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YouTube-simulations/sub_rde.c

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double courant2; /* Courant parameter squared */
double dx2; /* spatial step size squared */
double intstep; /* integration step */
double intstep1; /* integration step used in absorbing boundary conditions */
double viscosity; /* viscosity (parameter in front of Laplacian) */
double rpslzb; /* second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
double gaussian()
/* returns standard normal random variable, using Box-Mueller algorithm */
{
static double V1, V2, S;
static int phase = 0;
double X;
if (phase == 0)
{
do
{
double U1 = (double)rand() / RAND_MAX;
double U2 = (double)rand() / RAND_MAX;
V1 = 2 * U1 - 1;
V2 = 2 * U2 - 1;
S = V1 * V1 + V2 * V2;
}
while(S >= 1 || S == 0);
X = V1 * sqrt(-2 * log(S) / S);
}
else X = V2 * sqrt(-2 * log(S) / S);
phase = 1 - phase;
return X;
}
void init_random(double mean, double amplitude, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with gaussian at position (x,y) */
{
int i, j, k, in;
double xy[2], dist2, module, phase, scale2;
printf("Initialising xy_in\n");
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++)
{
if (i%100 == 0) printf("Column %i of %i\n", i, NX);
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
}
}
printf("Initialising fields\n");
for (k=0; k<NFIELDS; k++)
for (i=0; i<NX; i++)
{
if (i%100 == 0) printf("Field %i of %i, column %i of %i\n", k, NFIELDS, i, NX);
for (j=0; j<NY; j++)
{
if (xy_in[i*NY+j]) phi[k][i*NY+j] = mean + amplitude*(2.0*(double)rand()/RAND_MAX - 1.0);
else phi[k][i*NY+j] = 0.0;
}
}
printf("Fields initialised\n");
}
void init_gaussian(double x, double y, double mean, double amplitude, double scalex,
double *phi[NX], short int xy_in[NX*NY])
/* initialise field with gaussian at position (x,y) */
{
int i, j, in;
double xy[2], dist2, module, phase, scale2;
scale2 = scalex*scalex;
printf("Initialising field\n");
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
in = xy_in[i*NY+j];
if (in == 1)
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = amplitude*exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phi[i][j] = mean + module/scalex;
} /* boundary temperatures */
else if (in >= 2) phi[i][j] = T_IN*pow(0.75, (double)(in-2));
// else if (in >= 2) phi[i][j] = T_IN*pow(1.0 - 0.5*(double)(in-2), (double)(in-2));
// else if (in >= 2) phi[i][j] = T_IN*(1.0 - (double)(in-2)/((double)MDEPTH))*(1.0 - (double)(in-2)/((double)MDEPTH));
else phi[i][j] = T_OUT;
}
}
void init_coherent_state(double x, double y, double px, double py, double scalex, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with coherent state of position (x,y) and momentum (px, py) */
/* phi[0] is real part, phi[1] is imaginary part */
{
int i, j;
double xy[2], dist2, module, phase, scale2;
scale2 = scalex*scalex;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = (px*(xy[0]-x) + py*(xy[1]-y))/scalex;
phi[0][i*NY+j] = module*cos(phase);
phi[1][i*NY+j] = module*sin(phase);
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void add_coherent_state(double x, double y, double px, double py, double scalex, double *phi[NFIELDS], short int xy_in[NX*NY])
/* add to the field a coherent state of position (x,y) and momentum (px, py) */
/* phi[0] is real part, phi[1] is imaginary part */
{
int i, j;
double xy[2], dist2, module, phase, scale2;
scale2 = scalex*scalex;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = (px*(xy[0]-x) + py*(xy[1]-y))/scalex;
phi[0][i*NY+j] += module*cos(phase);
phi[1][i*NY+j] += module*sin(phase);
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void init_fermion_state(double x, double y, double px, double py, double scalex, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with antisymmetric coherent state of position (x,y) and momentum (px, py) */
/* phi[0] is real part, phi[1] is imaginary part */
{
int i, j;
double xy[2], dist2, module, phase, scale2;
scale2 = scalex*scalex;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = (px*(xy[0]-x) + py*(xy[1]-y))/scalex;
phi[0][i*NY+j] = module*cos(phase);
phi[1][i*NY+j] = module*sin(phase);
/* antisymmetrize wave function */
dist2 = (xy[1]-x)*(xy[1]-x) + (xy[0]-y)*(xy[0]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = (px*(xy[1]-x) + py*(xy[0]-y))/scalex;
phi[0][i*NY+j] -= module*cos(phase);
phi[1][i*NY+j] -= module*sin(phase);
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void init_boson_state(double x, double y, double px, double py, double scalex, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with symmetric coherent state of position (x,y) and momentum (px, py) */
/* phi[0] is real part, phi[1] is imaginary part */
{
int i, j;
double xy[2], dist2, module, phase, scale2;
scale2 = scalex*scalex;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = (px*(xy[0]-x) + py*(xy[1]-y))/scalex;
phi[0][i*NY+j] = module*cos(phase);
phi[1][i*NY+j] = module*sin(phase);
/* symmetrize wave function */
dist2 = (xy[1]-x)*(xy[1]-x) + (xy[0]-y)*(xy[0]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = (px*(xy[1]-x) + py*(xy[0]-y))/scalex;
phi[0][i*NY+j] += module*cos(phase);
phi[1][i*NY+j] += module*sin(phase);
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void init_fermion_state2(double x, double y, double px, double py, double scalex, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with antisymmetric coherent state of position (x,y) and momentum (px, py) */
/* phi[0] is real part, phi[1] is imaginary part */
{
int i, j;
double xy[2], dist2, module, phase, scale2, fx[2], fy[2], gx[2], gy[2];
