QImage CurveTransform::transform() {
for(unsigned int i = 0; i < image_width; i++) {
for(unsigned int j = 0; j < image_height; j++) {
CartesianPair coords = {i, j};
drawPixels(convertToPixels(convertToCartesian(convertToPolar(coords))),coords); //Lisp, eat your heart out
}
}
return out_image;
}
vector geodesicSolidBodyVelocityField::streamfunctionAt
(
const point& p,
const Time& t
) const
{
const dimensionedScalar T = (endTime.value() == -1 ) ? t.endTime() : endTime;
const scalar u0 = 2 * M_PI * radius.value() / T.value();
const polarPoint& polarp = convertToPolar(p);
const scalar lat = polarp.lat();
const scalar lon = polarp.lon();
const scalar psi = - u0 * (Foam::sin(lat) * Foam::cos(alpha) - Foam::cos(lon) * Foam::cos(lat) * Foam::sin(alpha));
return p/mag(p) * psi * radius.value();
}
point geodesicSolidBodyVelocityField::initialPositionOf
(
const point& p,
const Time& t
) const
{
// assume alpha = 0
const dimensionedScalar T = (endTime.value() == -1 ) ? t.endTime() : endTime;
const scalar u0 = 2 * M_PI * radius.value() / T.value();
const polarPoint& polarp = convertToPolar(p);
const scalar lat = polarp.lat();
scalar lon = polarp.lon();
lon -= u0/radius.value() * t.value();
const polarPoint departureP(lon, lat, radius.value());
return departureP.cartesian();
}
/**
* Find the equilibrium after placing the cylinders in the domain somewhere.
* Iterates until tolerence is met.
*/
void SwarmCylinders::findEquilibrium()
{
double dalpha = 2.0 * M_PI / (double) M;
vector<double> m;
for (int i = 0; i < M; i++)
{
m.push_back(spline.evaluate(i * dalpha) * dalpha); /// assuming constant density charge on boundary
}
vector<double> xs;
vector<double> ys;
for (int i = 0; i < M; i++)
{
xs.push_back(spline.evaluate(((double) i + 0.5) * dalpha));
ys.push_back(((double) i + 0.5) * dalpha);
}
convertToCartesian(xs, ys);
int nIter = 0;
bool steadyState = false;
while (!steadyState)
{
vector<double> xNew;
vector<double> yNew;
const int xsize = x.size();
for (int i = 0; i < xsize; i++)
{
xNew.push_back(0.0);
yNew.push_back(0.0);
}
for (int i = 0; i < xsize; i++)
{
double u = 0.0;
double v = 0.0;
for (int j = 0; j < xsize; j++) /// from each body
{
if (i != j)
{
double norm = sqrt((x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]));
double factor = factorCylinder / (norm * norm * norm);
u += (x[i] - x[j]) * factor;
v += (y[i] - y[j]) * factor;
}
}
for (int j = 0; j < M; j++) /// from boundary
{
double norm = sqrt((x[i] - xs[j]) * (x[i] - xs[j]) + (y[i] - ys[j]) * (y[i] - ys[j]));
double factor = factorBoundary * m[j] / (norm * norm * norm);
u += (x[i] - xs[j]) * factor;
v += (y[i] - ys[j]) * factor;
}
xNew[i] = x[i] + dt * u;
yNew[i] = y[i] + dt * v;
}
convertToPolar(xNew, yNew);
for (int i = 0; i < xsize; i++)
{
const double rMax = spline.evaluate(yNew[i]) - radius;
if (rMax < xNew[i])
xNew[i] = 0.1 * rMax; /// move it toward (0,0)
// xNew[i] = min(spline.evaluate(yNew[i])-radius, xNew[i]); /// make it sit on the boundary if it is not repelled enough (not exactly correct)
}
convertToCartesian(xNew, yNew);
double maxNorm = 0.0;
for (int i = 0; i < xsize; i++)
{
double norm = sqrt((xNew[i] - x[i]) * (xNew[i] - x[i]) + (yNew[i] - y[i]) * (yNew[i] - y[i])); /// relative difference
maxNorm = max(norm, maxNorm);
}
for (int i = 0; i < xsize; i++)
{
x[i] = xNew[i];
y[i] = yNew[i];
}
// TODO Remove this testing shit, writing the positions each iteration
if (nIter % 10 == 0)
{
FILE* fidx;
FILE* fidy;
if (nIter == 0)
{
fidx = fopen("x.txt", "w");
fidy = fopen("y.txt", "w");
}
else
{
fidx = fopen("x.txt", "a");
fidy = fopen("y.txt", "a");
}
const int xsize = x.size();
for (int i = 0; i < xsize; ++i)
{
fprintf(fidx, "%e ", x[i]);
fprintf(fidy, "%e ", y[i]);
}
fprintf(fidx, "\n");
fprintf(fidy, "\n");
fclose(fidx);
fclose(fidy);
}
nIter++;
if (maxNorm <= threshold)
break;
if (nIter % 5000 == 0)
printf("** Norm at iteration %d: %e\n", nIter, maxNorm);
if (nIter > 50000)
{
printf("** Something is wrong, swarm shape is not converging quickly enough... aborting... \n");
abort();
}
}
printf("** Number of iterations to steady state formation: %d\n", nIter);
}