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nilsberglund-orleans 2021-07-18 15:08:44 +02:00 committed by GitHub
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@ -1,6 +1,7 @@
long int global_time = 0; /* counter to keep track of global time of simulation */
int nparticles=NPART;
/*********************/
/* some basic math */
/*********************/
@ -660,7 +661,7 @@ void draw_billiard() /* draws the billiard boundary */
{
x = cos(i*omega + APOLY*PID);
y = sin(i*omega + APOLY*PID);
glVertex2d(x, y);
glVertex2d(SCALING_FACTOR*x, SCALING_FACTOR*y);
}
glEnd ();
break;
@ -682,7 +683,7 @@ void draw_billiard() /* draws the billiard boundary */
angle = i*omega + APOLY*PID;
x = cos(angle)*x1 - sin(angle)*y1;
y = sin(angle)*x1 + cos(angle)*y1;
glVertex2d(x, y);
glVertex2d(SCALING_FACTOR*x, SCALING_FACTOR*y);
}
}
glEnd ();
@ -768,6 +769,78 @@ void draw_billiard() /* draws the billiard boundary */
glEnd ();
break;
}
case (D_ANGLE):
{
if (DRAW_CONSTRUCTION_LINES)
{
glColor3f(0.5, 0.5, 0.5);
glBegin(GL_LINE_STRIP);
phi = LAMBDA*PI;
r = 2.0*YMAX;
for (i=-(int)(PI/phi)-1; i <= (int)(PI/phi)+2; i++)
{
// printf("%i \n", i);
glVertex2d(0.0, 0.0);
glVertex2d(-r*cos((double)i*phi), r*sin((double)i*phi));
}
glEnd();
}
if (PAINT_INT) glColor3f(0.5, 0.5, 0.5);
else
{
if (BLACK) glColor3f(1.0, 1.0, 1.0);
else glColor3f(0.0, 0.0, 0.0);
}
glBegin(GL_LINE_STRIP);
glVertex2d(XMIN, 0.0);
glVertex2d(0.0, 0.0);
glVertex2d(-YMAX/tan(LAMBDA*PI), YMAX);
glEnd ();
break;
}
case (D_LSHAPE):
{
glBegin(GL_LINE_LOOP);
glVertex2d(-1.0, -1.0);
glVertex2d(1.0, -1.0);
glVertex2d(1.0, 0.0);
glVertex2d(0.0, 0.0);
glVertex2d(0.0, 1.0);
glVertex2d(-1.0, 1.0);
glEnd();
break;
}
case (D_GENUSN): /* like for polygon */
{
omega = DPI/((double)NPOLY);
glBegin(GL_LINE_LOOP);
for (i=0; i<=NPOLY; i++)
{
x = cos(i*omega + APOLY*PID);
y = sin(i*omega + APOLY*PID);
glVertex2d(SCALING_FACTOR*x, SCALING_FACTOR*y);
}
glEnd ();
break;
}
case (D_CIRCLES):
{
for (k=0; k<ncircles; k++) if (circleactive[k])
{
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = circlex[k] + circlerad[k]*cos(phi);
y = circley[k] + circlerad[k]*sin(phi);
glVertex2d(x, y);
}
glEnd ();
}
break;
}
default:
{
printf("Function draw_billiard not defined for this billiard \n");
@ -1008,7 +1081,9 @@ int color[NPARTMAX];
}
/****************************************************************************************/
/* elliptic billiard */
/****************************************************************************************/
int pos_ellipse(conf, pos, alpha)
/* determine position on boundary of ellipse */
@ -2335,6 +2410,602 @@ int color[NPARTMAX];
return(c);
}
/****************************************************************************************/
/* angle billiard */
/****************************************************************************************/
int pos_angle(conf, pos, alpha)
/* determine position on boundary of triangle */
/* corner of angle is at (0,0), sides are horizontal and x*sin(a) = -y*cos(a), a=LAMBDA*PI */
/* we use arclength for horizontal and vertical side, y for diagonal */
double conf[2], pos[2], *alpha;
{
double s, theta;
s = conf[0];
theta = conf[1];
if (s<=0)
{
pos[0] = s;
pos[1] = 0.0;
*alpha = theta;
return(0);
}
else
{
pos[0] = - s/tan(LAMBDA*PI);
pos[1] = s;
*alpha = theta + (1.0-LAMBDA)*PI;