scale2 = scalex*scalex;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = px*(xy[0]-x)/scalex;
fx[0] = module*cos(phase);
fx[1] = module*sin(phase);
dist2 = (xy[0]-y)*(xy[0]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = px*(xy[0]-y)/scalex;
fy[0] = module*cos(phase);
fy[1] = module*sin(phase);
dist2 = (xy[1]-x)*(xy[1]-x);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = py*(xy[1]-x)/scalex;
gx[0] = module*cos(phase);
gx[1] = module*sin(phase);
dist2 = (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/scale2);
if (module < 1.0e-15) module = 1.0e-15;
phase = py*(xy[1]-y)/scalex;
gy[0] = module*cos(phase);
gy[1] = module*sin(phase);
phi[0][i*NY+j] = 0.5*(fx[0]*gy[0] - gx[0]*fy[0]);
phi[1][i*NY+j] = 0.5*(fx[1]*gy[1] - gx[1]*fy[1]);
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void antisymmetrize_wave_function(double *phi[NFIELDS], short int xy_in[NX*NY])
/* force the wave function to be antisymmetric, for simulations of fermions */
{
int i, j, k;
#pragma omp parallel for private(i,j,k)
for (i=0; i<NX; i++)
for (j=0; j<=i; j++) if ((j<NY)&&(xy_in[i*NY+j]))
for (k=0; k<2; k++)
{
phi[k][i*NY+j] = 0.5*(phi[k][i*NY+j] - phi[k][j*NY+i]);
phi[k][j*NY+i] = -phi[k][i*NY+j];
}
}
void init_vortex_state(double x, double y, double scale, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with vortex at position (x,y) with variance scale */
/* phi[0] is stream function, phi[1] is vorticity */
{
int i, j;
double xy[2], dist2, module, phase, scale2, sign;
// scale2 = scale*scale;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/vabs(scale));
if (scale > 0.0) sign = 1.0;
else sign = -1.0;
phi[1][i*NY+j] += sign*module;
phi[0][i*NY+j] -= sign*module; /* approximate, stream function should solve Poisson equation */
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void add_vortex_state(double x, double y, double scale, double *phi[NFIELDS], short int xy_in[NX*NY])
/* add vortex at position (x,y) with variance scale to field */
/* phi[0] is stream function, phi[1] is vorticity */
{
int i, j;
double xy[2], dist2, module, phase, scale2, sign;
// scale2 = scale*scale;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if (xy_in[i*NY+j])
{
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
module = exp(-dist2/vabs(scale));
if (scale > 0.0) sign = 1.0;
else sign = -1.0;
phi[1][i*NY+j] += sign*module;
phi[0][i*NY+j] -= sign*module; /* approximate, stream function should solve Poisson equation */
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void init_shear_flow(double amp, double delta, double rho, int nx, int ny, double yshift, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with a shear flow */
/* phi[0] is stream function, phi[1] is vorticity */
/* amp is global amplitude */
/* delta is the amplitude of the periodic perturbation in the x direction */
/* rho controls the size of the transition zone in the y direction */
/* nx is number of oscillations in x direction */
/* ny is number of layers in y direction */
{
int i, j;
double xy[2], y1, a, b, f, cplus, cminus;
a = (double)nx*DPI/(XMAX - XMIN);
b = 0.5;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
y1 = xy[1]*(double)ny/YMAX - yshift;
while (y1 > 1.0) y1 -= 2.0;
while (y1 < -1.0) y1 += 2.0;
if (xy_in[i*NY+j])
{
f = delta*cos(a*xy[0]);
cplus = cosh((y1 + b)/rho);
cminus = cosh((y1 - b)/rho);
if (y1 > 0.0)
{
phi[1][i*NY+j] = amp*(f + 1.0/(rho*cminus*cminus));
phi[0][i*NY+j] = amp*(f/(a*a) + rho/(cminus*cminus));
}
else
{
phi[1][i*NY+j] = amp*(f - 1.0/(rho*cplus*cplus));
phi[0][i*NY+j] = amp*(f/(a*a) - rho/(cplus*cplus));
}
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
void init_laminar_flow(double amp, double modulation, double period, double yshift, double *phi[NFIELDS], short int xy_in[NX*NY])
/* initialise field with a laminar flow in x direction */
/* phi[0] is stream function, phi[1] is vorticity */
/* amp is global amplitude */
{
int i, j;
double xy[2], y1, a, b, f, cplus, cminus;
a = period*PI/YMAX;
// a = PID/YMAX;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
y1 = xy[1] + yshift;
if (xy_in[i*NY+j])
{
phi[0][i*NY+j] = amp*(y1 + modulation*sin(a*y1)/a);
phi[1][i*NY+j] = amp*modulation*a*sin(a*y1);
// phi[0][i*NY+j] = amp*sin(a*xy[1]);
// phi[1][i*NY+j] = a*a*amp*sin(a*xy[1]);
}
else
{
phi[0][i*NY+j] = 0.0;
phi[1][i*NY+j] = 0.0;
}
}
}
/*********************/
/* animation part */
/*********************/
double wrap_angle(double angle)
{
if (angle < 0.0) return(angle + DPI);
else if (angle >= DPI) return (angle - DPI);
else return(angle);
}
double unwrap_angle(double angle1, double angle2)
{
if (angle2 - angle1 < -PI) return(angle2 + DPI);
else if (angle2 - angle1 >= PI) return (angle2 - DPI);
else return(angle2);
}
void compute_theta(double *phi[NFIELDS], short int xy_in[NX*NY], t_rde rde[NX*NY])
/* compute angle for rock-paper-scissors equation */
{
int i, j;
double u, v, w, rho, xc, yc, angle;
#pragma omp parallel for private(i,j,u, v, w, rho, xc, yc, angle)
for (i=0; i<NX; i++) for (j=0; j<NY; j++)
if (xy_in[i*NY+j])
{
u = phi[0][i*NY+j];
v = phi[1][i*NY+j];
w = phi[2][i*NY+j];
rho = u + v + w;
u = u/rho;
v = v/rho;
yc = 0.5*(v - 1.0/3.0);
xc = u - 1.0/3.0 + yc;
yc *= sqrt(3.0);
angle = argument(xc, yc);
if (angle < 0.0) angle += DPI;
if (angle >= DPI) angle -= DPI;
rde[i*NY+j].theta = angle;
}
else rde[i*NY+j].theta = 0.0;
}
double colors_rpslz(int type)
{
switch (type) {
case (0): return(0.0);
case (1): return(60.0);
case (2): return(120.0);
case (3): return(200.0);
case (4): return(270.0);
}
}
void compute_theta_rpslz(double *phi[NFIELDS], short int xy_in[NX*NY], t_rde rde[NX*NY], int cplot)
/* compute angle for rock-paper -scissors-lizard-Spock equation */
