/*
* ?---p0---p1---p2---p3--- ---pm'---?
* | | | | | ... | |
* | r0 | r1 | r2 | r3 | ... rm'| rm |
* | | | | | ... | |
* ?---n0---n1---n2---n3--- ---nm'---?
*/
void
interpolate_line(size_t m, float const *p, float const *n, float *r)
{
size_t i;
r[0] = extrapolate_point(p[0], n[0], p[1], n[1]);
r[m] = extrapolate_point(p[m-1], n[m-1], p[m-2], n[m-2]);
for (i = 0; i < m-1; i++)
{
r[i+1] = interpolate_point(p[i], n[i], p[i+1], n[i+1]);
}
}
// update particle position using 4th order Runge-Kutta method
void update_particle_position_rk4( e *E, double* cart_pos, double* vel, double dt, int dim){
int d;
double accumPos[DIM_MAX]; // where the pos[] solution vector is accumulated
double pos[DIM_MAX]; // position in longitude, latitude
double posPred[DIM_MAX]; // position in meters
double k1[DIM_MAX];
int whereILive;
double fac;
fac = 1.0/6.0;
for( d=0; d<dim; d++ ) {
accumPos[d] = cart_pos[d]; // initial step
k1[d] = dt * vel[d];
posPred[d] = cart_pos[d] + 0.5 * k1[d];
accumPos[d] = accumPos[d] + fac * k1[d]; // first step ( + 1/6 k1 )
}
// convert posPred back to lon lat so we can call get_owner_element
pos[1] = r2d(posPred[1]/R); // calc lat first
pos[0] = r2d(posPred[0] / (R*cos(d2r(pos[1])))); // now lon
// find out which element containts this position
whereILive = get_owner_element(E, pos);
// update weights
calculate_interpolation_weights(&E->el[whereILive], E->xi, E->eta, pos);
// interpolate the nodal velocity to the current point
interpolate_point(&E->el[whereILive], vel);
/* Reuse k1. Here k1 = k2 */
for( d=0; d<dim; d++ ) {
k1[d] = dt * vel[d];
posPred[d] = cart_pos[d] + 0.5 * k1[d];
accumPos[d] = accumPos[d] + 2.0*fac*k1[d]; /* second step ( + 1/3 k2 ) */
}
/* Put positions back in posPred */
//for( d=0; d<dim; d++ ) {
// posPred[d] = cart_pos[d] + 0.5 * k1[d];
//}
// convert cart_pos back to lon lat
pos[1] = r2d(posPred[1]/R); // calc lat first
pos[0] = r2d(posPred[0] / (R*cos(d2r(pos[1])))); // now lon
// find out which element containts this position
//printf("\t\t2: posPred[0] = %f, posPred[1] = %f\n", posPred[0], posPred[1]);
//printf("\t\t2: pos[0] = %f, pos[1] = %f\n", pos[0], pos[1]);
whereILive = get_owner_element(E, pos);
calculate_interpolation_weights(&E->el[whereILive], E->xi, E->eta, pos);
// interpolate the nodal velocity to the current point
interpolate_point(&E->el[whereILive], vel);
/* Reuse k1. Here k1 = k3 */
for( d=0; d<dim; d++ ) {
k1[d] = dt * vel[d];
posPred[d] = cart_pos[d] + k1[d];
accumPos[d] = accumPos[d] + 2.0*fac*k1[d]; /* third step ( + 1/3 k3 ) */
}
/* Put positions back in posPred */
//for( d=0; d<dim; d++ ) {
// posPred[d] = cart_pos[d] + k1[d];
//}
// convert cart_pos back to lon lat
pos[1] = r2d(posPred[1]/R); // calc lat first
pos[0] = r2d(posPred[0] / (R*cos(d2r(pos[1])))); // now lon
// find out which element containts this position
whereILive = get_owner_element(E, pos);
calculate_interpolation_weights(&E->el[whereILive], E->xi, E->eta, pos);
// interpolate the nodal velocity to the current point
interpolate_point(&E->el[whereILive], vel);
/* Reuse k1. Here k1 = k4 */
for( d=0; d<dim; d++ ) {
k1[d] = dt * vel[d];
accumPos[d] = accumPos[d] + fac*k1[d]; /* fourth step ( + 1/6 k4 ) */
// get new position
