inline void print_data_to_files(double *phi, double *density, double *residual, int tl) {
double x0 = get_center_x() + tl*TAU * func_u(tl*TAU, get_center_x(), get_center_y());
double y0 = get_center_y() + tl*TAU* func_v(tl*TAU, get_center_x(), get_center_y());
print_surface("phi", NX, NY, HX, HY, tl, A, C, x0, y0, TAU, U, V, phi);
print_surface("rho", NX, NY, HX, HY, tl, A, C, x0, y0, TAU, U, V, density);
// print_surface("res", NX, NY, HX, HY, tl, A, C, get_center_x_2(), get_center_y_2(), TAU,
// U, V, residual);
double *err_lock = calc_error_2(HX, HY, tl * TAU, density);
print_surface("err-l", NX, NY, HX, HY, tl, A, C, x0, y0, TAU, U, V, err_lock);
delete[] err_lock;
}
inline static double analytical_solution_circle(double t, double x, double y) {
double x0 = get_center_x() + t * func_u(t, x, y);
double y0 = get_center_y() + t * func_v(t, x, y);
double value = (x - x0) * (x - x0) + (y - y0) * (y - y0);
if (value <= R_SQ) return INN_DENSITY;
return OUT_DENSITY;
}
float Sprite::get_distance_to(Sprite *target)
{
/*
* Calculates the distance between two sprites center positions
*/
float delta_x = get_center_x() - target->get_center_x();
float delta_y = get_center_y() - target->get_center_y();
double distance = sqrt( pow(delta_x, 2.f) + pow(delta_y, 2.f) );
return (float)distance;
}
bool GridMap::_get(const StringName &p_name, Variant &r_ret) const {
String name = p_name;
if (name == "theme") {
r_ret = get_theme();
} else if (name == "cell_size") {
r_ret = get_cell_size();
} else if (name == "cell_octant_size") {
r_ret = get_octant_size();
} else if (name == "cell_center_x") {
r_ret = get_center_x();
} else if (name == "cell_center_y") {
r_ret = get_center_y();
} else if (name == "cell_center_z") {
r_ret = get_center_z();
} else if (name == "cell_scale") {
r_ret = cell_scale;
} else if (name == "data") {
Dictionary d;
PoolVector<int> cells;
cells.resize(cell_map.size() * 3);
{
PoolVector<int>::Write w = cells.write();
int i = 0;
for (Map<IndexKey, Cell>::Element *E = cell_map.front(); E; E = E->next(), i++) {
encode_uint64(E->key().key, (uint8_t *)&w[i * 3]);
encode_uint32(E->get().cell, (uint8_t *)&w[i * 3 + 2]);
}
}
d["cells"] = cells;
r_ret = d;
} else if (name.begins_with("areas/")) {
int which = name.get_slicec('/', 1).to_int();
String what = name.get_slicec('/', 2);
if (what == "bounds")
r_ret = area_get_bounds(which);
else if (what == "name")
r_ret = area_get_name(which);
else if (what == "disable_distance")
r_ret = area_get_portal_disable_distance(which);
else if (what == "exterior_portal")
r_ret = area_is_exterior_portal(which);
else
return false;
} else
return false;
return true;
}
float Sprite::get_distance_to_edge(Sprite* target)
{
float x1 = get_center_x();
float y1 = get_center_y();
float x2 = target->get_center_x();
float y2 = target->get_center_y();
float deltaY = y1 - y2;
float deltaX = x1 - x2;
float angleInRadians = atan2(deltaY, deltaX);
float extraLength = target->get_width() / 2.f ;
double distance = sqrt(pow(deltaX, 2.f) + pow(deltaY, 2.f));
return (float)distance - extraLength;
}
bool GridMap::_get(const StringName &p_name, Variant &r_ret) const {
String name = p_name;
if (name == "theme") {
r_ret = get_theme();
} else if (name == "cell_size") {
r_ret = get_cell_size();
} else if (name == "cell_octant_size") {
r_ret = get_octant_size();
} else if (name == "cell_center_x") {
r_ret = get_center_x();