{
int i, j, k, kmax;
double rho, xc, yc, angle, max;
static double sa[5], ca[5], shift;
static int first = 1;
if (first)
{
// shift = 0.0;
for (i = 0; i < 5; i++)
{
ca[i] = cos(colors_rpslz(i)*DPI/360.0);
sa[i] = sin(colors_rpslz(i)*DPI/360.0);
// ca[i] = cos(shift + 0.2*DPI*(double)i);
// sa[i] = sin(shift + 0.2*DPI*(double)i);
}
first = 0;
}
switch (cplot) {
case (Z_MAXTYPE_RPSLZ):
{
#pragma omp parallel for private(i,j,max,kmax)
for (i=0; i<NX; i++) for (j=0; j<NY; j++)
{
if (xy_in[i*NY+j])
{
max = 0.0;
kmax = 0;
for (k=0; k<5; k++)
{
if (phi[k][i*NY+j] > max)
{
max = phi[k][i*NY+j];
kmax = k;
}
}
angle = colors_rpslz(kmax);
rde[i*NY+j].theta = angle;
}
else rde[i*NY+j].theta = 0.0;
}
break;
}
// case (Z_THETA_RPSLZ):
default:
{
#pragma omp parallel for private(i,j,rho,xc,yc,angle)
for (i=0; i<NX; i++) for (j=0; j<NY; j++)
{
if (xy_in[i*NY+j])
{
xc = 0.0;
yc = 0.0;
for (k=0; k<5; k++)
{
xc += phi[k][i*NY+j]*ca[k];
yc += phi[k][i*NY+j]*sa[k];
}
angle = argument(xc, yc);
if (angle < 0.0) angle += DPI;
if (angle >= DPI) angle -= DPI;
rde[i*NY+j].theta = angle;
}
else rde[i*NY+j].theta = 0.0;
}
break;
}
}
}
void compute_gradient_xy(double phi[NX*NY], double gradient[2*NX*NY])
/* compute the gradient of the field */
{
int i, j, iplus, iminus, jplus, jminus, padding = 0;
double deltaphi, maxgradient = 1.0e10;
double dx = (XMAX-XMIN)/((double)NX);
dx = (XMAX-XMIN)/((double)NX);
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,deltaphi)
for (i=1; i<NX-1; i++)
for (j=1; j<NY-1; j++)
{
iplus = i+1;
iminus = i-1;
jplus = j+1;
jminus = j-1;
deltaphi = phi[iplus*NY+j] - phi[iminus*NY+j];
if (vabs(deltaphi) < maxgradient) gradient[i*NY+j] = (deltaphi)/dx;
else gradient[i*NY+j] = 0.0;
deltaphi = phi[i*NY+jplus] - phi[i*NY+jminus];
if (vabs(deltaphi) < maxgradient) gradient[NX*NY+i*NY+j] = (deltaphi)/dx;
else gradient[NX*NY+i*NY+j] = 0.0;
}
/* boundaries */
for (i=0; i<NX; i++)
{
gradient[i*NY] = 0.0;
gradient[NX*NY+i*NY] = 0.0;
gradient[i*NY+NY-1] = 0.0;
gradient[NX*NY+i*NY+NY-1] = 0.0;
}
for (j=1; j<NY-1; j++)
{
gradient[j] = 0.0;
gradient[(NX-1)*NY+j] = 0.0;
gradient[NX*NY+j] = 0.0;
gradient[NX*NY+(NX-1)*NY+j] = 0.0;
}
}
void compute_gradient_euler(double phi[NX*NY], double gradient[2*NX*NY], double yshift)
/* compute the gradient of the field */
{
int i, j, iplus, iminus, jplus, jminus, padding = 0;
double deltaphi, maxgradient = 1.0e10;
double dx = (XMAX-XMIN)/((double)NX);
dx = (XMAX-XMIN)/((double)NX);
// #pragma omp parallel for private(i)
// for (i=0; i<2*NX*NY; i++) gradient[i] = 0.0;
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus)
for (i=1; i<NX-1; i++)
for (j=1; j<NY-1; j++)
{
iplus = i+1;
iminus = i-1;
jplus = j+1;
jminus = j-1;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus]);
}
/* boundaries */
for (i=1; i<NX-1; i++)
{
iplus = i+1;
iminus = i-1;
j = 0;
jplus = 1;
jminus = NY-1;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus] - yshift);
// if (i == 1) printf("psi+ = %.5lg, psi- = %.5lg, gradient = %.5lg\n", phi[i*NY+jplus], phi[i*NY+jminus], gradient[NX*NY+i*NY+j]);
j = NY-1;
jplus = 0;
jminus = NY-2;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus] + yshift);
}
for (j=1; j<NY-1; j++)
{
jplus = j+1;
jminus = j-1;
i = 0;
iplus = 1;
iminus = NX-1;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus]);
// printf("j = %i, psi+ = %.5lg, psi- = %.5lg, gradient = %.5lg\n", j, phi[i*NY+jplus], phi[i*NY+jminus], gradient[NX*NY+i*NY+j]);
i = NX-1;
iplus = 0;
iminus = NX-2;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus]);
}
/* corners */
i = 0; iplus = 1; iminus = NX-1;
j = 0; jplus = 1; jminus = NY-1;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus] + yshift);
j = NY-1; jplus = 0; jminus = NY-2;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus] - yshift);
i = NX-1; iplus = 0; iminus = NX-2;
j = 0; jplus = 1; jminus = NY-1;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus] + yshift);
j = NY-1; jplus = 0; jminus = NY-2;
gradient[i*NY+j] = 0.5*(phi[iplus*NY+j] - phi[iminus*NY+j]);
gradient[NX*NY+i*NY+j] = 0.5*(phi[i*NY+jplus] - phi[i*NY+jminus] - yshift);
}
void compute_gradient_rde(double phi[NX*NY], t_rde rde[NX*NY])
/* compute the gradient of the field */
{
int i, j, iplus, iminus, jplus, jminus;
double deltaphi;
double dx = (XMAX-XMIN)/((double)NX);
dx = (XMAX-XMIN)/((double)NX);
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,deltaphi)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
iplus = i+1; if (iplus == NX) iplus = 0;
iminus = i-1; if (iminus == -1) iminus = NX-1;
jplus = j+1; if (jplus == NX) jplus = 0;
jminus = j-1; if (jminus == -1) jminus = NY-1;
deltaphi = phi[iplus*NY+j] - phi[iminus*NY+j];
if (deltaphi < -PI) deltaphi += DPI;
if (deltaphi > PI) deltaphi -= DPI;
if (vabs(deltaphi) < 1.0e9) rde[i*NY+j].nablax = (deltaphi)/dx;
else rde[i*NY+j].nablax = 0.0;
deltaphi = phi[i*NY+jplus] - phi[i*NY+jminus];
if (deltaphi < -PI) deltaphi += DPI;
if (deltaphi > PI) deltaphi -= DPI;
if (vabs(deltaphi) < 1.0e9) rde[i*NY+j].nablay = (deltaphi)/dx;
else rde[i*NY+j].nablay = 0.0;
/* TO DO: improve this computation */
rde[i*NY+j].field_norm = module2(rde[i*NY+j].nablax,rde[i*NY+j].nablay);
rde[i*NY+j].field_arg = argument(rde[i*NY+j].nablax,rde[i*NY+j].nablay);
}
}
void compute_gradient_theta(t_rde rde[NX*NY])
/* compute the gradient of the theta field */
{
int i, j, iplus, iminus, jplus, jminus;
double deltaphi;
double dx = (XMAX-XMIN)/((double)NX);
dx = (XMAX-XMIN)/((double)NX);
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,deltaphi)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