cart_pos[d] = accumPos[d];
}
//printf("done\n"); fflush(stdout);
}
void interp_bathy_on_grid(e *E){
int i,j;
int el;
double pos[2];
//double interp_value;
// setup the interpolation source grid data structures
E->nx = E->b.nlon-1; //E->nc.x-1;
E->ny = E->b.nlat-1; //E->nc.y-1;
E->nElements = E->nx*E->ny ;
E->ele = malloc(E->nElements*sizeof(element));
E->nodesPerEl = 4;
E->msh.x = malloc((E->nx+1) * sizeof(double));
E->msh.y = malloc((E->ny+1) * sizeof(double));
init_xi_eta(E);
el = 0;
for(i=0;i<E->ny;i++){
for(j=0;j<E->nx;j++){
// set positions for this element
// element node numbering is anti-clockwise
E->ele[el].node_coord[0][0] = E->b.lon[j];
E->ele[el].node_coord[0][1] = E->b.lat[i]; // 0
E->ele[el].node_coord[1][0] = E->b.lon[j+1];
E->ele[el].node_coord[1][1] = E->b.lat[i]; // 1
E->ele[el].node_coord[2][0] = E->b.lon[j+1];
E->ele[el].node_coord[2][1] = E->b.lat[i+1]; // 2
E->ele[el].node_coord[3][0] = E->b.lon[j];
E->ele[el].node_coord[3][1] = E->b.lat[i+1]; // 3
// now set the nodal value for this element
E->ele[el].node_value[0] = -E->b.field[i][j];
E->ele[el].node_value[1] = -E->b.field[i][j+1];
E->ele[el].node_value[2] = -E->b.field[i+1][j+1];
E->ele[el].node_value[3] = -E->b.field[i+1][j];
el++;
}
}
// the store_mesh call is required for the function get_owner_element
store_mesh(E, E->nx, E->ny);
//print_elements(E);
// for each rho grid point
for(i=0;i<E->g.nY;i++){
for(j=0;j<E->g.nX;j++){
// get pos of grid point
pos[0] = E->lon_rho[i][j];
pos[1] = E->lat_rho[i][j];
// find out which element this lies within
el = get_owner_element(E, pos);
calculate_interpolation_weights(&E->ele[el], E->xi, E->eta, pos);
interpolate_point(&E->ele[el], &E->h[i][j]);
}
}
}
int main(int argc, char* argv[])
{
char* bathyfname = NULL;
int nbathy = -1;
point* pbathy = NULL;
char* gridfname = NULL;
NODETYPE nt = NT_DD;
gridnodes* gn = NULL;
gridmap* gm = NULL;
char* maskfname = NULL;
int** mask = NULL;
int ppe = PPE_DEF;
double zmin = ZMIN_DEF;
double zmax = ZMAX_DEF;
delaunay* d = NULL;
void (*interpolate_point) (void*, point *) = NULL;
void* interpolator = NULL;
int i = -1, j = -1;
parse_commandline(argc, argv, &bathyfname, &gridfname, &maskfname, &nt, &ppe, &zmin, &zmax, &i, &j);
/*
* sanity check
*/
if (bathyfname == NULL)
quit("no input bathymetry data specified");
if (gridfname == NULL)
quit("no input grid data specified");
if (ppe <= 0 || ppe > PPE_MAX)
quit("number of points per edge specified = %d greater than %d", ppe, PPE_MAX);
if (zmin >= zmax)
quit("min depth = %.3g > max depth = %.3g", zmin, zmax);
if (nt != NT_DD && nt != NT_COR)
quit("unsupported node type");
/*
* read bathymetry
*/
points_read(bathyfname, 3, &nbathy, &pbathy);
if (gu_verbose)
fprintf(stderr, "## %d input bathymetry values", nbathy);
if (nbathy < 3)
quit("less than 3 input bathymetry values");
/*
* read and validate grid
*/
gn = gridnodes_read(gridfname, nt);
gridnodes_validate(gn);
/*
* read mask
*/
if (maskfname != NULL) {
int nx = gridnodes_getnce1(gn);
int ny = gridnodes_getnce2(gn);
mask = gu_readmask(maskfname, nx, ny);
}
/*
* transform grid nodes to corner type
*/
if (nt != NT_COR) {
gridnodes* newgn = gridnodes_transform(gn, NT_COR);
gridnodes_destroy(gn);
