static void mls_set_neighborhood(void* context, int i)
{
mls_t* mls = context;
// Extract the points.
mls->N = stencil_size(mls->neighborhoods, i);
int pos = 0, j, k = 0;
while (stencil_next(mls->neighborhoods, i, &pos, &j, NULL))
{
mls->xj[k] = mls->domain->points[j];
mls->hj[k] = mls->smoothing_lengths[j];
++k;
}
// Compute the basis vectors for the points in the neighborhood.
int dim = mls->basis_dim;
mls->basis = polymec_realloc(mls->basis, sizeof(real_t) * dim * mls->N);
mls->basis_ddx = polymec_realloc(mls->basis_ddx, sizeof(real_t) * dim * mls->N);
mls->basis_ddy = polymec_realloc(mls->basis_ddy, sizeof(real_t) * dim * mls->N);
mls->basis_ddz = polymec_realloc(mls->basis_ddz, sizeof(real_t) * dim * mls->N);
for (int n = 0; n < mls->N; ++n)
{
polynomial_compute_basis(mls->poly_degree, 0, 0, 0, &mls->xj[n], &mls->basis[dim*n]);
polynomial_compute_basis(mls->poly_degree, 1, 0, 0, &mls->xj[n], &mls->basis_ddx[dim*n]);
polynomial_compute_basis(mls->poly_degree, 0, 1, 0, &mls->xj[n], &mls->basis_ddy[dim*n]);
polynomial_compute_basis(mls->poly_degree, 0, 0, 1, &mls->xj[n], &mls->basis_ddz[dim*n]);
}
}
void polygon_clip(polygon_t* poly, polygon_t* other)
{
// Do the clipping in 2D.
point2_t pts[poly->num_vertices];
for (int i = 0; i < poly->num_vertices; ++i)
{
int I = poly->ordering[i];
plane_project(poly->plane, &poly->vertices[I], &pts[I]);
}
polygon2_t* poly2 = polygon2_new(pts, poly->num_vertices);
point2_t other_pts[other->num_vertices];
for (int i = 0; i < other->num_vertices; ++i)
{
int I = poly->ordering[i];
plane_project(other->plane, &other->vertices[I], &other_pts[I]);
}
polygon2_t* other2 = polygon2_new(other_pts, other->num_vertices);
polygon2_clip(poly2, other2);
// Now re-embed the vertices.
int num_vertices = polygon2_num_vertices(poly2);
if (poly->num_vertices < num_vertices)
poly->vertices = polymec_realloc(poly->vertices, sizeof(point_t)*num_vertices);
poly->num_vertices = num_vertices;
int pos = 0, offset = 0;
point2_t* vtx;
int* ordering2 = polygon2_ordering(poly2);
while (polygon2_next_vertex(poly2, &pos, &vtx))
{
int I = ordering2[offset++];
plane_embed(poly->plane, vtx, &poly->vertices[I]);
}
// Recompute geometry (plane remains unchanged).
compute_centroid(poly->vertices, poly->num_vertices, &poly->x0);
// Clean up.
poly2 = NULL;
other2 = NULL;
}
static int exchanger_send_message(exchanger_t* ex, void* data, mpi_message_t* msg)
{
START_FUNCTION_TIMER();
// If we are expecting data, post asynchronous receives.
int j = 0;
for (int i = 0; i < msg->num_receives; ++i)
{
ASSERT(ex->rank != msg->source_procs[i]);
int err = MPI_Irecv(msg->receive_buffers[i],
msg->stride * msg->receive_buffer_sizes[i],
msg->type, msg->source_procs[i], msg->tag, ex->comm,
&(msg->requests[j++]));
if (err != MPI_SUCCESS)
{
int resultlen;
char str[MPI_MAX_ERROR_STRING];
MPI_Error_string(err, str, &resultlen);
char err_msg[1024];
snprintf(err_msg, 1024, "%d: MPI Error posting receive from %d: %d\n(%s)\n",
ex->rank, msg->source_procs[i], err, str);
polymec_error(err_msg);
}
}
// Send the data asynchronously.
for (int i = 0; i < msg->num_sends; ++i)
{
int err = MPI_Isend(msg->send_buffers[i],
msg->stride * msg->send_buffer_sizes[i],
msg->type, msg->dest_procs[i], msg->tag, ex->comm,
&(msg->requests[j++]));
if (err != MPI_SUCCESS)
{
int resultlen;
char str[MPI_MAX_ERROR_STRING];
MPI_Error_string(err, str, &resultlen);
char err_msg[1024];
snprintf(err_msg, 1024, "%d: MPI Error sending to %d: %d\n(%s)\n",
ex->rank, msg->dest_procs[i], err, str);
polymec_error(err_msg);
}
}
msg->num_requests = j;
// Allocate a token.