iplus = i+1; if (iplus == NX) iplus = 0;
iminus = i-1; if (iminus == -1) iminus = NX-1;
jplus = j+1; if (jplus == NX) jplus = 0;
jminus = j-1; if (jminus == -1) jminus = NY-1;
deltaphi = rde[iplus*NY+j].theta - rde[iminus*NY+j].theta;
if (deltaphi < -PI) deltaphi += DPI;
if (deltaphi > PI) deltaphi -= DPI;
if (vabs(deltaphi) < 1.0e9) rde[i*NY+j].nablax = (deltaphi)/dx;
else rde[i*NY+j].nablax = 0.0;
deltaphi = rde[i*NY+jplus].theta - rde[i*NY+jminus].theta;
if (deltaphi < -PI) deltaphi += DPI;
if (deltaphi > PI) deltaphi -= DPI;
if (vabs(deltaphi) < 1.0e9) rde[i*NY+j].nablay = (deltaphi)/dx;
else rde[i*NY+j].nablay = 0.0;
}
}
void compute_curl(t_rde rde[NX*NY])
/* compute the curl of the field */
{
int i, j, iplus, iminus, jplus, jminus;
double delta;
double dx = (XMAX-XMIN)/((double)NX);
dx = (XMAX-XMIN)/((double)NX);
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
iplus = i+1; if (iplus == NX) iplus = 0;
iminus = i-1; if (iminus == -1) iminus = NX-1;
jplus = j+1; if (jplus == NX) jplus = 0;
jminus = j-1; if (jminus == -1) jminus = NY-1;
delta = (rde[i*NY+jplus].nablay - rde[i*NY+jminus].nablay - (rde[iplus*NY+j].nablax - rde[iminus*NY+j].nablax))/dx;
if (vabs(delta)*CURL_SCALE < 1.0e8) rde[i*NY+j].curl = CURL_SCALE*delta;
else rde[i*NY+j].curl = 0.0;
}
}
void compute_gradient_polar(t_rde rde[NX*NY], double factor)
/* compute the norm of the gradient field */
{
int i, j;
double angle;
#pragma omp parallel for private(i,j,angle)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
rde[i*NY+j].field_norm = factor*module2(rde[i*NY+j].nablax, rde[i*NY+j].nablay);
angle = argument(rde[i*NY+j].nablax, rde[i*NY+j].nablay) + PI*COLOR_PHASE_SHIFT;
if (angle < 0.0) angle += DPI;
if (angle >= DPI) angle -= DPI;
rde[i*NY+j].field_arg = angle;
}
}
void compute_field_module(double *phi[NFIELDS], t_rde rde[NX*NY], double factor)
/* compute the norm squared of first two fields */
{
int i, j;
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
rde[i*NY+j].field_norm = factor*(phi[0][i*NY+j]*phi[0][i*NY+j] + phi[1][i*NY+j]*phi[1][i*NY+j]);
}
}
void compute_field_argument(double *phi[NFIELDS], t_rde rde[NX*NY])
/* compute the norm squared of first two fields */
{
int i, j;
double arg;
#pragma omp parallel for private(i,j,arg)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
arg = argument(phi[0][i*NY+j], phi[1][i*NY+j]) + COLOR_PHASE_SHIFT*PI;
while (arg < 0.0) arg += DPI;
while (arg >= DPI) arg -= DPI;
rde[i*NY+j].field_arg = arg;
}
}
void compute_field_log(double *phi[NFIELDS], t_rde rde[NX*NY])
/* compute the norm squared of first two fields */
{
int i, j;
double value;
#pragma omp parallel for private(i,j,value)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
value = vabs(phi[1][i*NY+j]);
if (value < LOG_MIN) value = LOG_MIN;
rde[i*NY+j].log_vorticity = LOG_SHIFT + LOG_SCALE*log(value);
}
}
void compute_probabilities(t_rde rde[NX*NY], short int xy_in[NX*NY], double probas[2])
/* compute probabilities for Ehrenfest urns */
{
int i, j;
double pleft = 0.0, pright = 0.0, sum;
#pragma omp parallel for private(j)
for (j=0; j<NY; j++)
{
for (i=0; i<NX/2; i++) if (xy_in[i*NY+j]) pleft += rde[i*NY+j].field_norm;
for (i=NX/2; i<NX; i++) if (xy_in[i*NY+j]) pright += rde[i*NY+j].field_norm;
}
sum = pleft + pright;
probas[0] = pleft/sum;
probas[1] = pright/sum;
}
// void compute_field_norm(double phi_x[NX*NY], double phi_y[NX*NY], double phi_norm[NX*NY], double factor)
// /* compute the norm of (phi_x, phi_y) */
// {
// int i, j;
//
// #pragma omp parallel for private(i,j)
// for (i=0; i<NX; i++)
// for (j=0; j<NY; j++)
// {
// phi_norm[i*NY+j] = factor*module2(phi_x[i*NY+j],phi_y[i*NY+j]);
// }
// }
// void compute_field_argument(double phi_x[NX*NY], double phi_y[NX*NY], double phi_arg[NX*NY])
// /* compute the argument of (phi_x, phi_y) */
// {
// int i, j;
// double angle;
//
// #pragma omp parallel for private(i,j, angle)
// for (i=0; i<NX; i++)
// for (j=0; j<NY; j++)
// {
// angle = argument(phi_x[i*NY+j],phi_y[i*NY+j]) + PI*COLOR_PHASE_SHIFT;
// if (angle < 0.0) angle += DPI;
// if (angle >= DPI) angle -= DPI;
// phi_arg[i*NY+j] = 360.0*angle/DPI;
// // phi_arg[i*NY+j] = 180.0*angle/DPI;
// }
// }
void compute_laplacian_rde(double phi_in[NX*NY], double phi_out[NX*NY], short int xy_in[NX*NY])
/* computes the Laplacian of phi_in and stores it in phi_out */
{
int i, j, iplus, iminus, jplus, jminus;
#pragma omp parallel for private(i,j)
for (i=1; i<NX-1; i++){
for (j=1; j<NY-1; j++){
if (xy_in[i*NY+j]){
phi_out[i*NY+j] = phi_in[(i+1)*NY+j] + phi_in[(i-1)*NY+j]
+ phi_in[i*NY+j+1] + phi_in[i*NY+j-1] - 4.0*phi_in[i*NY+j];
}
}
}
/* boundary conditions */
switch (B_COND) {
case (BC_PERIODIC):
{
/* left and right side */
for (j = 0; j < NY; j++)
{
jplus = j+1; if (jplus == NY) jplus = 0;
jminus = j-1; if (jminus == -1) jminus = NY-1;
phi_out[j] = phi_in[jminus] + phi_in[jplus] + phi_in[(NX-1)*NY+j] + phi_in[NY+j] - 4.0*phi_in[j];
phi_out[(NX-1)*NY+j] = phi_in[(NX-1)*NY+jminus] + phi_in[(NX-1)*NY+jplus] + phi_in[(NX-2)*NY+j] + phi_in[j] - 4.0*phi_in[(NX-1)*NY+j];
}
/* top and bottom side */
for (i = 1; i < NX-1; i++)
{
iplus = i+1; /*if (iplus == NX) iplus = 0;*/
iminus = i-1; /*if (iminus == -1) iminus = NX-1;*/
phi_out[i*NY] = phi_in[iminus*NY] + phi_in[iplus*NY] + phi_in[i*NY+1] + phi_in[i*NY+NY-1] - 4.0*phi_in[i*NY];
phi_out[i*NY+NY-1] = phi_in[iminus*NY+NY-1] + phi_in[iplus*NY+NY-1] + phi_in[i*NY] + phi_in[i*NY+NY-2] - 4.0*phi_in[i*NY+NY-1];
}
break;
}
case (BC_DIRICHLET):
{
/* left and right side */
for (j = 1; j < NY-1; j++)
{
phi_out[j] = phi_in[j-1] + phi_in[j+1] + phi_in[NY+j] - 3.0*phi_in[j];
