NAG Library Manual, Mark 27.3
```/* nag_mesh_dim2_join (d06dbc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

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

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

static int ex1(void);
static int ex2(void);

int main(void) {
Integer exit_status_ex1 = 0;
Integer exit_status_ex2 = 0;

printf("nag_mesh_dim2_join (d06dbc) Example Program Results\n");
exit_status_ex1 = ex1();
exit_status_ex2 = ex2();

return (exit_status_ex1 == 0 && exit_status_ex2 == 0) ? 0 : 1;
}

int ex1(void) {
const Integer nvmax = 900, nedmx = 200, neltmx = 2 * nvmax + 5, ntrans = 1,
mode = 0;
double eps, dx, xint, pi2, pi4, ddx, ddy;
Integer exit_status, i, imax, itrace, itrans, j, jmax, jtrans, k, ktrans, l;
Integer nedge1, nedge2, nedge3, nelt1, nelt2, nelt3, nv1, nv2, nv3;
Integer imaxm1, jmaxm1, ind;
char pmesh[2];
double *coor1 = 0, *coor2 = 0, *coor3 = 0, *trans = 0;
Integer *conn1 = 0, *conn2 = 0, *conn3 = 0, *edge1 = 0, *edge2 = 0;
Integer *edge3 = 0, *itype = 0, *reft1 = 0, *reft2 = 0, *reft3 = 0;
NagError fail;

INIT_FAIL(fail);
exit_status = 0;

printf("\nExample 1\n\n");

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

/* Set sizes for the mesh: coordinates and connectivity of the 1st domain */
nv1 = 400;
nelt1 = 722;

nv2 = nv1;
nelt2 = nelt1;

imax = 20;
jmax = imax;
imaxm1 = imax - 1;
jmaxm1 = jmax - 1;
nedge1 = 2 * (imaxm1 + jmaxm1);
nedge2 = nedge1;

/* Allocate memory */

if (!(coor1 = NAG_ALLOC(2 * nv1, double)) ||
!(coor2 = NAG_ALLOC(2 * nv2, double)) ||
!(coor3 = NAG_ALLOC(2 * nvmax, double)) ||
!(trans = NAG_ALLOC(6 * ntrans, double)) ||
!(conn1 = NAG_ALLOC(3 * nelt1, Integer)) ||
!(conn2 = NAG_ALLOC(3 * nelt2, Integer)) ||
!(conn3 = NAG_ALLOC(3 * neltmx, Integer)) ||
!(edge1 = NAG_ALLOC(3 * nedge1, Integer)) ||
!(edge2 = NAG_ALLOC(3 * nedge2, Integer)) ||
!(edge3 = NAG_ALLOC(3 * nedmx, Integer)) ||
!(itype = NAG_ALLOC(ntrans, Integer)) ||
!(reft1 = NAG_ALLOC(nelt1, Integer)) ||
!(reft2 = NAG_ALLOC(nelt2, Integer)) ||
!(reft3 = NAG_ALLOC(neltmx, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Set up interior mesh as small perturbations on regular grid
* with regularity on the boundary of square on [0,1]x[0,1].
