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criticnew.c
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#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<fonction.h>
#include<constant.h>
#include<dimension.h>
#include<structure.h>
#include<errors.h>
/****************************************************************/
/* nom: critic */
/* auteur: Jean-Paul Kneib */
/* date: 10/02/92 */
/* place: Toulouse *
*
* Compute the critic and caustic lines.
*
* Output : tangeant[ntline] and radial[nrline]
*
* Global variables used :
* - G, CL, F, lens, radial, tangent, nrline, ntline, flagr, flagt
* - in dratio() : C
* - in chgsigne() : G, lens
* - in zeroamp() : G, lens, lens_table
* - in e_dpl() : G, lens, lens_table
* - in next() : G, lens
* - in follow() : CL, radial, nrline, flagr, G, lens, lens_table
* - in followi() : CL, tangent, ntline, flagt, G, lens, lens_table
*/
static void snake(int verbose);
static void marchingSquares(int verbose);
void criticnew(int verbose)
{
extern struct g_cline CL;
if ( !strcmp(CL.algorithm, "SNAKE") )
snake(verbose);
else
marchingSquares(verbose);
}
/* Variables definitions for the marchingSquare algorithm */
static double limitLow; // smaller area of a square
static double limitHigh; // minimal area of a square
static double z_cl; // redshift of the current CL.nplan[i]
static double dos; // distance to current CL.nplan[i]
static double dl0s; // distance between lens[0] and CL.nplan[i]
static double dlsds_cl; // dlsds ratio of dl0s/dos
/* Compute the amplification at the 4 cornes of the square and
* return the corresponding marching square type.
*
* The amplification is always computed at the center of the square.
*
* The points are ccw oriented and the 1st point coordinates are xmin, ymin.
*
* If squareNb = 4, force to compute the 4 corners.
*
* Parameters :
* - x, y, width, height : position and size of the square
* - parentType : marching square type for the parent square (see: cutSquare() )
* - squareNb : index of the current child square in the parent square
* - ampli (IN/OUT) : array of double[5] that contains the 5 computed
* amplification or 0. In input, it contains the parent values
*/
static unsigned char getSquareType(
double x, double y,
double width, double height,
unsigned char parentType, char squareNb, double *ampli )
{
struct point a;
unsigned char type;
// initialize type with parentType and squareNb
if ( squareNb == 0 )
type = (parentType & 1) | (parentType & 128 ? 8 : 0);
else if ( squareNb == 1 )
type = (parentType & 2) | (parentType & 128 ? 4 : 0);
else if ( squareNb == 2 )
type = (parentType & 8) | (parentType & 128 ? 1 : 0);
else if ( squareNb == 3 )
type = (parentType & 4) | (parentType & 128 ? 2 : 0);
else
type = 0;
// compute only 3 amplifications per square
if ( squareNb == 1 || squareNb == 3 || squareNb == 4)
{
a.x = x;
a.y = y;
ampli[0] = e_amp(&a, dl0s, dos, z_cl);
type |= ampli[0] > 0 ? 1 : 0;
}
if ( squareNb == 0 || squareNb == 2 || squareNb == 4 )
{
a.x = x + width;
a.y = y;
ampli[1] = e_amp(&a, dl0s, dos, z_cl);
type |= ampli[1] > 0 ? 2 : 0;
}
if ( squareNb == 0 || squareNb == 2 || squareNb == 4 )
{
a.x = x;
a.y = y + height ;
ampli[3] = e_amp(&a, dl0s, dos, z_cl);
type |= ampli[3] > 0 ? 4 : 0;
}
if ( squareNb == 1 || squareNb == 3 || squareNb == 4 )
{
a.x = x + width;
a.y = y + height ;
ampli[2] = e_amp(&a, dl0s, dos, z_cl);
type |= ampli[2] > 0 ? 8 : 0;
}
// center of the square... always computed
a.x = x + width / 2.;
a.y = y + height / 2.;
ampli[4] = e_amp(&a, dl0s, dos, z_cl);
type |= ampli[4] > 0 ? 128 : 0;
return type;
}
/* Append a segment to the tangent/radial arrays depending on the sign of
* the parities on each side of the segment.
