], co[3*i-1], ra[i-1], at_area[i-1]);
    }
  fprintf(fp, "\n");
  fprintf(fp, "DOTS : %8d\n", ndots);
  for (i=1; i<=ndots; i++) {
    fprintf(fp, "%4d DOTS %8.2f %8.2f %8.2f\n",
      i, dots[3*i-3], dots[3*i-2], dots[3*i-1]);
    }
  }
#endif