NAG Library Manual, Mark 28.4
```/* nag_mesh_dim2_gen_boundary (d06bac) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*/

#include <nag.h>
#include <stdio.h>

/* Structure to allow data to be passed into */
/* the user-supplied function fbnd */

struct user {
/* details of the ellipse containing the NAG logo */

double xa, xb, x0, y0;
};

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL fbnd(Integer, double, double, Nag_Comm *);
#ifdef __cplusplus
}
#endif

#define EDGE(I, J) edge[3 * (J - 1) + I - 1]
#define LINED(I, J) lined[4 * (J - 1) + I - 1]
#define CONN(I, J) conn[3 * (J - 1) + I - 1]
#define COOR(I, J) coor[2 * (J - 1) + I - 1]
#define COORCH(I, J) coorch[2 * (J - 1) + I - 1]
#define CRUS(I, J) crus[2 * (J - 1) + I - 1]

int main(void) {
const Integer sdcrus = 4, nvint = 0;
struct user ellipse;
Nag_Comm comm;
double x0, xa, xb, xmax, xmin, y0, ymax, ymin;
Integer exit_status, i, itrace, j, k, ncomp, nedge, nelt, nlines;
Integer npropa, nv, nvb, reftk, l, nvmax, nedmx;
char pmesh[2];
double *coor = 0, *coorch = 0, *crus = 0, *rate = 0, *weight = 0;
Integer *conn = 0, *edge = 0, *lcomp = 0, *lined = 0, *nlcomp = 0;
NagError fail;

INIT_FAIL(fail);

exit_status = 0;

printf(" nag_mesh_dim2_gen_boundary (d06bac) Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file */
scanf("%*[^\n] ");

/* Initialize boundary mesh inputs: */
/* the number of line and of the characteristic points of */
/* the boundary mesh */
scanf("%" NAG_IFMT " %" NAG_IFMT " %" NAG_IFMT " %*[^\n] ", &nlines, &nvmax,
&nedmx);

/* Allocate memory */

if (!(coor = NAG_ALLOC(2 * nvmax, double)) ||
!(coorch = NAG_ALLOC(2 * nlines, double)) ||
!(crus = NAG_ALLOC(2 * sdcrus, double)) ||
!(rate = NAG_ALLOC(nlines, double)) || !(weight = NAG_ALLOC(1, double)) ||
!(conn = NAG_ALLOC(3 * (2 * nvmax + 5), Integer)) ||
!(edge = NAG_ALLOC(3 * nedmx, Integer)) ||
!(lined = NAG_ALLOC(4 * nlines, Integer)) ||
!(lcomp = NAG_ALLOC(nlines, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* The lines of the boundary mesh */

for (j = 1; j <= nlines; ++j) {
for (i = 1; i <= 4; ++i)
scanf("%" NAG_IFMT "", &LINED(i, j));
scanf("%lf", &rate[j - 1]);
}
scanf("%*[^\n] ");

/* The ellipse boundary which envelops  */
/* the NAG Logo, the N, the A and the G */
for (j = 1; j <= nlines; ++j)
scanf("%lf", &COORCH(1, j));
scanf("%*[^\n] ");
for (j = 1; j <= nlines; ++j)
scanf("%lf", &COORCH(2, j));
scanf("%*[^\n] ");
for (j = 1; j <= sdcrus; ++j)
scanf("%lf", &CRUS(1, j));
scanf("%*[^\n] ");
for (j = 1; j <= sdcrus; ++j)
scanf("%lf", &CRUS(2, j));
scanf("%*[^\n] ");

/* The number of connected components  */
/* to the boundary and their information */
scanf("%" NAG_IFMT "%*[^\n] ", &ncomp);

/* Allocate memory */

if (!(nlcomp = NAG_ALLOC(ncomp, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

j = 0;
for (i = 0; i < ncomp; ++i) {
scanf("%" NAG_IFMT "", &nlcomp[i]);
scanf("%*[^\n] ");
l = j + NAG_IABS(nlcomp[i]);
for (k = j; k < l; ++k)
scanf("%" NAG_IFMT "", &lcomp[k]);
scanf("%*[^\n] ");

j += NAG_IABS(nlcomp[i]);
}
scanf(" %1s %*[^\n] ", pmesh);

/* Data passed to the user-supplied function */

xmin = COORCH(1, 4);
xmax = COORCH(1, 2);
ymin = COORCH(2, 1);
ymax = COORCH(2, 3);

xa = (xmax - xmin) / 2.0;
xb = (ymax - ymin) / 2.0;

x0 = (xmin + xmax) / 2.0;
y0 = (ymin + ymax) / 2.0;

comm.p = (Pointer)&ellipse;

ellipse.xa = xa;
ellipse.xb = xb;
ellipse.x0 = x0;
ellipse.y0 = y0;

itrace = -1;

/* Call to the boundary mesh generator */

/* nag_mesh_dim2_gen_boundary (d06bac).