* Parameters :
* - x1, y1 : head of the segment
* - x2, y2 : end of the segment
* - signe_flag : 1 for radial line, 2 for tangeant line (see : chgsigne() )
*/
static void appendSegment( double x1, double y1, double x2, double y2, int signe_flag )
{
extern struct biline radial[NMAX], tangent[NMAX];
extern int nrline, ntline, flagr, flagt;
if ( signe_flag == 1 )
{
radial[nrline].i = flagr;
radial[nrline].I.x = x1;
radial[nrline].I.y = y1;
e_dpl(&radial[nrline].I, dlsds_cl, &radial[nrline].S);
nrline++;
radial[nrline].i = flagr;
radial[nrline].I.x = x2;
radial[nrline].I.y = y2;
e_dpl(&radial[nrline].I, dlsds_cl, &radial[nrline].S);
nrline++;
flagr++;
}
else if (signe_flag == 2)
{
tangent[ntline].i = flagt;
tangent[ntline].I.x = x1;
tangent[ntline].I.y = y1;
e_dpl(&tangent[ntline].I, dlsds_cl, &tangent[ntline].S);
ntline++;
tangent[ntline].i = flagt;
tangent[ntline].I.x = x2;
tangent[ntline].I.y = y2;
e_dpl(&tangent[ntline].I, dlsds_cl, &tangent[ntline].S);
ntline++;
flagt++;
}
#ifdef DEBUG
else
fprintf( stderr, "ERROR with chsigne!!!\n" );
#endif
if( ntline > NMAX || nrline > NMAX )
{
fprintf(stderr, "Error: Too many critical line segments. Maximum set to NMAX = %d\n", NMAX);
exit(E_NMAX_REACHED);
}
}
/* Given a square, compute its type with getSquareType() function.
*
* If the square has at least one corner with a sign different from
* the other corners, then the square is divided in 4 squares and
* cutSquare is called for each of the 4 children.
*
* Stop when the square size is lower than the limitLow global variable.
*
* Parameters :
* - x, y, width, height : position and size of the square
* - parentType : marching square type for the parent square (see: cutSquare() )
* - squareNb : index of the current child square in the parent square
* - ampli (IN) : array of double[5] that contains the 5 computed
* amplification or 0. In input, it contains the parent values
*/
static void cutSquare(
double x, double y, double width, double height,
unsigned char parentType, int squareNb, double *parentAmpli )
{
#ifdef DEBUG
extern struct g_mode M;
FILE * dbg;
#endif
struct point A, B; //check points for radial/tangeantial line detection
double sizeSquare;
unsigned char type;
double tmp1, tmp2; //segment coordinates for the smallest square
double ampli[5]; // amplifications for this square
#ifdef DEBUG
dbg = fopen( "cidbg.reg", "a" );
fprintf( dbg, "fk5;box(%lf,%lf,%lf\",%lf\") # color=green\n",
M.ref_ra + (x + width / 2.) / -3600 / cos(M.ref_dec*DTR),
M.ref_dec + (y + height / 2.) / 3600,
width, height );
fclose(dbg);
#endif
sizeSquare = width > height ? width : height;
// initialise the amplifications of this square
ampli[squareNb] = parentAmpli[squareNb];
ampli[(squareNb + 2) % 4] = parentAmpli[4];
type = getSquareType( x, y, width, height, parentType, squareNb, ampli );
if ( sizeSquare > limitLow )
{
// divide the square in 4 children
if ( sizeSquare > limitHigh || ( type != 0 && type != 15 && type != 143) )
{
width /= 2.;
height /= 2.;
// square 1
cutSquare( x, y, width, height, type, 0, ampli);
// square 2
cutSquare( x + width, y, width, height, type, 1, ampli);
// square 3
cutSquare( x + width, y + height, width, height, type, 2, ampli);
//square 4
cutSquare( x, y + width, width, height, type, 3, ampli);
}
}
else
{
// Remove the detection of the central point (bit 7 = 128)
if ( type != 137 && type != 134 ) type &= 127;
// append a square marching square edge to the tangent/radial list
switch ( type )
{
case 1:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[0] / (ampli[1] - ampli[0]) * width;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y;
appendSegment(x, y + tmp1, x + tmp2, y, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 2:
tmp1 = -ampli[0] / (ampli[1] - ampli[0]) * width;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x + width;
A.y = y;
B.x = x;
B.y = y;
appendSegment(x + tmp1, y, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 3:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x;
A.y = y;
B.x = x;
B.y = y + height;
appendSegment(x, y + tmp1, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 4:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A. y = y + height;
B.x = x;
B.y = y;
appendSegment(x, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 5:
tmp1 = -ampli[0] / (ampli[1] - ampli[0]) * width;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y;