phi_out[(NX-1)*NY+j] = phi_in[(NX-1)*NY+j-1] + phi_in[(NX-1)*NY+j+1] + phi_in[(NX-2)*NY+j] - 3.0*phi_in[(NX-1)*NY+j];
}
/* top and bottom side */
for (i = 1; i < NX-1; i++)
{
phi_out[i*NY] = phi_in[(i-1)*NY] + phi_in[(i+1)*NY] + phi_in[i*NY+1] - 3.0*phi_in[i*NY];
phi_out[i*NY+NY-1] = phi_in[(i-1)*NY+NY-1] + phi_in[(i+1)*NY+NY-1] + phi_in[i*NY+NY-2] - 3.0*phi_in[i*NY+NY-1];
}
/* corners */
phi_out[0] = phi_in[1] + phi_in[NY] - 2.0*phi_in[0];
phi_out[NY-1] = phi_in[NY-2] + phi_in[NY+NY-1] - 2.0*phi_in[NY-1];
phi_out[(NX-1)*NY] = phi_in[(NX-2)*NY] + phi_in[(NX-1)*NY+1] - 2.0*phi_in[(NX-1)*NY];
phi_out[(NX-1)*NY+NY-1] = phi_in[(NX-2)*NY+NY-1] + phi_in[(NX-1)*NY-2] - 2.0*phi_in[(NX-1)*NY+NY-1];
break;
}
}
}
void compute_light_angle_rde(short int xy_in[NX*NY], t_rde rde[NX*NY], double potential[NX*NY], int movie)
/* computes cosine of angle between normal vector and vector light */
{
int i, j;
double gradx, grady, norm, pscal;
static double dx, dy;
static int first = 1;
if (first)
{
dx = 2.0*(XMAX - XMIN)/(double)NX;
dy = 2.0*(YMAX - YMIN)/(double)NY;
first = 0;
}
#pragma omp parallel for private(i,j,gradx, grady, norm, pscal)
for (i=1; i<NX-2; i++)
for (j=1; j<NY-2; j++)
{
if ((TWOSPEEDS)||(xy_in[i*NY+j]))
{
gradx = (*rde[(i+1)*NY+j].p_zfield[movie] - *rde[(i-1)*NY+j].p_zfield[movie])/dx;
grady = (*rde[i*NY+j+1].p_zfield[movie] - *rde[i*NY+j-1].p_zfield[movie])/dy;
/* case where the potential is added to the z coordinate */
if (((ADD_POTENTIAL)||(ADD_MAGNETIC_FIELD))&&(ADD_POTENTIAL_TO_Z))
{
gradx += ADD_POT_CONSTANT*(potential[(i+1)*NY+j] - potential[(i-1)*NY+j])/dx;
grady += ADD_POT_CONSTANT*(potential[i*NY+j+1] - potential[i*NY+j-1])/dx;
}
norm = sqrt(1.0 + gradx*gradx + grady*grady);
pscal = -gradx*light[0] - grady*light[1] + 1.0;
rde[i*NY+j].cos_angle = pscal/norm;
}
}
}
void draw_field_line(double x, double y, short int *xy_in[NX], double *nablax[NX],
double *nablay[NX], double delta, int nsteps)
/* draw a field line of the gradient, starting in (x,y) - OLD VERSION */
{
double x1, y1, x2, y2, pos[2], nabx, naby, norm2, norm;
int i = 0, ij[2], cont = 1;
glColor3f(1.0, 1.0, 1.0);
// glColor3f(0.0, 0.0, 0.0);
glLineWidth(FIELD_LINE_WIDTH);
x1 = x;
y1 = y;
// printf("Drawing field line \n");
glEnable(GL_LINE_SMOOTH);
glBegin(GL_LINE_STRIP);
xy_to_pos(x1, y1, pos);
glVertex2d(pos[0], pos[1]);
i = 0;
while ((cont)&&(i < nsteps))
{
xy_to_ij(x1, y1, ij);
if (ij[0] < 0) ij[0] = 0;
if (ij[0] > NX-1) ij[0] = NX-1;
if (ij[1] < 0) ij[1] = 0;
if (ij[1] > NY-1) ij[1] = NY-1;
nabx = nablax[ij[0]][ij[1]];
naby = nablay[ij[0]][ij[1]];
norm2 = nabx*nabx + naby*naby;
if (norm2 > 1.0e-14)
{
/* avoid too large step size */
if (norm2 < 1.0e-9) norm2 = 1.0e-9;
norm = sqrt(norm2);
x1 = x1 + delta*nabx/norm;
y1 = y1 + delta*naby/norm;
}
else cont = 0;
if (!xy_in[ij[0]*NY + ij[1]]) cont = 0;
/* stop if the boundary is hit */
// if (xy_in[ij[0]][ij[1]] != 1) cont = 0;
// printf("x1 = %.3lg \t y1 = %.3lg \n", x1, y1);
xy_to_pos(x1, y1, pos);
glVertex2d(pos[0], pos[1]);
i++;
}
glEnd();
}
void compute_field_color_rde(double value, int cplot, int palette, double rgb[3])
/* compute the color depending on the field value and color palette */
{
switch (cplot) {
case (Z_AMPLITUDE):
{
color_scheme_palette(COLOR_SCHEME, palette, value, 1.0, 0, rgb);
break;
}
case (Z_RGB):
{
/* TO DO */
break;
}
case (Z_POLAR):
{
// hsl_to_rgb_palette(360.0*value/DPI, 0.9, 0.5, rgb, palette);
color_scheme_palette(C_ONEDIM_LINEAR, palette, value/DPI, 1.0, 1, rgb);
break;
}
case (Z_NORM_GRADIENT):
{
// color_scheme_palette(COLOR_SCHEME, palette, value, 1.0, 0, rgb);
color_scheme_asym_palette(COLOR_SCHEME, palette, value, 1.0, 0, rgb);
break;
}
case (Z_ANGLE_GRADIENT):
{
color_scheme_palette(C_ONEDIM_LINEAR, palette, value/DPI, 1.0, 1, rgb);
break;
}
case (Z_NORM_GRADIENTX):
{
hsl_to_rgb_palette(360.0*value/DPI, 0.9, 0.5, rgb, palette);
break;
}
case (Z_ANGLE_GRADIENTX):
{
color_scheme_palette(C_ONEDIM_LINEAR, palette, value/DPI, 1.0, 1, rgb);
break;
}
case (Z_NORM_GRADIENT_INTENSITY):
{
hsl_to_rgb_palette(360.0*value/DPI, 0.9, 0.5, rgb, palette);
break;
}
case (Z_VORTICITY):
{
hsl_to_rgb_palette(180.0*(1.0 - color_amplitude(value, 1.0, 0)), 0.9, 0.5, rgb, palette);
break;
}
case (Z_VORTICITY_ABS):
{
hsl_to_rgb_palette(360.0*(1.0 - vabs(color_amplitude(value, 1.0, 0))), 0.9, 0.5, rgb, palette);
break;
}
case (Z_MAXTYPE_RPSLZ):
{
hsl_to_rgb_palette(value, 0.9, 0.5, rgb, palette);
break;
}
case (Z_THETA_RPSLZ):
{
color_scheme_palette(C_ONEDIM_LINEAR, palette, value/DPI, 1.0, 1, rgb);
break;
}
case (Z_NORM_GRADIENT_RPSLZ):
{
color_scheme_palette(COLOR_SCHEME, palette, value, 1.0, 0, rgb);
break;
}
case (Z_MODULE):
{
color_scheme_asym_palette(COLOR_SCHEME, palette, VSCALE_AMPLITUDE*value, 1.0, 0, rgb);
break;
}
case (Z_ARGUMENT):
{
// color_scheme_palette(C_ONEDIM_LINEAR, palette, value/DPI, 1.0, 1, rgb);
hsl_to_rgb_palette(360.0*value/DPI, 0.9, 0.5, rgb, palette);
break;
}
case (Z_REALPART):
{
color_scheme_palette(COLOR_SCHEME, palette, VSCALE_AMPLITUDE*value, 1.0, 0, rgb);
break;
}
case (Z_EULER_VORTICITY):
{
if (value < 0.0) value = -value;
color_scheme_asym_palette(COLOR_SCHEME, palette, VSCALE_AMPLITUDE*value, 1.0, 0, rgb);
break;
}
case (Z_EULER_LOG_VORTICITY):
{
// if (value < 0.0) value = -value;
// if (value < 1.0e-10) value = 1.0e-10;
// color_scheme_palette(COLOR_SCHEME, palette, LOG_SCALE*value + LOG_SHIFT, 1.0, 0, rgb);
color_scheme_palette(COLOR_SCHEME, palette, LOG_SCALE*value, 1.0, 0, rgb);
break;
}
case (Z_EULER_VORTICITY_ASYM):
{
color_scheme_palette(COLOR_SCHEME, palette, VSCALE_AMPLITUDE*value, 1.0, 0, rgb);
break;
}
}
}
double adjust_field(double z, double pot)