gn = newgn;
}
/*
* build the grid map for physical <-> index space conversions
*/
gm = gridmap_build(gridnodes_getnce1(gn), gridnodes_getnce2(gn), gridnodes_getx(gn), gridnodes_gety(gn));
/*
* convert bathymetry to index space if necessary
*/
if (indexspace) {
point* newpbathy = malloc(nbathy * sizeof(point));
int newnbathy = 0;
int ii;
for (ii = 0; ii < nbathy; ++ii) {
point* p = &pbathy[ii];
point* newp = &newpbathy[newnbathy];
double ic, jc;
if (gridmap_xy2fij(gm, p->x, p->y, &ic, &jc)) {
newp->x = ic;
newp->y = jc;
newp->z = p->z;
newnbathy++;
}
}
free(pbathy);
pbathy = newpbathy;
nbathy = newnbathy;
}
/*
* create interpolator
*/
if (rule == CSA) { /* using libcsa */
interpolator = csa_create();
csa_addpoints(interpolator, nbathy, pbathy);
csa_calculatespline(interpolator);
interpolate_point = (void (*)(void*, point *)) csa_approximatepoint;
} else if (rule == AVERAGE) {
interpolator = ga_create(gm);
ga_addpoints(interpolator, nbathy, pbathy);
interpolate_point = (void (*)(void*, point *)) ga_getvalue;
ppe = 1;
} else { /* using libnn */
/*
* triangulate
*/
if (gu_verbose) {
fprintf(stderr, "## triangulating...");
fflush(stdout);
}
d = delaunay_build(nbathy, pbathy, 0, NULL, 0, NULL);
if (gu_verbose) {
fprintf(stderr, "done\n");
fflush(stderr);
}
if (rule == NN_SIBSON || rule == NN_NONSIBSONIAN) {
interpolator = nnpi_create(d);
if (rule == NN_SIBSON)
nn_rule = SIBSON;
else
nn_rule = NON_SIBSONIAN;
interpolate_point = (void (*)(void*, point *)) nnpi_interpolate_point;
} else if (rule == LINEAR) {
interpolator = lpi_build(d);
interpolate_point = (void (*)(void*, point *)) lpi_interpolate_point;
}
}
/*
* main cycle -- over grid cells
*/
{
double** gx = gridnodes_getx(gn);
int jmin, jmax, imin, imax;
if (i < 0) {
imin = 0;
imax = gridnodes_getnce1(gn) - 1;
jmin = 0;
jmax = gridnodes_getnce2(gn) - 1;
} else {
if (gu_verbose)
fprintf(stderr, "## calculating depth for cell (%d,%d)\n", i, j);
imin = i;
imax = i;
jmin = j;
jmax = j;
}
for (j = jmin; j <= jmax; ++j) {
for (i = imin; i <= imax; ++i) {
double sum = 0.0;
int count = 0;
int ii, jj;
if ((mask != NULL && mask[j][i] == 0) || isnan(gx[j][i]) || isnan(gx[j + 1][i + 1]) || isnan(gx[j][i + 1]) || isnan(gx[j + 1][i])) {
printf("NaN\n");
continue;
}
for (ii = 0; ii < ppe; ++ii) {
for (jj = 0; jj < ppe; ++jj) {
double fi = (double) i + 0.5 / (double) ppe * (1.0 + 2.0 * (double) ii);
double fj = (double) j + 0.5 / (double) ppe * (1.0 + 2.0 * (double) jj);
point p;
if (!indexspace)
gridmap_fij2xy(gm, fi, fj, &p.x, &p.y);
else {
p.x = fi;
p.y = fj;
}
interpolate_point(interpolator, &p);
if (isnan(p.z))
continue;
else if (p.z < zmin)
p.z = zmin;
else if (p.z > zmax)
p.z = zmax;
sum += p.z;
count++;
}
}
if (count == 0)
printf("NaN\n");
else
printf("%.2f\n", sum / (double) count);
fflush(stdout);
}
}
}
/*
* clean up, just because
*/
if (rule == CSA)
csa_destroy(interpolator);
else if (rule == AVERAGE)
ga_destroy(interpolator);
else {
if (rule == NN_SIBSON || rule == NN_NONSIBSONIAN)
nnpi_destroy(interpolator);
else if (rule == LINEAR)
lpi_destroy(interpolator);
delaunay_destroy(d);
}
if (mask != NULL)
gu_free2d(mask);
gridmap_destroy(gm);
gridnodes_destroy(gn);
free(pbathy);
return 0;
}