} else if (name == "cell_center_y") {
r_ret = get_center_y();
} else if (name == "cell_center_z") {
r_ret = get_center_z();
} else if (name == "cell_scale") {
r_ret = cell_scale;
} else if (name == "data") {
Dictionary d;
PoolVector<int> cells;
cells.resize(cell_map.size() * 3);
{
PoolVector<int>::Write w = cells.write();
int i = 0;
for (Map<IndexKey, Cell>::Element *E = cell_map.front(); E; E = E->next(), i++) {
encode_uint64(E->key().key, (uint8_t *)&w[i * 3]);
encode_uint32(E->get().cell, (uint8_t *)&w[i * 3 + 2]);
}
}
d["cells"] = cells;
r_ret = d;
} else
return false;
return true;
}
double *solve_2(double &tme) {
fflush(stdout);
int ic = 0;
double *phi = new double[XY];
double *prev_density = new double[XY];
double *density = new double[XY];
double *residual = new double[XY];
//<editor-fold desc="Fill initial data">
for (int i = 0; i < NX_1; ++i) {
for (int j = 0; j < NY_1; ++j) {
density[NY_1 * i + j] = 0.;
prev_density[NY_1 * i + j] = 0.;
residual[NY_1 * i + j] = 0.;
phi[NY_1 * i + j] = 0.;
}
}
// G1 -- (x_i, 0=C) -- bottom boundary
for (int i = 0; i < NX_1; ++i) {
prev_density[NY_1 * i] = analytical_solution_circle(0., A + HX * i, C);
if (fabs(prev_density[NY_1 * i]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * i] = 0;
}
// G2 -- (NX=B, y_j) -- right boundary
for (int j = 1; j < NY; ++j) {
prev_density[NY_1 * NX + j] = analytical_solution_circle(0., A + HX * NX, C + HY * j);
if (fabs(prev_density[NY_1 * NX + j]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * NX + j] = 0;
}
// G3 -- (x_i, NY=D) -- top boundary
for (int i = 0; i < NX_1; ++i) {
prev_density[NY_1 * i + NY] = analytical_solution_circle(0., A + HX * i, C + HY * NY);
if (fabs(prev_density[NY_1 * i + NY]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * i + NY] = 0;
}
// G4 -- (0=A, y_j) -- left boundary
for (int j = 1; j < NY; ++j) {
prev_density[j] = analytical_solution_circle(0., A, C + HY * j);
if (fabs(prev_density[j]) < fabs(DBL_MIN_TRIM)) prev_density[j] = 0;
}
memcpy(density, prev_density, XY * sizeof(double));
// inner points
for (int i = 1; i < NX; ++i) {
for (int j = 1; j < NY; ++j) {
prev_density[NY_1 * i + j] = analytical_solution_circle(0., A + HX * i, C + HY * j);
//if (fabs(prev_density[NY_1 * i + j]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * i + j] = 0;
}
}
//</editor-fold>
double sum_rho = calc_array_sum(prev_density, NX_1, NY_1, 0);
double sum_abs_rho = calc_array_sum(prev_density, NX_1, NY_1, 1);
printf("SUM RHO INIT = %le\n", sum_rho);
printf("SUM ABS RHO INIT= %le\n", sum_abs_rho);
fflush(stdout);
double maxRes = FLT_MAX;
double *extrems = new double[2];
double *extrems_err = new double[2];
for (int tl = 1; tl <= TIME_STEP_CNT; tl++) {
//<editor-fold desc="Calculate phi">
// with usage of prev_density we calculate phi function values
// G3 -- (x_i, NY=D) -- top boundary
for (int i = 1; i < NX; ++i) {
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(i, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(i, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(i, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(i, NY, prev_density, TAU * tl);
}
phi[NY_1 * i + NY] = integ;
}
// G2 -- (NX=B, y_j) -- right boundary
for (int j = 1; j < NY; ++j) {
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(NX, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(NX, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(NX, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(NX, j, prev_density, TAU * tl);