return(1);
}
}
int vangle_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
/* Warning: reflection in the corners is not yet implemented correctly */
double config[8], alpha, pos[2];
{
double s0, c0, t, x, y, x1, y1, phi;
int c, intb=1, intc, i;
/* initial position and velocity */
s0 = sin(alpha);
c0 = cos(alpha);
/* intersection with lower part of boundary */
if (s0<0.0)
{
x1 = pos[0] - pos[1]*c0/s0;
y1 = 0.0;
if (x1<=0.0)
{
config[0] = x1;
config[1] = -alpha;
intb = 0;
}
}
/* intersection with diagonal part of boundary */
if ((intb)&&(sin(alpha+LAMBDA*PI)>0.0))
{
phi = LAMBDA*PI;
t = -(pos[0]*sin(phi) + pos[1]*cos(phi))/sin(alpha+phi);
x1 = pos[0] + t*c0;
y1 = pos[1] + t*s0;
if (y1 > 0.0)
{
config[0] = y1;
config[1] = PI - alpha - phi;
intb = 0;
}
}
/* other cases, assign a dummy coordinate */
if (intb)
{
if (s0 > 0.0)
{
t = (1000.0 - pos[0])/s0;
x1 = pos[0] + t*c0;
y1 = 1000.0;
}
else
{
t = -(1000.0 + pos[0])/c0;
x1 = -1000.0;
y1 = pos[1] + t*s0;
}
config[0] = -1000.0;
config[1] = PID;
}
config[2] = 0.0; /* running time */
config[3] = module2(x1-pos[0], y1-pos[1]);
config[4] = pos[0];
config[5] = pos[1];
config[6] = x1;
config[7] = y1;
return(c);
}
int vangle(config)
double config[8];
{
double alpha, pos[2];
int c;
/* position et vitesse de depart */
c = pos_angle(config, pos, &alpha);
vangle_xy(config, alpha, pos);
return(c);
}
/****************************************************************************************/
/* L-shaped billiard (conical singularity) */
/****************************************************************************************/
int pos_lshape(conf, pos, alpha)
/* determine position on boundary of L-shaped billiard */
/* the corners of the L shape are (-1,-1), (1,-1), (1,0), (0,0), (0,1), (-1,1) */
/* returns the number of the side hit, or 0 if hitting a corner */
double conf[2], pos[2], *alpha;
{
double s, theta;
s = conf[0];
if (s<0.0) s = 0.0;
if (s>8.0) s = 8.0;
theta = conf[1];
/* bottom side */
if ((s>0)&&(s<2.0))
{
pos[0] = s -1.0;
pos[1] = -1.0;
*alpha = theta;
return(1);
}
/* lower right side */
else if (s<3.0)
{
pos[0] = 1.0;
pos[1] = s - 3.0;
*alpha = theta + PID;
return(2);
}
/* lower top side */
else if (s<4.0)
{
pos[0] = 4.0 - s;
pos[1] = 0.0;
*alpha = theta + PI;
return(3);
}
/* upper right side */
else if (s<5.0)
{
pos[0] = 0.0;
pos[1] = s - 4.0;
*alpha = theta + PID;
return(4);
}
/* upper top side */
else if (s<6.0)
{
pos[0] = 5.0 - s;
pos[1] = 1.0;
*alpha = theta + PI;
return(5);
}
/* left side */
else
{
pos[0] = -1.0;
pos[1] = 7.0 - s;
*alpha = theta - PID;
return(6);
}
}
int vlshape_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
double config[8], alpha, pos[2];
{
double t, l, s0, c0, margin = 1e-12, tmin;
double x1[6], y1[6], tval[6], tempconf[6][2];
int i, c, intb=1, cval[6], nt = 0, ntmin;
/* initial position and velocity */
s0 = sin(alpha);
c0 = cos(alpha);
// print_config(config);
/* intersection with lower part of boundary */
if (s0<0.0)
{
t = - (1.0 + pos[1])/s0;
x1[nt] = pos[0] + c0*t;
y1[nt] = -1.0;
if ((x1[nt]>=-1.0)&&(x1[nt]<=0.0))
{
tempconf[nt][0] = 5.0 - x1[nt];
tempconf[nt][1] = alpha + PI;
cval[nt] = 5;
tval[nt] = t;
nt++;
}
else if ((x1[nt]>0.0)&&(x1[nt]<=1.0))
{
tempconf[nt][0] = 4.0 - x1[nt];
tempconf[nt][1] = alpha + PI;
cval[nt] = 3;
tval[nt] = t;
nt++;
}
}