appendSegment(x + tmp1, y, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 6:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A.y = y + height;
B.x = x + width / 2.;
B.y = y + height / 2.;
appendSegment( x, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
tmp1 = -ampli[0] / (ampli[1] - ampli[0]) * width;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x + width;
A.y = y;
appendSegment( x + tmp1, y, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 134:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[0] / (ampli[1] - ampli[0]) * width;
A.x = x;
A.y = y;
B.x = x + width / 2.;
B.y = y + height / 2.;
appendSegment( x, y + tmp1, x + tmp2, y, chsigne(A, B, dl0s, dos, z_cl) );
tmp1 = -ampli[1] / (ampli[2] - ampli[1]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x + width;
A.y = y + height;
appendSegment( x + width, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 7:
tmp1 = -ampli[1] / (ampli[2] - ampli[1]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y + height;
appendSegment( x + width, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 8:
tmp1 = -ampli[3] / (ampli[2] - ampli[3]) * width;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y + height;
appendSegment( x + tmp1, y + height, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 9:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[0] / (ampli[1] - ampli[0]) * width;
A.x = x;
A.y = y;
B.x = x + width / 2.;
B.y = y + height / 2.;
appendSegment( x, y + tmp1, x + tmp2, y, chsigne(A, B, dl0s, dos, z_cl) );
tmp1 = -ampli[1] / (ampli[2] - ampli[1]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x + width;
A.y = y + height;
appendSegment( x + width, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 137:
tmp1 = -ampli[0] / (ampli[1] - ampli[0]) * width;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x + width;
A.y = y;
B.x = x + width / 2.;
B.y = y + height / 2.;
appendSegment( x + tmp1, y, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A.y = y + height;
appendSegment( x, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 10:
tmp1 = -ampli[0] / (ampli[1] - ampli[0]) * width;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y;
appendSegment( x + tmp1, y, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 11:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[3] / (ampli[2] - ampli[3]) * width;
A.x = x;
A.y = y;
B.x = x;
B.y = y + height;
appendSegment( x, y + tmp1, x + tmp2, y + height, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 12:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x;
A.y = y;
B.x = x;
B.y = y + height;
appendSegment( x, y + tmp1, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 13:
tmp1 = -ampli[0] / (ampli[1] - ampli[0]) * width;
tmp2 = -ampli[1] / (ampli[2] - ampli[1]) * height;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y;
appendSegment( x + tmp1, y, x + width, y + tmp2, chsigne(A, B, dl0s, dos, z_cl) );
break;
case 14:
tmp1 = -ampli[0] / (ampli[3] - ampli[0]) * height;
tmp2 = -ampli[0] / (ampli[1] - ampli[0]) * width;
A.x = x;
A.y = y;
B.x = x + width;
B.y = y;
appendSegment( x, y + tmp1, x + tmp2, y, chsigne(A, B, dl0s, dos, z_cl) );
break;
}
}
}
/* Browse the marching square segments and update the flag to
* associate them into independent critical lines
*/
static void reflag()
{
extern struct biline radial[NMAX], tangent[NMAX];
extern int nrline, ntline, flagr, flagt;
struct point pi0, pi1;
double dx, dy;
int i, j;
// for tangent critical lines
flagt = 0;
for( i = 0; i < ntline; i+=2 )
{
tangent[i].i = flagt;
tangent[i+1].i = flagt;
pi0 = tangent[i].I;
pi1 = tangent[i+1].I;
j = 0;
dx = tangent[j].I.x - pi1.x;
dy = tangent[j].I.y - pi1.y;
while( dx * dx + dy * dy > limitHigh * limitHigh / 4 && j < ntline )
{
dx = tangent[j].I.x - pi1.x;
dy = tangent[j].I.y - pi1.y;
j += 2;
}
tangent[j].i = flagt;
tangent[j+1].i = flagt;
}
// for radial critical lines
flagr = 0;
for( i = 0; i < nrline; i+=2 )
{
radial[i].i = flagr;
radial[i+1].i = flagr;
pi0 = radial[i].I;
pi1 = radial[i+1].I;
j = 0;
dx = radial[j].I.x - pi1.x;
dy = radial[j].I.y - pi1.y;
while( dx * dx + dy * dy > limitHigh * limitHigh / 4 && j < nrline )
{
dx = radial[j].I.x - pi1.x;
dy = radial[j].I.y - pi1.y;
j += 2;
}
radial[j].i = flagr;
radial[j+1].i = flagr;
}
}
/* Find the caustic/critical lines with a multiresolution
* marching squares algorithm.