}
phi[NY_1 * NX + j] = integ;
}
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(NX, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(NX, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(NX, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(NX, NY, prev_density, TAU * tl);
}
// point (1,1)
phi[NY_1 * NX + NY] = integ;
// inner points
for (int i = 1; i < NX; ++i)
for (int j = 1; j < NY; ++j) {
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(i, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(i, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(i, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(i, j, prev_density, TAU * tl);
}
phi[NY_1 * i + j] = integ;
}
//</editor-fold>
ic = 0;
double maxErr = FLT_MAX;
while (((maxErr > EPS) || (maxRes > RES_EPS)) && (ic < NX_1 * NY_1)) {
//<editor-fold desc="Calculate density">
// point 1,1
double rpCoef = 64. / (9. * HX * HY);
density[NY_1 * NX + NY] = -1. / 3. * (prev_density[NY_1 * NX + NY - 1]
+ prev_density[NY_1 * (NX - 1) + NY])
- 1. / 9. * prev_density[NY_1 * (NX - 1) + NY - 1]
+ rpCoef * phi[NY_1 * NX + NY];
if (fabs(density[NY_1 * NX + NY]) < fabs(DBL_MIN_TRIM)) density[NY_1 * NX + NY] = 0;
// G3 -- (x_i, NY=D) -- top boundary
rpCoef = 32. / (9. * HX * HY);
for (int i = 1; i < NX; ++i) {
density[NY_1 * i + NY] = -1. / 3. * prev_density[NY_1 * i + NY - 1]
- 1. / 6. * (prev_density[NY_1 * (i + 1) + NY] +
prev_density[NY_1 * (i - 1) + NY])
- 1. / 18. * (prev_density[NY_1 * (i + 1) + NY - 1] +
prev_density[NY_1 * (i - 1) + NY - 1])
+ rpCoef * phi[NY_1 * i + NY];
if (fabs(density[NY_1 * i + NY]) < fabs(DBL_MIN_TRIM)) density[NY_1 * i + NY] = 0;
}
// G2 -- (NX=B, y_j) -- right boundary
rpCoef = 32. / (9. * HX * HY);
for (int j = 1; j < NY; ++j) {
density[NY_1 * NX + j] = -1. / 3. * prev_density[NY_1 * (NX - 1) + j]
- 1. / 6. * (prev_density[NY_1 * NX + j - 1] +
prev_density[NY_1 * NX + j + 1])
- 1. / 18. * (prev_density[NY_1 * (NX - 1) + j - 1] +
prev_density[NY_1 * (NX - 1) + j + 1])
+ rpCoef * phi[NY_1 * NX + j];
if (fabs(density[NY_1 * NX + j]) < fabs(DBL_MIN_TRIM)) density[NY_1 * NX + j] = 0;
}
rpCoef = 16. / (9. * HX * HY);
for (int i = 1; i < NX; ++i) {
for (int j = 1; j < NY; ++j) {
density[NY_1 * i + j] = -1. / 6. * (
prev_density[NY_1 * i + j - 1] + // left
prev_density[NY_1 * (i - 1) + j] + // upper
prev_density[NY_1 * i + j + 1] + // right
prev_density[NY_1 * (i + 1) + j] // bottom
) - 1. / 36. * (
prev_density[NY_1 * (i + 1) + j + 1] + // bottom right
prev_density[NY_1 * (i + 1) + j - 1] + // bottom left
prev_density[NY_1 * (i - 1) + j + 1] + // upper right
prev_density[NY_1 * (i - 1) + j - 1] // upper left
) + rpCoef * phi[NY_1 * i + j];
if (fabs(density[NY_1 * i + j]) < fabs(DBL_MIN_TRIM)) density[NY_1 * i + j] = 0;
}
}
++ic;
maxErr = FLT_MIN;
for (int i = 0; i < NX_1; ++i)
for (int j = 0; j < NY_1; ++j) {
double val = fabs(density[i * NY_1 + j] - prev_density[i * NY_1 + j]);
if (val > maxErr) maxErr = val;
}
//</editor-fold>
//<editor-fold desc="Calculate residual">
// point 1,1
rpCoef = HX * HY / 64.;
residual[NY_1 * NX + NY] = rpCoef * (
9. * density[NY_1 * NX + NY] +
3. * (
density[NY_1 * NX + NY - 1] +
density[NY_1 * (NX - 1) + NY]
) +
density[NY_1 * (NX - 1) + NY - 1]
) - phi[NY_1 * NX + NY];
// G3 -- (x_i, NY=D) -- top boundary
for (int i = 1; i < NX; ++i)