/* intersection with lower part of right-hand boundary */
if (c0>0.0)
{
t = (1.0 - pos[0])/c0;
x1[nt] = 1.0;
y1[nt] = pos[1] + s0*t;
if ((y1[nt]>=-1.0)&&(y1[nt]<=0.0))
{
tempconf[nt][0] = 7.0 - y1[nt];
tempconf[nt][1] = PID + alpha;
cval[nt] = 6;
tval[nt] = t;
nt++;
}
}
/* intersection with upper part of right-hand boundary */
if ((pos[0] < 0.0)&&(c0>0.0))
{
t = - pos[0]/c0;
x1[nt] = 0.0;
y1[nt] = pos[1] + s0*t;
if ((y1[nt]>=0.0)&&(y1[nt]<=1.0))
{
tempconf[nt][0] = 7.0 - y1[nt];
tempconf[nt][1] = PID + alpha;
cval[nt] = 4;
tval[nt] = t;
nt++;
}
}
/* intersection with right-hand part of upper boundary */
if ((pos[1] < 0.0)&&(s0>0.0))
{
t = - pos[1]/s0;
x1[nt] = pos[0] + c0*t;
y1[nt] = 0.0;
if ((x1[nt]>=-0.0)&&(x1[nt]<=1.0))
{
tempconf[nt][0] = 1.0 + x1[nt];
tempconf[nt][1] = alpha;
cval[nt] = 1;
tval[nt] = t;
nt++;
}
}
/* intersection with left-hand part of upper boundary */
if (s0>0.0)
{
t = (1.0 - pos[1])/s0;
x1[nt] = pos[0] + c0*t;
y1[nt] = 1.0;
if ((x1[nt]>=-1.0)&&(x1[nt]<=0.0))
{
tempconf[nt][0] = 1.0 + x1[nt];
tempconf[nt][1] = alpha;
cval[nt] = 1;
tval[nt] = t;
nt++;
}
}
/* intersection with left-hand part of boundary */
if (c0<0.0)
{
t = (-1.0 - pos[0])/c0;
x1[nt] = -1.0;
y1[nt] = pos[1] + s0*t;
if ((y1[nt]>=0.0)&&(y1[nt]<=1.0))
{
tempconf[nt][0] = 4.0 + y1[nt];
tempconf[nt][1] = alpha - PID;
cval[nt] = 4;
tval[nt] = t;
nt++;
}
else if ((y1[nt]>=-1.0)&&(y1[nt]<0.0))
{
tempconf[nt][0] = 3.0 + y1[nt];
tempconf[nt][1] = alpha - PID;
cval[nt] = 2;
tval[nt] = t;
nt++;
}
}
/* find earliest intersection */
tmin = tval[0];
ntmin = 0;
for (i=1; i<nt; i++)
if (tval[i] < tmin)
{
tmin = tval[i];
ntmin = i;
}
// printf("nt = %i, ntmin = %i, cmin = %i\n", nt, ntmin, cval[ntmin]);
config[0] = tempconf[ntmin][0];
config[1] = tempconf[ntmin][1];
c = cval[ntmin];
if (config[1] < 0.0) config[1] += DPI;
config[2] = 0.0; /* running time */
config[3] = module2(x1[ntmin]-pos[0], y1[ntmin]-pos[1]);
config[4] = pos[0];
config[5] = pos[1];
config[6] = x1[ntmin];
config[7] = y1[ntmin];
// print_config(config);
return(c);
}
int vlshape(config)
double config[8];
{
double pos[2], alpha;
int c;
/* position et vitesse de depart */
c = pos_lshape(config, pos, &alpha);
vlshape_xy(config, alpha, pos);
return(c);
}
/****************************************************************************************/
/* genus n surface - polygon with opposite sides identified */
/****************************************************************************************/
int pos_genusn(conf, pos, alpha)
/* determine position on boundary of polygon */
/* conf[0] is arclength on boundary */
double conf[2], pos[2], *alpha;
{
double s, theta, omega, length, s1, angle, x, y;
int c;
s = conf[0];
theta = conf[1];
omega = DPI/((double)NPOLY);
length = 2.0*sin(0.5*omega);
c = (int)(s/length); /* side of polygon */
s1 = s - ((double)c)*length;
x = 1.0 + (cos(omega) - 1.0)*s1/length;
y = sin(omega)*s1/length;
angle = (double)c*omega + PID*APOLY;
pos[0] = x*cos(angle) - y*sin(angle);
pos[1] = x*sin(angle) + y*cos(angle);
*alpha = (0.5 + (double)c)*omega + theta + PID*(1.0 + APOLY);
return(c);
}
int vgenusn_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
double config[8], alpha, pos[2];
{
double s, theta, omega, length, rlength, s1, rangle, x, y, xp, yp, x1, y1, ca, sa, margin = 1.0e-14;
int k, c, intb=1, intc, i;