*
* The initial square is defined by the CL or F global variables
*
* The critical line is used to compute the caustic one in the
* source plane.
*
*/
static void marchingSquares(int verbose)
{
extern struct g_cline CL;
extern struct g_frame F;
extern struct pot lens[];
extern int nrline, ntline, flagr, flagt;
double xmin, ymin, xmax, ymax;
double ampli[5]; // amplifications of the root square
int k;
/* Definition de la fenetre de calcul */
if (CL.dmax != 0.)
{
xmin = -CL.dmax;
xmax = CL.dmax;
ymin = -CL.dmax;
ymax = CL.dmax;
}
else
{
xmin = (F.xmax - F.xmin) / 2.;
ymax = (F.ymin + F.ymax) / 2. + xmin;
ymin = (F.ymin + F.ymax) / 2. - xmin;
xmax = (F.xmin + F.xmax) / 2. + xmin;
xmin = (F.xmin + F.xmax) / 2. - xmin;
}
// Limit definitions
// we don't want square side lengths smaller than CL.cpas
limitLow = CL.cpas;
// we want to divide the field at least in 64x64 squares
if ( CL.limitHigh != 0 )
limitHigh = CL.limitHigh;
else
limitHigh = (xmax - xmin) / 64.;
/* initialisation de quelques constantes */
nrline = 0;
ntline = 0;
#ifdef DEBUG
system( "rm -f cidbg.reg" );
#endif
for (k = 0; k < CL.nplan; k++)
{
if (verbose)
{
fprintf(stderr, "COMP%d: critic and caustic lines for source plane at z=%.3lf\n",
k + 1, CL.cz[k]);
fprintf(stderr, "limitHigh(in arcsec)=%.3lf limitLow(in arcsec)=%.3lf\n",
limitHigh, limitLow);
}
dl0s = distcosmo2(lens[0].z, CL.cz[k]);
dos = distcosmo1(CL.cz[k]);
dlsds_cl = dl0s / dos;
z_cl = CL.cz[k];
flagr = 1;
flagt = 1;
/* prepare the tree*/
cutSquare( xmin, ymin, xmax - xmin, ymax - ymin, 15, 4, ampli);
}
}
/* Find the caustic/critical lines with the snake algorithm.
*
* It's an iterative method that start from a point and looks
* always for the next point in a cone oriented along the
* previous direction.
*
* */
static void snake(int verbose)
{
extern struct g_cline CL;
extern struct biline radial[NMAX], tangent[NMAX];
extern struct pot lens[];
extern struct g_frame F;
extern struct g_grille G;
extern int nrline, ntline, flagr, flagt;
struct point A, B, DPL, N, O, OI, OS, P, Q;
struct point LP[NLMAX+1], LDPL[NLMAX+1];
int lnpas[NLMAX+1];
int nu[NLMAX+1];
int fsel[NLMAX+1];
double ppas, Dmin, dc;
double J;
double xmin, ymin, xmax, ymax;
register int j, k, ii;
register int i;
int signe_flag;
/* Definition de la fenetre de calcul */
if (CL.dmax != 0.)