/* add potential in case of option ADD_POTENTIAL_TO_Z */
{
if (((ADD_POTENTIAL)||(ADD_MAGNETIC_FIELD))&&(ADD_POTENTIAL_TO_Z)) return (z + ADD_POT_CONSTANT*pot);
else return(z);
}
double compute_interpolated_colors_rde(int i, int j, t_rde rde[NX*NY], double potential[NX*NY], double palette, int cplot,
double rgb_e[3], double rgb_w[3], double rgb_n[3], double rgb_s[3],
double *z_sw, double *z_se, double *z_nw, double *z_ne,
int fade, double fade_value, int movie)
{
int k;
double cw, ce, cn, cs, c_sw, c_se, c_nw, c_ne, c_mid, ca, z_mid;
double lum;
*z_sw = *rde[i*NY+j].p_zfield[movie];
*z_se = *rde[(i+1)*NY+j].p_zfield[movie];
*z_nw = *rde[i*NY+j+1].p_zfield[movie];
*z_ne = *rde[(i+1)*NY+j+1].p_zfield[movie];
if (((ADD_POTENTIAL)||(ADD_MAGNETIC_FIELD))&&(ADD_POTENTIAL_TO_Z))
{
*z_sw += ADD_POT_CONSTANT*potential[i*NY+j];
*z_se += ADD_POT_CONSTANT*potential[(i+1)*NY+j];
*z_nw += ADD_POT_CONSTANT*potential[i*NY+j+1];
*z_ne += ADD_POT_CONSTANT*potential[(i+1)*NY+j+1];
}
z_mid = 0.25*(*z_sw + *z_se + *z_nw + *z_ne);
c_sw = *rde[i*NY+j].p_cfield[movie];
c_se = *rde[(i+1)*NY+j].p_cfield[movie];
c_nw = *rde[i*NY+j+1].p_cfield[movie];
c_ne = *rde[(i+1)*NY+j+1].p_cfield[movie];
if (COMPUTE_WRAP_ANGLE)
{
c_se = unwrap_angle(c_sw,c_se);
c_nw = unwrap_angle(c_sw,c_nw);
c_ne = unwrap_angle(c_sw,c_ne);
}
c_mid = 0.25*(c_sw + c_se + c_nw + c_ne);
cw = (c_sw + c_nw + c_mid)/3.0;
ce = (c_se + c_ne + c_mid)/3.0;
cs = (c_sw + c_se + c_mid)/3.0;
cn = (c_nw + c_ne + c_mid)/3.0;
if (COMPUTE_WRAP_ANGLE)
{
cw = wrap_angle(cw);
ce = wrap_angle(ce);
cs = wrap_angle(cs);
cn = wrap_angle(cn);
}
compute_field_color_rde(ce, cplot, palette, rgb_e);
compute_field_color_rde(cw, cplot, palette, rgb_w);
compute_field_color_rde(cn, cplot, palette, rgb_n);
compute_field_color_rde(cs, cplot, palette, rgb_s);
// if ((cplot == Z_ARGUMENT)||(cplot == Z_REALPART))
if (cplot == Z_ARGUMENT)
{
lum = tanh(SLOPE_SCHROD_LUM*rde[i*NY+j].field_norm) + MIN_SCHROD_LUM;
for (k=0; k<3; k++)
{
rgb_e[k] *= lum;
rgb_w[k] *= lum;
rgb_n[k] *= lum;
rgb_s[k] *= lum;
}
}
if (SHADE_3D)
{
ca = rde[i*NY+j].cos_angle;
ca = (ca + 1.0)*0.4 + 0.2;
for (k=0; k<3; k++)
{
rgb_e[k] *= ca;
rgb_w[k] *= ca;
rgb_n[k] *= ca;
rgb_s[k] *= ca;
}
}
if (fade)
for (k=0; k<3; k++)
{
rgb_e[k] *= fade_value;
rgb_w[k] *= fade_value;
rgb_n[k] *= fade_value;
rgb_s[k] *= fade_value;
}
return(z_mid);
}
void compute_rde_fields(double *phi[NFIELDS], short int xy_in[NX*NY], int zplot, int cplot, t_rde rde[NX*NY])
/* compute the necessary auxiliary fields */
{
int i, j;
switch (RDE_EQUATION) {
case (E_RPS):
{
if ((COMPUTE_THETA)||(COMPUTE_THETAZ))
compute_theta(phi, xy_in, rde);
if ((zplot == Z_NORM_GRADIENT)||(cplot == Z_NORM_GRADIENT))
{
compute_gradient_theta(rde);
// compute_gradient_polar(rde, 1.0);
compute_gradient_polar(rde, 0.003);
}
if ((zplot == Z_NORM_GRADIENTX)||(cplot == Z_NORM_GRADIENTX)||(zplot == Z_ANGLE_GRADIENTX)||(cplot == Z_ANGLE_GRADIENTX))
{
compute_gradient_rde(phi[0], rde);
compute_gradient_polar(rde, 0.03);
}
if ((zplot == Z_VORTICITY)||(cplot == Z_VORTICITY)||(zplot == Z_VORTICITY_ABS)||(cplot == Z_VORTICITY_ABS))
{
compute_gradient_theta(rde);
compute_curl(rde);
}
break;
}
case (E_RPSLZ):
{
compute_theta_rpslz(phi, xy_in, rde, cplot);
if ((zplot == Z_NORM_GRADIENT_RPSLZ)||(cplot == Z_NORM_GRADIENT_RPSLZ))
{
compute_gradient_theta(rde);
compute_gradient_polar(rde, 0.005);
}
break;
}
case (E_SCHRODINGER):
{
compute_field_module(phi, rde, 1.0);
if ((zplot == Z_ARGUMENT)||(cplot == Z_ARGUMENT))
{
compute_field_argument(phi, rde);
}
break;
}
case (E_EULER_INCOMP):
{
if ((zplot == Z_EULER_LOG_VORTICITY)||(cplot == Z_EULER_LOG_VORTICITY))
compute_field_log(phi, rde);
break;
}
default : break;
}
}
void init_zfield_rde(double *phi[NFIELDS], short int xy_in[NX*NY], int zplot, t_rde rde[NX*NY], int movie)
/* compute the necessary fields for the z coordinate */
{
int i, j;
switch(zplot) {
case (Z_AMPLITUDE):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &phi[0][i*NY+j];
break;
}
case (Z_POLAR):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].theta;
break;
}
case (Z_NORM_GRADIENT):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_ANGLE_GRADIENT):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_arg;
break;
}
case (Z_NORM_GRADIENTX):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_ANGLE_GRADIENTX):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_arg;
break;
}
case (Z_NORM_GRADIENT_INTENSITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_VORTICITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].curl;
break;
}
case (Z_VORTICITY_ABS):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].curl;
break;
}
case (Z_MAXTYPE_RPSLZ):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].theta;
break;
}
case (Z_THETA_RPSLZ):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].theta;
break;
}
case (Z_NORM_GRADIENT_RPSLZ):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_MODULE):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_ARGUMENT):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].field_arg;
break;
}
case (Z_REALPART):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &phi[0][i*NY+j];
break;
}
case (Z_EULER_VORTICITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &phi[1][i*NY+j];
break;
}
case (Z_EULER_LOG_VORTICITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &rde[i*NY+j].log_vorticity;
break;
}
case (Z_EULER_VORTICITY_ASYM):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_zfield[movie] = &phi[1][i*NY+j];
break;
}
}
}
void init_cfield_rde(double *phi[NFIELDS], short int xy_in[NX*NY], int cplot, t_rde rde[NX*NY], int movie)
/* compute the colors */
{