*/
dx = 1.0 / ((double)(imaxm1));
xint = 1.0 / ((double)(imax));
pi2 = X01AAC + X01AAC;
pi4 = pi2 + pi2;
k = 0;
ddy = 0.0;
for (j = 0; j < jmax; ++j) {
ddx = 0.0;
for (i = 0; i < imax; ++i) {
coor1[k] = ddx + dx * xint * sin(pi4 * ddx) * sin(pi4 * ddy);
coor1[k + 1] = ddy + dx * xint * sin(pi2 * ddx) * sin(pi2 * ddy);
k = k + 2;
ddx = ddx + dx;
}
ddy = ddy + dx;
}

/* Triangulate using skew-diagonals on grid squares */
k = 0;
l = 0;
for (i = 0; i < imaxm1; ++i) {
for (j = 0; j < jmaxm1; ++j) {
l = l + 1;
conn1[k] = l;
conn1[k + 1] = l + 1;
conn1[k + 2] = l + imaxm1 + 2;
k = k + 3;
conn1[k] = l;
conn1[k + 1] = l + imaxm1 + 2;
conn1[k + 2] = l + imaxm1 + 1;
k = k + 3;
}
l = l + 1;
}

for (i = 0; i < nelt1; ++i) {
reft1[i] = 1;
reft2[i] = 2;
}

pmesh[0] = 'N';

/* the edges of the boundary */
ind = 0;

for (i = 1; i <= imaxm1; ++i) {
edge1[ind] = i;
edge1[ind + 1] = i + 1;
edge1[ind + 2] = 1;
ind = ind + 3;
}

for (i = 1; i <= jmaxm1; ++i) {
edge1[ind] = i * imax;
edge1[ind + 1] = (i + 1) * imax;
edge1[ind + 2] = 1;
ind = ind + 3;
}

for (i = 1; i <= imaxm1; ++i) {
edge1[ind] = imax * jmax - i + 1;
edge1[ind + 1] = imax * jmax - i;
edge1[ind + 2] = 1;
ind = ind + 3;
}

for (i = 1; i <= jmaxm1; ++i) {
edge1[ind] = (jmax - i) * imax + 1;
edge1[ind + 1] = (jmax - i - 1) * imax + 1;
edge1[ind + 2] = 1;
ind = ind + 3;
}

for (ktrans = 0; ktrans < 2; ++ktrans) {
/* Translation of the 1st domain to obtain the 2nd domain
* ktrans = 0 leading to a domain overlapping
* ktrans = 1 leading to a domain partition
*/

if (ktrans == 0) {
itrans = imax - 5;
jtrans = jmax - 3;
} else {
itrans = imax - 1;
jtrans = 0;
}

itype[0] = 1;
trans[0] = (double)itrans / (imax - 1.0);
trans[1] = (double)jtrans / (jmax - 1.0);
itrace = 0;

/* nag_mesh_dim2_transform_affine (d06dac).
* Generates a mesh resulting from an affine transformation
* of a given mesh
*/
nag_mesh_dim2_transform_affine(mode, nv2, nedge2, nelt2, ntrans, itype,
trans, coor1, edge1, conn1, coor2, edge2,
conn2, itrace, 0, &fail);
if (fail.code == NE_NOERROR) {
for (i = 0; i < nedge2; ++i)
edge2[3 * i + 2] = 2;

/* Call to the restitching driver */

itrace = 0;
eps = 0.01;

/* nag_mesh_dim2_join (d06dbc).
* Joins together two given adjacent (possibly overlapping)
* meshes
*/
nag_mesh_dim2_join(eps, nv1, nelt1, nedge1, coor1, edge1, conn1, reft1,
nv2, nelt2, nedge2, coor2, edge2, conn2, reft2, &nv3,
&nelt3, &nedge3, coor3, edge3, conn3, reft3, itrace, 0,
&fail);
if (fail.code == NE_NOERROR) {
if (pmesh[0] == 'N') {
if (ktrans == 0) {
printf("The restitched mesh characteristics\n");
printf("in the overlapping case\n");
} else {
printf("in the partition case\n");
}
printf(" nv    =%6" NAG_IFMT "\n", nv3);
printf(" nelt  =%6" NAG_IFMT "\n", nelt3);
printf(" nedge =%6" NAG_IFMT "\n", nedge3);
} else if (pmesh[0] == 'Y') {
/* Output the mesh to view it using the
NAG Graphics Library */

printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "\n", nv3, nelt3,
nedge3);

for (i = 0; i < nv3; ++i)
printf("  %15.6e  %15.6e\n", coor3[2 * i], coor3[2 * i + 1]);

for (k = 0; k < nelt3; ++k)
printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT ""
"%10" NAG_IFMT "\n",
conn3[3 * k], conn3[3 * k + 1], conn3[3 * k + 2], reft3[k]);

for (k = 0; k < nedge3; ++k)
printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "\n",
edge3[3 * k], edge3[3 * k + 1], edge3[3 * k + 2]);
} else {
printf("Problem with the printing option Y or N\n");
exit_status = -1;
goto END;
}
} else {
printf("Error from nag_mesh_dim2_join (d06dbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
} else {