{
xmin = -CL.dmax;
xmax = CL.dmax;
ymin = -CL.dmax;
ymax = CL.dmax;
}
else
{
xmin = F.xmin;
xmax = F.xmax;
ymin = F.ymin;
ymax = F.ymax;
}
/* initialisation de quelques constantes */
nrline = 0;
flagr = 1;
ntline = 0;
flagt = 1;
J = NPOINT;
ppas = sqrt((xmax - xmin) * (xmax - xmin) + (ymax - ymin) * (ymax - ymin)) / NPOINT;
/* liste des points a suivre */
if (G.nlens_crit == 1)
{
LP[0] = lens[0].C;
LDPL[0].x = Max(xmax - lens[0].C.x, xmin - lens[0].C.x) / J;
LDPL[0].y = Max(ymax - lens[0].C.y, ymin - lens[0].C.y) / J;
if ((lens[0].type == 5) || (lens[0].type == 7) ||
(lens[0].type == 0) || (lens[0].type == -1) || (lens[0].type == 1))
{
LP[0].x += LDPL[0].x;
LP[0].y += LDPL[0].y;
};
lnpas[0] = NPOINT;
}
else
{
LP[0].x = xmin;
LP[0].y = ymin;
Dmin = 9999.;
for (i = 0; i < G.nlens_crit; i++)
{
nu[i] = 99;
fsel[i] = 0;
};
/* on cherche le centre le plus pres du bord en bas a gauche*/
for (i = 0; i < G.nlens_crit; i++)
{
dc = dist(LP[0], lens[i].C);
if (dc < Dmin)
{
Dmin = dc;
nu[0] = i;
};
};
LP[1] = lens[nu[0]].C;
fsel[nu[0]] = 1;
for (i = 1; i < G.nlens_crit; i++)
{
Dmin = 9999.;
for (j = 0; j < G.nlens_crit; j++)
{
if (fsel[j] != 1)
{
dc = dist(LP[i], lens[j].C);
if (dc < Dmin)
{
Dmin = dc;
nu[i] = j;
};
};
};
LP[i+1] = lens[nu[i]].C;
fsel[nu[i]] = 1;
};
for (i = 0; i < G.nlens_crit; i++)
{
if ((lens[nu[i]].type == 5) || (lens[nu[i]].type == 7) ||
(lens[nu[i]].type == 0) || (lens[nu[i]].type == 1))
{
LP[i+1].x += 0.01;
LP[i+1].y += 0.015;
};
lnpas[i] = (int) (dist(LP[i], LP[i+1]) / 2. / ppas);
LDPL[i].x = (LP[i+1].x - LP[i].x) / lnpas[i];
LDPL[i].y = (LP[i+1].y - LP[i].y) / lnpas[i];
};
};
for (k = 0; k < CL.nplan; k++)
{
z_cl = CL.cz[k];
dl0s = distcosmo2(lens[0].z, z_cl);
dos = distcosmo1(z_cl);
dlsds_cl = dl0s / dos;
if (verbose)
fprintf(stderr, "COMP%d: critic and caustic lines for source plane at z=%.3lf\n",
k + 1, z_cl);
for (ii = 0; ii < G.nlens_crit; ii++)
{
A = LP[ii];
DPL = LDPL[ii];
if (verbose)
fprintf(stderr, "\tnlens=%d npas=%d x0=%.3lf y0=%.3lf\n",
ii + 1, lnpas[ii], A.x, A.y);
for (i = 1; i < lnpas[ii]; A = B, i++)
{
B.x = A.x + DPL.x;
B.y = A.y + DPL.y;
signe_flag = chsigne(A, B, dl0s, dos, z_cl);
if (signe_flag == 1)
{
radial[nrline].i = flagr;
OI = O = radial[nrline].I = e_zeroamp(A, B, dl0s, dos, z_cl);
e_dpl(&O, dlsds_cl, &OS);
radial[nrline++].S = OS;
N.x = O.x - DPL.y / 2.;
N.y = O.y + DPL.x / 2.;
radial[nrline].i = flagr;
P = radial[nrline].I = next(N, O, CL.cpas / 2., dl0s, dos, z_cl);
e_dpl(&P, dlsds_cl, &radial[nrline++].S);
radial[nrline].i = flagr;
Q = radial[nrline].I = next(O, P, CL.cpas / 2., dl0s, dos, z_cl);
e_dpl(&Q, dlsds_cl, &radial[nrline++].S);
follow(P, Q, O, dl0s, dos, z_cl);
radial[nrline].i = flagr;
radial[nrline].I = OI;
radial[nrline++].S = OS;
flagr++;
}
else if (signe_flag == 2)
{
tangent[ntline].i = flagt;
OI = O = tangent[ntline].I = e_zeroamp(A, B, dl0s, dos, z_cl);
e_dpl(&O, dlsds_cl, &OS);
tangent[ntline++].S = OS;
N.x = O.x - DPL.y / 2.;
N.y = O.y + DPL.x / 2.;
tangent[ntline].i = flagt;
P = tangent[ntline].I = next(N, O, CL.cpas, dl0s, dos, z_cl);
e_dpl(&P, dlsds_cl, &tangent[ntline++].S);
tangent[ntline].i = flagt;
Q = tangent[ntline].I = next(O, P, CL.cpas, dl0s, dos, z_cl);
e_dpl(&Q, dlsds_cl, &tangent[ntline++].S);
followi(P, Q, O, dl0s, dos, z_cl);
tangent[ntline].i = flagt;
tangent[ntline].I = OI;
tangent[ntline++].S = OS;
flagt++;
};
};
};
};
}

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