/* dimensions/angles of polygon */
omega = DPI/((double)NPOLY);
length = 2.0*sin(0.5*omega);
rlength = cos(0.5*omega);
for (k=0; k<NPOLY; k++)
{
/* rotate position so that kth side is vertical */
rangle = (0.5 + (double)k)*omega + APOLY*PID;
theta = alpha - rangle;
if ((cos(theta) > 0.0)&&(intb))
{
ca = cos(rangle);
sa = sin(rangle);
x = pos[0]*ca + pos[1]*sa;
y = -pos[0]*sa + pos[1]*ca;
// xp = -rlength;
xp = rlength;
yp = y + (xp-x)*tan(theta);
if (vabs(yp) < 0.5*length - margin)
{
/* rotate back */
x1 = xp*ca - yp*sa;
y1 = xp*sa + yp*ca;
intb = 0;
c = k + NPOLY/2;
if (c > NPOLY) c -= NPOLY;
config[0] = ((double)c + 0.5)*length - yp;
// if (config[0] > (double)NPOLY*length) config[0] -= (double)NPOLY*length;
config[1] = PID + theta;
// config[0] = ((double)k + 0.5)*length + yp;
// config[1] = PID - theta;
}
}
}
if (intb) x1 = 1.0e12; /* to make inactive particles too close to a corner */
if (config[1] < 0.0) config[1] += DPI;
config[2] = 0.0; /* running time */
config[3] = module2(x1-pos[0], y1-pos[1]); /* distance to collision */
config[4] = pos[0]; /* start position */
config[5] = pos[1];
config[6] = x1; /* position of collision */
config[7] = y1;
return(c);
}
int vgenusn(config)
/* determine initial configuration when starting from boundary */
double config[8];
{
double pos[2], alpha;
int c;
c = pos_genusn(config, pos, &alpha);
vgenusn_xy(config, alpha, pos);
return(c);
}
/****************************************************************************************/
/* elliptic billiard */
/****************************************************************************************/
int pos_circles(conf, pos, alpha)
/* determine position on boundary of circle */
/* position varies between 0 and ncircles*2Pi */
/* returns number of hit circle */
double conf[2], pos[2], *alpha;
{
double angle;
int ncirc;
ncirc = (int)(conf[0]/DPI);
if (ncirc >= ncircles) ncirc = ncircles - 1;
angle = conf[0] - (double)ncirc*DPI;
pos[0] = circlex[ncirc] + circlerad[ncirc]*cos(angle);
pos[1] = circley[ncirc] + circlerad[ncirc]*sin(angle);
*alpha = angle + PID + conf[1];
return(ncirc);
}
int vcircles_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
double config[8], alpha, pos[2];
{
double c0, s0, b, c, t, theta, delta, margin = 1.0e-12, tmin, rlarge = 1.0e10;
double tval[ncircles], xint[ncircles], yint[ncircles], phiint[ncircles];
int i, nt = 0, nscat[ncircles], ntmin;
c0 = cos(alpha);
s0 = sin(alpha);
for (i=0; i<ncircles; i++)
{
b = (pos[0]-circlex[i])*c0 + (pos[1]-circley[i])*s0;
c = (pos[0]-circlex[i])*(pos[0]-circlex[i]) + (pos[1]-circley[i])*(pos[1]-circley[i]) - circlerad[i]*circlerad[i];
delta = b*b - c;
if (delta > margin) /* there is an intersection with circle i */
{
t = -b - sqrt(delta);
if (t > margin)
{
nscat[nt] = i;
tval[nt] = t;
xint[nt] = pos[0] + t*c0;
yint[nt] = pos[1] + t*s0;
phiint[nt] = argument(xint[nt] - circlex[i], yint[nt] - circley[i]);
nt++;
}
}
}
if (nt > 0) /* there is at least one intersection */
{
/* find earliest intersection */
tmin = tval[0];
ntmin = 0;
for (i=1; i<nt; i++)
if (tval[i] < tmin)
{
tmin = tval[i];
ntmin = i;
}
while (phiint[ntmin] < 0.0) phiint[ntmin] += DPI;
while (phiint[ntmin] >= DPI) phiint[ntmin] -= DPI;
config[0] = (double)nscat[ntmin]*DPI + phiint[ntmin];
config[1] = PID - alpha + phiint[ntmin]; /* CHECK */