int token = 0;
while ((token < ex->num_pending_msgs) && (ex->pending_msgs[token] != NULL))
++token;
if (token == ex->num_pending_msgs) ++ex->num_pending_msgs;
if (ex->num_pending_msgs == ex->pending_msg_cap)
{
ex->pending_msg_cap *= 2;
ex->pending_msgs = polymec_realloc(ex->pending_msgs, ex->pending_msg_cap*sizeof(mpi_message_t));
ex->orig_buffers = polymec_realloc(ex->orig_buffers, ex->pending_msg_cap*sizeof(void*));
ex->transfer_counts = polymec_realloc(ex->transfer_counts, ex->pending_msg_cap*sizeof(int*));
}
ex->pending_msgs[token] = msg;
ex->orig_buffers[token] = data;
STOP_FUNCTION_TIMER();
return token;
}
void polygon2_clip(polygon2_t* poly, polygon2_t* other)
{
// This implementation is based on that shown in Chapter 7.6.1 of
// Joseph O'Rourke's _Computational_Geometry_In_C_.
int a = 0, b = 0, aa = 0, ba = 0;
int n = poly->num_vertices, m = other->num_vertices;
polygon2_inout_t inflag = UNKNOWN;
static point2_t origin = {.x = 0.0, .y = 0.0};
point2_t p0; // First point.
// We'll store the coordinates of the vertices of the
// clipped polygon here.
real_slist_t* xlist = real_slist_new();
real_slist_t* ylist = real_slist_new();
do
{
// Computations of key variables.
int a1 = (a + n - 1) % n;
int b1 = (b + m - 1) % m;
int aa = poly->ordering[a];
int aa1 = poly->ordering[a1];
int bb = poly->ordering[b];
int bb1 = poly->ordering[b1];
point2_t* Pa = &poly->vertices[aa];
point2_t* Pa1 = &poly->vertices[aa1];
point2_t* Qb = &other->vertices[bb];
point2_t* Qb1 = &other->vertices[bb1];
point2_t A, B;
A.x = Pa1->x - Pa->x;
A.y = Pa1->y - Pa->y;
B.x = Qb1->x - Qb->x;
B.y = Qb1->y - Qb->y;
int cross = SIGN(triangle_area(&origin, &A, &B));
int aHB = SIGN(triangle_area(Qb1, Qb, Pa));
int bHA = SIGN(triangle_area(Pa1, Pa, Qb));
// If A and B intersect, update inflag.
point2_t p;
char code = seg_set_int(Pa1, Pa, Qb1, Qb, &p);
if ((code == '1') || (code == 'v'))
{
if ((inflag == UNKNOWN) && (real_slist_empty(xlist)))
{
aa = ba = 0;
p0.x = p.x;
p0.y = p.y;
real_slist_append(xlist, p0.x);
real_slist_append(ylist, p0.y);
}
inflag = in_out(&p, inflag, aHB, bHA, xlist, ylist);
}
// Advance rules.
else if (cross >= 0)
{
if (bHA > 0)
a = advance(a, &aa, n, (inflag == PIN), Pa, xlist, ylist);
else
b = advance(b, &ba, m, (inflag == QIN), Qb, xlist, ylist);
}
else // if (cross < 0)
{
if (aHB > 0)
b = advance(b, &ba, m, (inflag == QIN), Qb, xlist, ylist);
else
a = advance(a, &aa, n, (inflag == PIN), Pa, xlist, ylist);
}
}
while (((aa < n) || (ba < m)) && (aa < 2*n) && (ba < 2*m));
// Replace this polygon with its clipped version.
ASSERT(xlist->size > 0);
ASSERT(xlist->size == ylist->size);
if (xlist->size > poly->num_vertices)
poly->vertices = polymec_realloc(poly->vertices, sizeof(point2_t)*xlist->size);
poly->num_vertices = xlist->size;
for (int i = 0; i < xlist->size; ++i)
{
// FIXME: Verify!
poly->vertices[i].x = real_slist_pop(xlist, NULL);
poly->vertices[i].y = real_slist_pop(ylist, NULL);
}
polygon2_compute_area(poly);
// Clean up.
real_slist_free(xlist);
real_slist_free(ylist);
}
mesh_t* create_pebi_mesh(MPI_Comm comm,
point_t* cell_centers, real_t* cell_volumes, int num_cells,
int* faces, real_t* face_areas, point_t* face_centers,
int num_faces)
{
// Check input.