int i, j, k;
switch(cplot) {
case (Z_AMPLITUDE):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &phi[0][i*NY+j];
break;
}
case (Z_POLAR):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].theta;
break;
}
case (Z_NORM_GRADIENT):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_ANGLE_GRADIENT):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_arg;
break;
}
case (Z_NORM_GRADIENTX):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_ANGLE_GRADIENTX):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_arg;
break;
}
case (Z_NORM_GRADIENT_INTENSITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_VORTICITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].curl;
break;
}
case (Z_VORTICITY_ABS):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].curl;
break;
}
case (Z_MAXTYPE_RPSLZ):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].theta;
break;
}
case (Z_THETA_RPSLZ):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].theta;
break;
}
case (Z_NORM_GRADIENT_RPSLZ):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_MODULE):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_norm;
break;
}
case (Z_ARGUMENT):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].field_arg;
break;
}
case (Z_REALPART):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &phi[0][i*NY+j];
break;
}
case (Z_EULER_VORTICITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &phi[1][i*NY+j];
break;
}
case (Z_EULER_LOG_VORTICITY):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &rde[i*NY+j].log_vorticity;
break;
}
case (Z_EULER_VORTICITY_ASYM):
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++) for (j=0; j<NY; j++) rde[i*NY+j].p_cfield[movie] = &phi[1][i*NY+j];
break;
}
}
}
void compute_cfield_rde(short int xy_in[NX*NY], int cplot, int palette, t_rde rde[NX*NY], int fade, double fade_value, int movie)
/* compute the colors */
{
int i, j, k;
double ca, lum;
#pragma omp parallel for private(i,j,k,ca,lum)
for (i=0; i<NX; i++) for (j=0; j<NY; j++)
{
compute_field_color_rde(*rde[i*NY+j].p_cfield[movie], cplot, palette, rde[i*NY+j].rgb);
// if ((cplot == Z_ARGUMENT)||(cplot == Z_REALPART))
if (cplot == Z_ARGUMENT)
{
lum = tanh(SLOPE_SCHROD_LUM*rde[i*NY+j].field_norm);
for (k=0; k<3; k++) rde[i*NY+j].rgb[k] *= lum;
}
if (SHADE_3D)
{
ca = rde[i*NY+j].cos_angle;
ca = (ca + 1.0)*0.4 + 0.2;
if ((FADE_IN_OBSTACLE)&&(!xy_in[i*NY+j])) ca *= 1.6;
for (k=0; k<3; k++) rde[i*NY+j].rgb[k] *= ca;
}
if (fade) for (k=0; k<3; k++) rde[i*NY+j].rgb[k] *= fade_value;
}
}
void draw_wave_2d_rde(short int xy_in[NX*NY], t_rde rde[NX*NY])
{
int i, j;
glBegin(GL_QUADS);
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
if (xy_in[i*NY+j])
{
glColor3f(rde[i*NY+j].rgb[0], rde[i*NY+j].rgb[1], rde[i*NY+j].rgb[2]);
glVertex2i(i, j);
glVertex2i(i+1, j);
glVertex2i(i+1, j+1);
glVertex2i(i, j+1);
}
}
glEnd ();
if (DRAW_BILLIARD) draw_billiard(0, 1.0);
}
void draw_wave_3d_ij_rde(int i, int j, int movie, double *phi[NFIELDS], short int xy_in[NX*NY], t_rde rde[NX*NY],
double potential[NX*NY], int zplot, int cplot, int palette, int fade, double fade_value)
{
int k, l, draw = 1;
double xy[2], xy_screen[2], rgb[3], pos[2], ca, rgb_e[3], rgb_w[3], rgb_n[3], rgb_s[3];
double z, z_sw, z_se, z_nw, z_ne, z_mid, zw, ze, zn, zs, min = 1000.0, max = 0.0;
double xy_sw[2], xy_se[2], xy_nw[2], xy_ne[2], xy_mid[2];
double energy;
if (NON_DIRICHLET_BC)
draw = (xy_in[i*NY+j])&&(xy_in[(i+1)*NY+j])&&(xy_in[i*NY+j+1])&&(xy_in[(i+1)*NY+j+1]);
else draw = (TWOSPEEDS)||(xy_in[i*NY+j]);
if (draw)
{
if (AMPLITUDE_HIGH_RES > 0)
{
z_mid = compute_interpolated_colors_rde(i, j, rde, potential, palette, cplot,
rgb_e, rgb_w, rgb_n, rgb_s, &z_sw, &z_se, &z_nw, &z_ne,
fade, fade_value, movie);
ij_to_xy(i, j, xy_sw);
ij_to_xy(i+1, j, xy_se);
ij_to_xy(i, j+1, xy_nw);
ij_to_xy(i+1, j+1, xy_ne);
for (k=0; k<2; k++) xy_mid[k] = 0.25*(xy_sw[k] + xy_se[k] + xy_nw[k] + xy_ne[k]);
if (AMPLITUDE_HIGH_RES == 1)
{
glBegin(GL_TRIANGLE_FAN);
glColor3f(rgb_w[0], rgb_w[1], rgb_w[2]);
draw_vertex_xyz(xy_mid, z_mid);
draw_vertex_xyz(xy_nw, z_nw);
draw_vertex_xyz(xy_sw, z_sw);
glColor3f(rgb_s[0], rgb_s[1], rgb_s[2]);
draw_vertex_xyz(xy_se, z_se);
glColor3f(rgb_e[0], rgb_e[1], rgb_e[2]);
draw_vertex_xyz(xy_ne, z_ne);
glColor3f(rgb_n[0], rgb_n[1], rgb_n[2]);
draw_vertex_xyz(xy_nw, z_nw);
glEnd ();
}
}
else
{
glColor3f(rde[i*NY+j].rgb[0], rde[i*NY+j].rgb[1], rde[i*NY+j].rgb[2]);
glBegin(GL_TRIANGLE_FAN);
ij_to_xy(i, j, xy);
draw_vertex_xyz(xy, adjust_field(*rde[i*NY+j].p_zfield[movie], potential[i*NY+j]));
ij_to_xy(i+1, j, xy);
draw_vertex_xyz(xy, adjust_field(*rde[(i+1)*NY+j].p_zfield[movie], potential[(i+1)*NY+j]));
ij_to_xy(i+1, j+1, xy);
draw_vertex_xyz(xy, adjust_field(*rde[(i+1)*NY+j+1].p_zfield[movie], potential[(i+1)*NY+j+1]));
ij_to_xy(i, j+1, xy);
draw_vertex_xyz(xy, adjust_field(*rde[i*NY+j+1].p_zfield[movie], potential[i*NY+j+1]));
glEnd ();
}
}
}
void draw_wave_3d_ij_rde_periodic(int shiftx, int shifty, int i, int j, int movie, double *phi[NFIELDS],
short int xy_in[NX*NY], t_rde rde[NX*NY], double potential[NX*NY], int zplot, int cplot, int palette, int fade, double fade_value)
{
int k, l, draw = 1;
double xy[2], xy_screen[2], rgb[3], pos[2], ca, rgb_e[3], rgb_w[3], rgb_n[3], rgb_s[3];
double z, z_sw, z_se, z_nw, z_ne, z_mid, zw, ze, zn, zs, min = 1000.0, max = 0.0;
double xy_sw[2], xy_se[2], xy_nw[2], xy_ne[2], xy_mid[2];
double energy;
if (NON_DIRICHLET_BC)
draw = (xy_in[i*NY+j])&&(xy_in[(i+1)*NY+j])&&(xy_in[i*NY+j+1])&&(xy_in[(i+1)*NY+j+1]);
else draw = (TWOSPEEDS)||(xy_in[i*NY+j]);
if (draw)
{
if (AMPLITUDE_HIGH_RES > 0)
{
z_mid = compute_interpolated_colors_rde(i, j, rde, potential, palette, cplot,