printf("Error from nag_mesh_dim2_transform_affine (d06dac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
}

END:
NAG_FREE(coor1);
NAG_FREE(coor2);
NAG_FREE(coor3);
NAG_FREE(trans);
NAG_FREE(conn1);
NAG_FREE(conn2);
NAG_FREE(conn3);
NAG_FREE(edge1);
NAG_FREE(edge2);
NAG_FREE(edge3);
NAG_FREE(itype);
NAG_FREE(reft1);
NAG_FREE(reft2);
NAG_FREE(reft3);

return exit_status;
}

int ex2(void) {
const Integer nvmax = 900, nedmx = 200, neltmx = 2 * nvmax + 5, ntrans = 1,
nus = 0, nvint = 0, nvfix = 0;
static double ruser[1] = {-1.0};
double eps;
Integer exit_status, i, itrace, j, k, l, ncomp, nedge1, nedge2, nedge3;
Integer nedge4, nedge5, nelt1, nelt2, nelt3, nelt4, nelt5, nlines;
Integer npropa, nqint, nv1, nv2, nv3, nv4, nv5, nvb1, nvb2, mode;
char pmesh[2];
double *coor1 = 0, *coor2 = 0, *coor3 = 0, *coor4 = 0, *coor5 = 0;
double *coorch = 0, *coorus = 0, *rate = 0, *trans = 0, *weight = 0;
Integer *conn1 = 0, *conn2 = 0, *conn3 = 0, *conn4 = 0, *conn5 = 0;
Integer *edge1 = 0, *edge2 = 0, *edge3 = 0, *edge4 = 0, *edge5 = 0;
Integer *itype = 0, *lcomp = 0, *lined = 0, *nlcomp = 0, *numfix = 0;
Integer *reft1 = 0, *reft2 = 0, *reft3 = 0, *reft4 = 0, *reft5 = 0;
NagError fail;
Nag_Comm comm;

INIT_FAIL(fail);

/* For communication with user-supplied functions: */
comm.user = ruser;

exit_status = 0;

printf("\nExample 2\n\n");

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

/* Build the mesh of the 1st domain */
/* Initialize boundary mesh inputs: */
/* the number of line and of the characteristic points of */
/* the boundary mesh */
scanf("%" NAG_IFMT "", &nlines);
scanf("%*[^\n] ");

/* Allocate memory */

if (!(coor1 = NAG_ALLOC(2 * nvmax, double)) ||
!(coor2 = NAG_ALLOC(2 * nvmax, double)) ||
!(coor3 = NAG_ALLOC(2 * nvmax, double)) ||
!(coor4 = NAG_ALLOC(2 * nvmax, double)) ||
!(coor5 = NAG_ALLOC(2 * nvmax, double)) ||
!(coorch = NAG_ALLOC(2 * nlines, double)) ||
!(coorus = NAG_ALLOC(1, double)) || !(rate = NAG_ALLOC(nlines, double)) ||
!(trans = NAG_ALLOC(6 * ntrans, double)) ||
!(weight = NAG_ALLOC(1, double)) ||
!(conn1 = NAG_ALLOC(3 * neltmx, Integer)) ||
!(conn2 = NAG_ALLOC(3 * neltmx, Integer)) ||
!(conn3 = NAG_ALLOC(3 * neltmx, Integer)) ||
!(conn4 = NAG_ALLOC(3 * neltmx, Integer)) ||
!(conn5 = NAG_ALLOC(3 * neltmx, Integer)) ||
!(edge1 = NAG_ALLOC(3 * nedmx, Integer)) ||
!(edge2 = NAG_ALLOC(3 * nedmx, Integer)) ||
!(edge3 = NAG_ALLOC(3 * nedmx, Integer)) ||
!(edge4 = NAG_ALLOC(3 * nedmx, Integer)) ||
!(edge5 = NAG_ALLOC(3 * nedmx, Integer)) ||
!(itype = NAG_ALLOC(ntrans, Integer)) ||
!(lcomp = NAG_ALLOC(nlines, Integer)) ||
!(lined = NAG_ALLOC(4 * nlines, Integer)) ||
!(numfix = NAG_ALLOC(1, Integer)) ||
!(reft1 = NAG_ALLOC(2 * nvmax + 5, Integer)) ||
!(reft2 = NAG_ALLOC(2 * nvmax + 5, Integer)) ||
!(reft3 = NAG_ALLOC(2 * nvmax + 5, Integer)) ||
!(reft4 = NAG_ALLOC(2 * nvmax + 5, Integer)) ||
!(reft5 = NAG_ALLOC(2 * nvmax + 5, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Characteristic points of the boundary geometry */

for (j = 0; j < nlines; ++j) {
scanf("%lf", &coorch[2 * j]);
}
scanf("%*[^\n] ");

for (j = 0; j < nlines; ++j) {
scanf("%lf", &coorch[2 * j + 1]);
}
scanf("%*[^\n] ");

/* The lines of the boundary mesh */

for (j = 0; j < nlines; ++j) {
for (i = 0; i < 4; ++i)
scanf("%" NAG_IFMT "", &lined[4 * j + i]);
scanf("%lf", &rate[j]);
}
scanf("%*[^\n] ");

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

/* 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]);
}

itrace = 0;

/* Call to the 2D boundary mesh generator */

/* nag_mesh_dim2_gen_boundary (d06bac).