if (config[1] < 0.0) config[1] += DPI;
if (config[1] >= PI) config[1] -= DPI;
config[2] = 0.0; /* running time */
config[3] = module2(xint[ntmin]-pos[0], yint[ntmin]-pos[1]); /* distance to collision */
config[4] = pos[0]; /* start position */
config[5] = pos[1];
config[6] = xint[ntmin]; /* position of collision */
config[7] = yint[ntmin];
return(nscat[ntmin]);
}
else /* there is no intersection - set dummy values */
{
config[0] = 0.0;
config[1] = 0.0;
config[2] = 0.0;
config[3] = rlarge;
config[4] = pos[0]; /* start position */
config[5] = pos[1];
config[6] = rlarge*cos(alpha);
config[7] = rlarge*sin(alpha);
return(-1);
}
}
int vcircles(config)
/* determine initial configuration when starting from boundary */
double config[8];
{
double pos[2], alpha;
int c;
c = pos_circles(config, pos, &alpha);
vcircles_xy(config, alpha, pos);
return(c);
}
/****************************************************************************************/
@ -2396,6 +3067,26 @@ int color[NPARTMAX];
return(pos_alt_reuleaux(conf, pos, &alpha));
break;
}
case (D_ANGLE):
{
return(pos_angle(conf, pos, &alpha));
break;
}
case (D_LSHAPE):
{
return(pos_lshape(conf, pos, &alpha));
break;
}
case (D_GENUSN):
{
return(pos_genusn(conf, pos, &alpha));
break;
}
case (D_CIRCLES):
{
return(pos_circles(conf, pos, &alpha));
break;
}
default:
{
printf("Function pos_billiard not defined for this billiard \n");
@ -2460,6 +3151,26 @@ int color[NPARTMAX];
return(valt_reuleaux_xy(config, alpha, pos));
break;
}
case (D_ANGLE):
{
return(vangle_xy(config, alpha, pos));
break;
}
case (D_LSHAPE):
{
return(vlshape_xy(config, alpha, pos));
break;
}
case (D_GENUSN):
{
return(vgenusn_xy(config, alpha, pos));
break;
}
case (D_CIRCLES):
{
return(vcircles_xy(config, alpha, pos));
break;
}
default:
{
printf("Function vbilliard_xy not defined for this billiard \n");
@ -2547,6 +3258,34 @@ int color[NPARTMAX];
return(valt_reuleaux(config, alpha, pos));
break;
}
case (D_ANGLE):
{
c = pos_angle(config, pos, &alpha);
return(vangle(config, alpha, pos));
break;
}
case (D_LSHAPE):
{
c = pos_lshape(config, pos, &alpha);
return(vlshape(config, alpha, pos));
break;
}
case (D_GENUSN):
{
c = pos_genusn(config, pos, &alpha);
return(vgenusn(config, alpha, pos));
break;
}
case (D_CIRCLES):
{
c = pos_circles(config, pos, &alpha);
return(vcircles(config, alpha, pos));
break;
}
default:
{
printf("Function vbilliard not defined for this billiard \n");
@ -2676,6 +3415,44 @@ int color[NPARTMAX];
return(condition);
break;
}
case D_ANGLE:
{
if (y <= 0.0) return(0);
else if (x*sin(LAMBDA*PI) < -y*cos(LAMBDA*PI)) return(1);
else return(0);
break;
}
case D_LSHAPE:
{
if ((y <= 0.0)&&(x >= -1.0)&&(x <= 1.0)) return(1);
else if ((x >= -1.0)&&(x <= 0.0)) return(1);
else return(0);
break;
}
case D_GENUSN: /* same as polygon */
{
condition = 1;
omega = DPI/((double)NPOLY);
c = cos(omega*0.5);
for (k=0; k<NPOLY; k++)
{
angle = APOLY*PID + (k+0.5)*omega;
condition = condition*(x*cos(angle) + y*sin(angle) < c);
}
return(condition);
break;
}
case D_CIRCLES:
{
condition = 1;
for (k=0; k<ncircles; k++)
{
r2 = (x-circlex[k])*(x-circlex[k]) + (y-circley[k])*(y-circley[k]);
condition = condition*(r2 > circlerad[k]*circlerad[k])*circleactive[k];
}
return(condition);
break;
}
default:
{
printf("Function ij_in_billiard not defined for this billiard \n");