residual[NY_1 * i + NY] = rpCoef * (
18. * density[NY_1 * i + NY] +
6. * density[NY_1 * i + NY - 1] +
3. * (
density[NY_1 * (i + 1) + NY] +
density[NY_1 * (i - 1) + NY]
) +
density[NY_1 * (i + 1) + NY - 1] +
density[NY_1 * (i - 1) + NY - 1]
) - phi[NY_1 * i + NY];
// G2 -- (NX=B, y_j) -- right boundary
for (int j = 1; j < NY; ++j)
residual[NY_1 * NX + j] = rpCoef * (
18. * density[NY_1 * NX + j] +
6. * density[NY_1 * (NX - 1) + j] +
3. * (
density[NY_1 * NX + j - 1] +
density[NY_1 * NX + j + 1]
) +
density[NY_1 * (NX - 1) + j - 1] +
density[NY_1 * (NX - 1) + j + 1]
) - phi[NY_1 * NX + j];
// inner points
for (int i = 1; i < NX; ++i) {
for (int j = 1; j < NY; ++j) {
residual[NY_1 * i + j] = rpCoef * (
36. * density[NY_1 * i + j] +
6. * (
density[NY_1 * i + j - 1] + // left
density[NY_1 * (i - 1) + j] + // upper
density[NY_1 * i + j + 1] + // right
density[NY_1 * (i + 1) + j] // bottom
) +
prev_density[NY_1 * (i + 1) + j + 1] + // bottom right
prev_density[NY_1 * (i + 1) + j - 1] + // bottom left
prev_density[NY_1 * (i - 1) + j + 1] + // upper right
prev_density[NY_1 * (i - 1) + j - 1] // upper left
) - phi[NY_1 * i + j];
}
}
maxRes = FLT_MIN;
for (int i = 0; i < NX_1; ++i) {
for (int j = 0; j < NY_1; ++j) {
double val = fabs(residual[i * NY_1 + j]);
if (val > maxRes) maxRes = val;
}
}
//</editor-fold>
memcpy(prev_density, density, XY * sizeof(double));
}
sum_rho = calc_array_sum(density, NX_1, NY_1, 0);
sum_abs_rho = calc_array_sum(density, NX_1, NY_1, 1);
extrems = calc_array_extrems(density, NX_1, NY_1);
printf("tl = %d IterCount = %d Max(Residual) = %le Sum(Rho) = %le Sum(absRho) = %le "
"Min(Rho) = %le Max(Rho) = %le\n",
tl, ic, maxRes, sum_rho, sum_abs_rho, extrems[0], extrems[1]);
fflush(stdout);
if (tl % 1 == 0) {
print_data_to_files(phi, density, residual, tl);
double x_0 = get_center_x() + tl * TAU * func_u(0, 0, 0);
double y_0 = get_center_y() + tl * TAU * func_v(0, 0, 0);
int fixed_x = (int) (x_0 / HX);
int fixed_y = (int) (y_0 / HY);
print_line_along_x("rho", NX, NY, HX, HY, tl, A, C, x_0, y_0, TAU,
U, V, density, fixed_y);
print_line_along_y("rho", NX, NY, HX, HY, tl, A, C, x_0, y_0, TAU,
U, V, density, fixed_x);
}
}
double x_0 = get_center_x() + TIME_STEP_CNT * TAU * func_u(0, 0, 0);
double y_0 = get_center_y() + TIME_STEP_CNT * TAU * func_v(0, 0, 0);
int fixed_x = (int) (x_0 / HX);
int fixed_y = (int) (y_0 / HY);
/* print_line_along_x("rho", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, density, fixed_y);
print_line_along_y("rho", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, density, fixed_x);
*/
double *err = calc_error_22(HX, HY, TAU * TIME_STEP_CNT, density);
print_line_along_x("err", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, err, fixed_y);
print_line_along_y("err", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, err, fixed_x);
extrems_err = calc_array_extrems(err, NX_1, NY_1);
err = calc_error_2(HX, HY, TAU * TIME_STEP_CNT, density);
double l1_err_vec = get_l1_norm_vec(NX_1, NY_1, err);
double l1_err_tr = get_l1_norm_int_trapezoidal(HX, HY, NX, NY, err); // note! a loop boundary
extrems = calc_array_extrems(density, NX_1, NY_1);
append_statistics(NX_1, NY_1, TAU, ic, l1_err_vec, l1_err_tr, maxRes, extrems, extrems_err, TIME_STEP_CNT);
delete[] prev_density;
delete[] phi;
delete[] err;
delete[] residual;
delete[] extrems;
delete[] extrems_err;
return density;
}