* Generates a boundary mesh
*/
nag_mesh_dim2_gen_boundary(nlines, coorch, lined, fbnd, coorus, nus, rate,
ncomp, nlcomp, lcomp, nvmax, nedmx, &nvb1, coor1,
&nedge1, edge1, itrace, 0, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_gen_boundary (d06bac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Generate mesh using Delaunay-Voronoi method */

/* Initialize mesh control parameters */

itrace = 0;
npropa = 1;

/* nag_mesh_dim2_gen_delaunay (d06abc).
* Generates a two-dimensional mesh using a Delaunay-Voronoi
* process
*/
nag_mesh_dim2_gen_delaunay(nvb1, nvint, nvmax, nedge1, edge1, &nv1, &nelt1,
coor1, conn1, weight, npropa, itrace, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_gen_delaunay (d06abc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

for (k = 0; k < nelt1; ++k)
reft1[k] = 1;

/* Call the smoothing routine */

nqint = 10;
/* nag_mesh_dim2_smooth_bary (d06cac).
* Uses a barycentering technique to smooth a given mesh
*/
nag_mesh_dim2_smooth_bary(nv1, nelt1, nedge1, coor1, edge1, conn1, nvfix,
numfix, itrace, 0, nqint, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_smooth_bary (d06cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Build the mesh of the 2nd domain */
scanf("%" NAG_IFMT "", &nlines);
scanf("%*[^\n] ");

/* Characteristic points of the boundary geometry */
for (j = 0; j < nlines; ++j)
scanf("%lf", &coorch[2 * j]);
scanf("%*[^\n] ");
for (j = 0; j < nlines; ++j)
scanf("%lf", &coorch[2 * j + 1]);
scanf("%*[^\n] ");

/* The lines of the boundary mesh */

for (j = 0; j < nlines; ++j) {
for (i = 0; i < 4; ++i)
scanf("%" NAG_IFMT "", &lined[4 * j + i]);
scanf("%lf", &rate[j]);
}
scanf("%*[^\n] ");

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

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

for (k = j; k <= j + NAG_IABS(nlcomp[i]); ++k)
scanf("%" NAG_IFMT "", &lcomp[k]);
scanf("%*[^\n] ");
j += NAG_IABS(nlcomp[i]);
}
scanf(" ' %1s '", pmesh);
scanf("%*[^\n] ");

itrace = 0;

/* Call to the 2D boundary mesh generator */

/* nag_mesh_dim2_gen_boundary (d06bac), see above. */
nag_mesh_dim2_gen_boundary(nlines, coorch, lined, fbnd, coorus, nus, rate,
ncomp, nlcomp, lcomp, nvmax, nedmx, &nvb2, coor2,
&nedge2, edge2, itrace, 0, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_gen_boundary (d06bac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Generate mesh using the advancing front method */

itrace = 0;

/* nag_mesh_dim2_gen_front (d06acc).