ASSERT(cell_centers != NULL);
ASSERT(cell_volumes != NULL);
ASSERT(num_cells > 0);
ASSERT(faces != NULL);
ASSERT(face_areas != NULL);
ASSERT(num_faces >= 0);
#ifndef NDEBUG
for (int f = 0; f < num_faces; ++f)
{
ASSERT(faces[2*f] >= 0);
ASSERT((faces[2*f+1] >= 0) || (faces[2*f+1] == -1));
}
#endif
mesh_t* mesh = mesh_new(comm, num_cells, 0, num_faces, 0);
// Transcribe the mesh cell centers, which are the only connection to
// spatial geometry.
memcpy(mesh->cell_centers, cell_centers, sizeof(point_t)*num_cells);
// Copy over the face-cell connectivity directly.
memcpy(mesh->face_cells, faces, 2*sizeof(int)*num_faces);
// Copy over the face areas directly.
memcpy(mesh->face_areas, face_areas, sizeof(real_t)*num_faces);
// Go through the list of faces and count the faces attached to each cell,
// storing the tally in the set of cell face offsets.
for (int f = 0; f < num_faces; ++f)
{
mesh->cell_face_offsets[faces[2*f]] += 1;
if (faces[2*f+1] != -1)
mesh->cell_face_offsets[faces[2*f]] += 1;
}
// Convert these face offsets to compressed row storage format.
for (int c = 1; c <= num_cells; ++c)
mesh->cell_face_offsets[c] += mesh->cell_face_offsets[c-1];
// Now fill the mesh's cell_faces array.
int* cell_face_count = polymec_malloc(sizeof(int) * num_cells);
memset(cell_face_count, 0, sizeof(int) * num_cells);
mesh->cell_faces = polymec_realloc(mesh->cell_faces, sizeof(int) * mesh->cell_face_offsets[num_cells]);
for (int f = 0; f < num_faces; ++f)
{
int c1 = faces[2*f];
mesh->cell_faces[mesh->cell_face_offsets[c1] + cell_face_count[c1]] = f;
++cell_face_count[c1];
int c2 = faces[2*f+1];
if (c2 != -1)
{
mesh->cell_faces[mesh->cell_face_offsets[c2] + cell_face_count[c2]] = f;
++cell_face_count[c2];
}
}
polymec_free(cell_face_count);
// Set the cell volumes.
memcpy(mesh->cell_volumes, cell_volumes, sizeof(real_t)*num_cells);
// Set or compute face centers.
// We compute information for interior faces first.
for (int f = 0; f < num_faces; ++f)
{
point_t* xf = &mesh->face_centers[f];
vector_t* nf = &mesh->face_normals[f];
int c1 = mesh->face_cells[2*f];
int c2 = mesh->face_cells[2*f];
if (c2 != -1) // Interior face
{
point_t* xc1 = &mesh->cell_centers[c1];
point_t* xc2 = &mesh->cell_centers[c2];
if (face_centers == NULL)
{
// Assume each face center lies at the midpoint between its cells.
xf->x = 0.5 * (xc1->x + xc2->x);
xf->y = 0.5 * (xc1->y + xc2->y);
xf->z = 0.5 * (xc1->z + xc2->z);
}
else
{
xf->x = face_centers[f].x;
xf->y = face_centers[f].y;
xf->z = face_centers[f].z;
}
// The face normal should connect xc1 and xc2.
point_displacement(xc1, xc2, nf);
vector_normalize(nf);
}
// Now use the existing information to compute information for
// boundary faces.
for (int f = 0; f < num_faces; ++f)
{
int c1 = mesh->face_cells[2*f];
int c2 = mesh->face_cells[2*f];
if (c2 == -1)
{
// Estimate the cell-face distance by assuming an isotropic cell.
real_t V = mesh->cell_volumes[c1];
real_t d = pow(V, 1.0/3.0);
// Form the normal vector for the face by assuming that all face
// normals sum to zero.
vector_t* nf = &mesh->face_normals[f];
nf->x = nf->y = nf->z = 0.0;
for (int ff = mesh->cell_face_offsets[c1]; ff < mesh->cell_face_offsets[c1+1]; ++ff)
{
vector_t* nff = &mesh->face_normals[ff];
nf->x -= nff->x;
nf->y -= nff->y;
nf->z -= nff->z;
}
// Compute the face center.
if (face_centers == NULL)
{
point_t* xc = &mesh->cell_centers[c1];
point_t* xf = &mesh->face_centers[f];
xf->x = xc->x + d*nf->x;
xf->y = xc->y + d*nf->y;
xf->z = xc->z + d*nf->z;
}
else
{
xf->x = face_centers[f].x;
xf->y = face_centers[f].y;
xf->z = face_centers[f].z;
}
}
}
}
mesh_add_feature(mesh, PEBI);
return mesh;
}