rgb_e, rgb_w, rgb_n, rgb_s, &z_sw, &z_se, &z_nw, &z_ne,
fade, fade_value, movie);
ij_to_xy(i, j, xy_sw);
ij_to_xy(i+1, j, xy_se);
ij_to_xy(i, j+1, xy_nw);
ij_to_xy(i+1, j+1, xy_ne);
for (k=0; k<2; k++) xy_mid[k] = 0.25*(xy_sw[k] + xy_se[k] + xy_nw[k] + xy_ne[k]);
if (AMPLITUDE_HIGH_RES == 1)
{
glBegin(GL_TRIANGLE_FAN);
glColor3f(rgb_w[0], rgb_w[1], rgb_w[2]);
draw_vertex_xyz_shift(xy_mid, z_mid, shiftx, shifty);
draw_vertex_xyz_shift(xy_nw, z_nw, shiftx, shifty);
draw_vertex_xyz_shift(xy_sw, z_sw, shiftx, shifty);
glColor3f(rgb_s[0], rgb_s[1], rgb_s[2]);
draw_vertex_xyz_shift(xy_se, z_se, shiftx, shifty);
glColor3f(rgb_e[0], rgb_e[1], rgb_e[2]);
draw_vertex_xyz_shift(xy_ne, z_ne, shiftx, shifty);
glColor3f(rgb_n[0], rgb_n[1], rgb_n[2]);
draw_vertex_xyz_shift(xy_nw, z_nw, shiftx, shifty);
glEnd ();
}
}
else
{
glColor3f(rde[i*NY+j].rgb[0], rde[i*NY+j].rgb[1], rde[i*NY+j].rgb[2]);
glBegin(GL_TRIANGLE_FAN);
ij_to_xy(i, j, xy);
draw_vertex_xyz_shift(xy, adjust_field(*rde[i*NY+j].p_zfield[movie], potential[i*NY+j]), shiftx, shifty);
ij_to_xy(i+1, j, xy);
draw_vertex_xyz_shift(xy, adjust_field(*rde[(i+1)*NY+j].p_zfield[movie], potential[(i+1)*NY+j]), shiftx, shifty);
ij_to_xy(i+1, j+1, xy);
draw_vertex_xyz_shift(xy, adjust_field(*rde[(i+1)*NY+j+1].p_zfield[movie], potential[(i+1)*NY+j+1]), shiftx, shifty);
ij_to_xy(i, j+1, xy);
draw_vertex_xyz_shift(xy, adjust_field(*rde[i*NY+j+1].p_zfield[movie], potential[i*NY+j+1]), shiftx, shifty);
glEnd ();
}
}
}
void draw_wave_3d_rde(int movie, double *phi[NFIELDS], short int xy_in[NX*NY], t_rde rde[NX*NY], double potential[NX*NY],
int zplot, int cplot, int palette, int fade, double fade_value)
{
int i, j;
double observer_angle;
blank();
if (DRAW_BILLIARD) draw_billiard_3d(fade, fade_value);
if (!ROTATE_VIEW)
{
for (i=BORDER_PADDING; i<NX-2-BORDER_PADDING; i++)
for (j=BORDER_PADDING; j<NY-2-BORDER_PADDING; j++)
draw_wave_3d_ij_rde(i, j, movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
else /* draw facets in an order depending on the position of the observer */
{
observer_angle = argument(observer[0], observer[1]);
observer_angle -= 0.5*PID;
if (observer_angle < 0.0) observer_angle += DPI;
printf("Observer_angle = %.3lg\n", observer_angle*360.0/DPI);
if ((observer_angle > 0.0)&&(observer_angle < PID))
{
for (j=0; j<NY-2; j++)
for (i=0; i<NX-2; i++)
draw_wave_3d_ij_rde(i, j, movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
else if (observer_angle < PI)
{
for (i=NX-3; i>0; i--)
for (j=0; j<NY-2; j++)
draw_wave_3d_ij_rde(i, j, movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
else if (observer_angle < 1.5*PI)
{
for (j=NY-3; j>0; j--)
for (i=0; i<NX-2; i++)
draw_wave_3d_ij_rde(i, j, movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
else
{
for (i=0; i<NX-2; i++)
for (j=0; j<NY-2; j++)
draw_wave_3d_ij_rde(i, j, movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
}
if (DRAW_BILLIARD_FRONT) draw_billiard_3d_front(fade, fade_value);
}
void draw_periodicised_wave_3d(int movie, double *phi[NFIELDS], short int xy_in[NX*NY], t_rde rde[NX*NY], double potential[NX*NY],
int zplot, int cplot, int palette, int fade, double fade_value)
/* a variant where the wave is repeated periodically in x and y directions (beta) */
{
int i, j, shiftx, shifty;
double observer_angle;
blank();
if (DRAW_BILLIARD) draw_billiard_3d(fade, fade_value);
if (!ROTATE_VIEW)
{
for (shiftx = -1; shiftx < 2; shiftx++)
for (shifty = -2; shifty < 2; shifty++)
for (i=BORDER_PADDING; i<NX-1-BORDER_PADDING; i++)
for (j=BORDER_PADDING; j<NY-1-BORDER_PADDING; j++)
draw_wave_3d_ij_rde_periodic(shiftx, shifty, i, j, movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
}
void draw_wave_rde(int movie, double *phi[NFIELDS], short int xy_in[NX*NY], t_rde rde[NX*NY], double potential[NX*NY],
int zplot, int cplot, int palette, int fade, double fade_value, int refresh)
{
int i, j, k, l, draw = 1;
double xy[2], xy_screen[2], rgb[3], pos[2], ca, rgb_e[3], rgb_w[3], rgb_n[3], rgb_s[3];
double z_sw, z_se, z_nw, z_ne, z_mid, zw, ze, zn, zs, min = 1000.0, max = 0.0;
double xy_sw[2], xy_se[2], xy_nw[2], xy_ne[2], xy_mid[2];
double energy;
if (refresh)
{
// printf("Computing fields\n");
compute_rde_fields(phi, xy_in, zplot, cplot, rde);
// printf("Computed fields\n");
if ((PLOT_3D)&&(SHADE_3D)) compute_light_angle_rde(xy_in, rde, potential, movie);
}
compute_cfield_rde(xy_in, cplot, palette, rde, fade, fade_value, movie);
if (PLOT_3D)
{
if (DRAW_PERIODICISED)
draw_periodicised_wave_3d(movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
else draw_wave_3d_rde(movie, phi, xy_in, rde, potential, zplot, cplot, palette, fade, fade_value);
}
else draw_wave_2d_rde(xy_in, rde);
}
void draw_tracers(double *phi[NFIELDS], double tracers[2*N_TRACERS*NSTEPS], int time, int fade, double fade_value)
/* draw trajectories of tracers */
{
int tracer, t, t1, length = 50;
double x1, y1, x2, y2, lum;
glColor3f(1.0, 1.0, 1.0);
glLineWidth(1);
t1 = time - length;
if (t1 < 1) t1 = 1;
for (t = t1 + 1; t < time; t++)
for (tracer = 0; tracer < N_TRACERS; tracer++)
{
x1 = tracers[2*(t-1)*N_TRACERS + 2*tracer];
y1 = tracers[2*(t-1)*N_TRACERS + 2*tracer + 1];
x2 = tracers[2*t*N_TRACERS + 2*tracer];
y2 = tracers[2*t*N_TRACERS + 2*tracer + 1];
lum = 1.0 - 0.75*(double)(time - t)/(double)length;
if (fade) lum *= fade_value;
glColor3f(lum, lum, lum);
if (module2(x2 - x1, y2 - y1) < 0.2) draw_line(x1, y1, x2, y2);
// printf("time = %i, tracer = %i, coord = %i, x1 = %.2lg, y1 = %.2lg, x2 = %.2lg, y2 = %.2lg\n", t, tracer,2*t*N_TRACERS + 2*tracer, x1, y1, x2, y2);
}
}
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