* Generates a two-dimensional mesh using an Advancing-front
* method
*/
nag_mesh_dim2_gen_front(nvb2, nvint, nvmax, nedge2, edge2, &nv2, &nelt2,
coor2, conn2, weight, itrace, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_gen_front (d06acc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

for (k = 0; k < nelt2; ++k)
reft2[k] = 2;

/* Rotation of the 2nd domain mesh */
/* to produce the 3rd mesh domain */

itype[0] = 3;
trans[0] = 6.0;
trans[1] = -1.0;
trans[2] = -90.0;
itrace = 0;
mode = 0;

/* nag_mesh_dim2_transform_affine (d06dac), see above. */
nag_mesh_dim2_transform_affine(mode, nv2, nedge2, nelt2, ntrans, itype, trans,
coor2, edge2, conn2, coor3, edge3, conn3,
itrace, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_transform_affine (d06dac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

nv3 = nv2;
nelt3 = nelt2;
nedge3 = nedge2;

for (k = 0; k < nelt3; ++k)
reft3[k] = 3;

/* Restitching meshes 1 and 2 to form mesh 4 */

eps = 0.001;
itrace = 0;

/* nag_mesh_dim2_join (d06dbc), see above. */
nag_mesh_dim2_join(eps, nv1, nelt1, nedge1, coor1, edge1, conn1, reft1, nv2,
nelt2, nedge2, coor2, edge2, conn2, reft2, &nv4, &nelt4,
&nedge4, coor4, edge4, conn4, reft4, itrace, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_join (d06dbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Restitching meshes 3 and 4 to form mesh 5 */

itrace = 0;

/* nag_mesh_dim2_join (d06dbc), see above. */
nag_mesh_dim2_join(eps, nv4, nelt4, nedge4, coor4, edge4, conn4, reft4, nv3,
nelt3, nedge3, coor3, edge3, conn3, reft3, &nv5, &nelt5,
&nedge5, coor5, edge5, conn5, reft5, itrace, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mesh_dim2_join (d06dbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

if (pmesh[0] == 'N') {
printf("The restitched mesh characteristics\n");
printf(" nv    =%6" NAG_IFMT "\n", nv5);
printf(" nelt  =%6" NAG_IFMT "\n", nelt5);
printf(" nedge =%6" NAG_IFMT "\n", nedge5);
} else if (pmesh[0] == 'Y') {
/* Output the mesh to view it using the NAG Graphics Library */

printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "\n", nv5, nelt5,
nedge5);

for (i = 0; i < nv5; ++i)
printf("  %15.6e  %15.6e\n", coor5[2 * i], coor5[2 * i + 1]);

for (k = 0; k < nelt5; ++k)
printf("%10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "\n",
conn5[3 * k], conn5[3 * k + 1], conn5[3 * k + 2], reft5[k]);

for (k = 0; k < nedge5; ++k)
printf(" %10" NAG_IFMT "%10" NAG_IFMT "%10" NAG_IFMT "\n", edge5[3 * k],
edge5[3 * k + 1], edge5[3 * k + 2]);
} else {
printf("Problem with the printing option Y or N\n");
}

END:
NAG_FREE(coor1);
NAG_FREE(coor2);
NAG_FREE(coor3);
NAG_FREE(coor4);
NAG_FREE(coor5);
NAG_FREE(coorch);
NAG_FREE(coorus);
NAG_FREE(rate);
NAG_FREE(trans);
NAG_FREE(weight);
NAG_FREE(conn1);
NAG_FREE(conn2);
NAG_FREE(conn3);
NAG_FREE(conn4);
NAG_FREE(conn5);
NAG_FREE(edge1);
NAG_FREE(edge2);
NAG_FREE(edge3);
NAG_FREE(edge4);
NAG_FREE(edge5);
NAG_FREE(itype);
NAG_FREE(lcomp);
NAG_FREE(lined);
NAG_FREE(nlcomp);
NAG_FREE(numfix);
NAG_FREE(reft1);
NAG_FREE(reft2);
NAG_FREE(reft3);
NAG_FREE(reft4);
NAG_FREE(reft5);

return exit_status;
}

double NAG_CALL fbnd(Integer i, double x, double y, Nag_Comm *pcomm) {

if (pcomm->user[0] == -1.0) {
printf("(User-supplied callback fbnd, first invocation.)\n");
pcomm->user[0] = 0.0;
}

ret_val = 0.0;
switch (i) {
case 1:

/* inner circle */

x0 = 0.0;
y0 = 0.0;
ret_val = (x - x0) * (x - x0) + (y - y0) * (y - y0) - radius2;
break;

case 2:

/* outer circle */

x0 = 0.0;
y0 = 0.0;