* Generates a boundary mesh
*/
nag_mesh_dim2_gen_boundary(nlines, coorch, lined, fbnd, crus, sdcrus, rate,
ncomp, nlcomp, lcomp, nvmax, nedmx, &nvb, coor,
&nedge, edge, itrace, 0, &comm, &fail);
if (fail.code == NE_NOERROR) {
if (pmesh[0] == 'N') {
printf(" Boundary mesh characteristics\n");
printf(" nvb   =%6" NAG_IFMT "\n", nvb);
printf(" nedge =%6" NAG_IFMT "\n", nedge);
} else if (pmesh[0] == 'Y') {
/* Output the mesh to view it using the NAG Graphics Library */

printf(" %10" NAG_IFMT "%10" NAG_IFMT "\n", nvb, nedge);

for (i = 1; i <= nvb; ++i)
printf("  %4" NAG_IFMT "  %15.6e  %15.6e  \n", i, COOR(1, i),
COOR(2, i));

for (i = 1; i <= nedge; ++i)
printf(" %4" NAG_IFMT "%4" NAG_IFMT "%4" NAG_IFMT "%4" NAG_IFMT "\n", i,
EDGE(1, i), EDGE(2, i), EDGE(3, i));
} else {
printf("Problem with the printing option Y or N\n");
exit_status = -1;
goto END;
}
} else {
printf("Error from nag_mesh_dim2_gen_boundary (d06bac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Initialize mesh control parameters */

itrace = 0;
npropa = 1;

/* Call to the 2D Delaunay-Voronoi mesh generator */

/* nag_mesh_dim2_gen_delaunay (d06abc).
* Generates a two-dimensional mesh using a Delaunay-Voronoi
* process
*/
nag_mesh_dim2_gen_delaunay(nvb, nvint, nvmax, nedge, edge, &nv, &nelt, coor,
conn, weight, npropa, itrace, 0, &fail);
if (fail.code == NE_NOERROR) {
if (pmesh[0] == 'N') {
printf(" Complete mesh characteristics (Delaunay-Voronoi)\n");
printf("   nv (rounded to nearest 10) =%6" NAG_IFMT "\n",
10 * ((nv + 5) / 10));
printf(" nelt (rounded to nearest 10) =%6" NAG_IFMT "\n",
10 * ((nelt + 5) / 10));
} else if (pmesh[0] == 'Y') {
/* Output the mesh to view it using the NAG Graphics Library */

printf(" %10" NAG_IFMT "%10" NAG_IFMT "\n", nv, nelt);

for (i = 1; i <= nv; ++i)
printf("  %15.6e  %15.6e  \n", COOR(1, i), COOR(2, i));

reftk = 0;
for (k = 1; k <= nelt; ++k)
printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT
"\n",
CONN(1, k), CONN(2, k), CONN(3, k), reftk);
} else {
printf("Problem with the printing option Y or N\n");
exit_status = -1;
goto END;
}
} else {
printf("Error from nag_mesh_dim2_gen_delaunay (d06abc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Call to the 2D Advancing front mesh generator */

/* nag_mesh_dim2_gen_front (d06acc).
* Generates a two-dimensional mesh using an Advancing-front
* method
*/
nag_mesh_dim2_gen_front(nvb, nvint, nvmax, nedge, edge, &nv, &nelt, coor,
conn, weight, itrace, 0, &fail);
if (fail.code == NE_NOERROR) {
if (pmesh[0] == 'N') {
printf(" Complete mesh characteristics (Advancing Front)\n");
printf("   nv (rounded to nearest 10) =%6" NAG_IFMT "\n",
10 * ((nv + 5) / 10));
printf(" nelt (rounded to nearest 10) =%6" NAG_IFMT "\n",
10 * ((nelt + 5) / 10));
} else if (pmesh[0] == 'Y') {
/* Output the mesh to view it using the NAG Graphics Library */

printf(" %10" NAG_IFMT "%10" NAG_IFMT "\n", nv, nelt);

for (i = 1; i <= nv; ++i)
printf("  %15.6e  %15.6e  \n", COOR(1, i), COOR(2, i));

reftk = 0;
for (k = 1; k <= nelt; ++k)
printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT
"\n",
CONN(1, k), CONN(2, k), CONN(3, k), reftk);
} else {
printf("Problem with the printing option Y or N\n");
exit_status = -1;
goto END;
}
} else {
printf("Error from nag_mesh_dim2_gen_front (d06acc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

END:
NAG_FREE(coor);
NAG_FREE(coorch);
NAG_FREE(crus);
NAG_FREE(rate);
NAG_FREE(weight);
NAG_FREE(conn);
NAG_FREE(edge);
NAG_FREE(lcomp);
NAG_FREE(lined);
NAG_FREE(nlcomp);

return exit_status;
}

static double NAG_CALL fbnd(Integer i, double x, double y, Nag_Comm *pcomm) {
double ret_val, d1, d2;
double radius2, x0, xa, xb, y0;
struct user *ellipse = (struct user *)pcomm->p;

xa = ellipse->xa;
xb = ellipse->xb;
x0 = ellipse->x0;
y0 = ellipse->y0;

ret_val = 0.0;

switch (i) {
case 1:

/* line 1,2,3, and 4: ellipse centred in (X0,Y0) with */
/* XA and XB as coefficients */

d1 = (x - x0) / xa;
d2 = (y - y0) / xb;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;

case 2:

/* line 7, lower arc on letter n, is a circle centred in (X0,Y0)
*/

x0 = 0.5;
y0 = 6.25;
d1 = x - x0;
d2 = y - y0;

ret_val = d1 * d1 + d2 * d2 - radius2;
break;

case 3:

/* line 11, upper arc on letter n, is a circle centred in (X0,Y0)
*/

x0 = 1.0;
y0 = 4.0;
radius2 = 9.0 + (11.0 - y0) * (11.0 - y0);
d1 = x - x0;
d2 = y - y0;

ret_val = d1 * d1 + d2 * d2 - radius2;
break;

case 4:
/* line 15, upper arc on letter a, is a circle centred in (X0,Y0)
*/

x0 = 8.5;
y0 = 2.75;
radius2 = (x0 - 5.0) * (x0 - 5.0) + (11.0 - y0) * (11.0 - y0);
d1 = x - x0;
d2 = y - y0;

ret_val = d1 * d1 + d2 * d2 - radius2;
break;

case 5:

/* line 25, lower arc on hat of 'a', is a circle centred in (X0,Y0)
*/

x0 = 8.5;
y0 = 4.0;
radius2 = 2.5 * 2.5 + (10.0 - y0) * (10.0 - y0);
d1 = x - x0;
d2 = y - y0;

ret_val = d1 * d1 + d2 * d2 - radius2;
break;
case 6:

/* lines 20, 21 and 22, belly of letter a, is an ellipse centered
* in (X0, Y0) with semi-axes 3.5 and 2.75.
*/

x0 = 8.5;
y0 = 5.75;
d1 = (x - x0) / 3.5;
d2 = (y - y0) / 2.75;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 7:

/* lines 43, 44 and 45, outer curve on bottom of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 3.5 and 2.5.
*/

x0 = 17.5;
y0 = 2.5;
d1 = (x - x0) / 3.5;
d2 = (y - y0) / 2.5;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 8:

/* lines 28, 29 and 30, inner curve on bottom of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 2.0 and 1.5.
*/

x0 = 17.5;
y0 = 2.5;
d1 = (x - x0) / 2.0;
d2 = (y - y0) / 1.5;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 9:

/* line 42, inner curve on lower middle of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 1.5 and 0.5.
*/

x0 = 17.5;
y0 = 5.5;
d1 = (x - x0) / 1.5;
d2 = (y - y0) / 0.5;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 10:

/* line 31, outer curve on lower middle of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 2.0 and 1.5.
*/

x0 = 17.5;
y0 = 5.5;
d1 = (x - x0) / 3.0;
d2 = (y - y0) / 1.5;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 11:

/* line 41, inner curve on upper middle of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 1.0 and 1.0.
*/

x0 = 17.0;
y0 = 5.5;
d1 = (x - x0);
d2 = (y - y0);

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 12:

/* line 32, outer curve on upper middle of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 1.5 and 1.1573.
*/

x0 = 16.0;
y0 = 5.5;
d1 = (x - x0) / 1.5;
d2 = (y - y0) / 1.1573;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
case 13:

/* lines 33, 33, 34, 39 and 40, upper portion of 'g', is an ellipse
* centered in (X0, Y0) with semi-axes 3.0 and 2.75.
*/

x0 = 17.0;
y0 = 9.25;
d1 = (x - x0) / 3.0;
d2 = (y - y0) / 2.75;

ret_val = d1 * d1 + d2 * d2 - 1.0;
break;
default:
break;
}

return ret_val;
}
```