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nilsberglund-orleans
2021-06-20 23:31:23 +02:00
committed by GitHub
parent bd6aa073a7
commit 279a6e8801
7 changed files with 2149 additions and 141 deletions
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726
sub_part_billiard.c
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@@ -239,10 +239,45 @@ void write_text( double x, double y, char *st)
}
void paint_billiard_interior() /* points billiard interior, for use before draw_conf */
void compute_flower_parameters(omega, co, so, axis1, axis2, phimax)
/* compute parameters needed for the flower billiard in terms of LAMBDA and NPOLY */
double *omega, *co, *so, *axis1, *axis2, *phimax;
{
double omega2, co2, so2, r, a, gamma, axissquare1;
/* various angles */
*omega = DPI/((double)NPOLY);
omega2 = PI/((double)NPOLY);
co2 = cos(omega2);
so2 = sin(omega2);
*co = cos(*omega);
*so = sin(*omega);
// *co = co2*co2 - so2*so2;
// *so = 2.0*co2*so2;
/* distance of edge of ellipse to the origin */
r = LAMBDA*co2/(*co);
a = (r*co2 - *co)*(r*co2 - *co);
gamma = 0.5*r*r - r*co2*(*co) + 0.5*cos(2.0*(*omega));
axissquare1 = gamma + sqrt(gamma*gamma + a*(*so)*(*so));
/* semi-minor axis */
*axis1 = sqrt(axissquare1);
/* semi-major axis */
*axis2 = sqrt(axissquare1 + (*so)*(*so));
/* max angle in ellipse parametrization */
*phimax = asin(r*so2/(*axis2));
}
void paint_billiard_interior() /* paints billiard interior, for use before draw_conf */
{
double x0, x, y, phi, r = 0.01, alpha, dphi, omega;
int i, k, c;
double x0, x, y, phi, r = 0.01, alpha, dphi, omega, beta2, x2, s, x1, y1, angle, co, so, axis1, axis2, phimax;
int i, j, k, c;
glLineWidth(4);
@@ -273,6 +308,64 @@ void paint_billiard_interior() /* points billiard interior, for use before
}
break;
}
case (D_REULEAUX):
{
omega = DPI/((double)NPOLY);
beta2 = asin(sin(omega*0.5)/LAMBDA);
if (LAMBDA > 0.0) x2 = cos(omega*0.5) + sqrt(LAMBDA*LAMBDA - sin(omega*0.5)*sin(omega*0.5));
else x2 = cos(omega*0.5) - sqrt(LAMBDA*LAMBDA - sin(omega*0.5)*sin(omega*0.5));
if (PAINT_INT)
{
if (BLACK) glColor3f(1.0, 1.0, 1.0);
else glColor3f(0.0, 0.0, 0.0);
glBegin(GL_TRIANGLE_FAN);
glVertex2d(0.0, 0.0);
for (i=0; i<=NPOLY; i++)
{
for (j=0; j<NSEG; j++)
{
s = 2.0*(((double)j/(double)NSEG)-0.5)*beta2;
x1 = x2 - LAMBDA*cos(s);
y1 = LAMBDA*sin(s);
angle = i*omega + APOLY*PID;
x = cos(angle)*x1 - sin(angle)*y1;
y = sin(angle)*x1 + cos(angle)*y1;
glVertex2d(x, y);
}
}
glEnd();
}
break;
}
case (D_FLOWER):
{
compute_flower_parameters(&omega, &co, &so, &axis1, &axis2, &phimax);
if (PAINT_INT)
{
if (BLACK) glColor3f(1.0, 1.0, 1.0);
else glColor3f(0.0, 0.0, 0.0);
glBegin(GL_TRIANGLE_FAN);
glVertex2d(0.0, 0.0);
for (i=0; i<=NPOLY; i++)
{
for (j=0; j<NSEG; j++)
{
s = 2.0*(((double)j/(double)NSEG)-0.5)*phimax;
x1 = co + axis1*cos(s);
y1 = axis2*sin(s);
angle = i*omega + APOLY*PID;
x = cos(angle)*x1 - sin(angle)*y1;
y = sin(angle)*x1 + cos(angle)*y1;
glVertex2d(SCALING_FACTOR*x, SCALING_FACTOR*y);
}
}
glEnd();
}
break;
}
default:
{
@@ -282,7 +375,8 @@ void paint_billiard_interior() /* points billiard interior, for use before
void draw_billiard() /* draws the billiard boundary */
{
double x0, x, y, phi, r = 0.01, alpha, dphi, omega, x1, y1, x2, beta2, angle, s;
double x0, x, y, phi, r = 0.01, alpha, dphi, omega, x1, y1, x2, beta2, angle, s, x2plus, x2minus;
double omega2, co, so, axis1, axis2, phimax;
int i, j, k, c;
if (PAINT_INT) glColor3f(0.5, 0.5, 0.5);
@@ -366,6 +460,20 @@ void draw_billiard() /* draws the billiard boundary */
glVertex2d(x, y);
}
glEnd();
if (DRAW_CONSTRUCTION_LINES)
{
glColor3f(0.5, 0.5, 0.5);
glBegin(GL_LINE_STRIP);
glVertex2d(-LAMBDA, -1.0);
glVertex2d(-LAMBDA, 1.0);
glEnd();
glBegin(GL_LINE_STRIP);
glVertex2d(LAMBDA, -1.0);
glVertex2d(LAMBDA, 1.0);
glEnd();
}
break;
}
case D_SINAI:
@@ -580,6 +688,86 @@ void draw_billiard() /* draws the billiard boundary */
glEnd ();
break;
}
case (D_FLOWER):
{
compute_flower_parameters(&omega, &co, &so, &axis1, &axis2, &phimax);
/* draw inner polygon and radial lines */
if (DRAW_CONSTRUCTION_LINES)
{
glColor3f(0.5, 0.5, 0.5);
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 ();
r = LAMBDA*cos(0.5*omega)/co;
for (i=0; i<=NPOLY; i++)
{
glBegin(GL_LINE_STRIP);
glVertex2d(0.0, 0.0);
x = r*cos(((double)i + 0.5)*omega + APOLY*PID);
y = r*sin(((double)i + 0.5)*omega + APOLY*PID);
glVertex2d(SCALING_FACTOR*x, SCALING_FACTOR*y);
glEnd ();
}
}
/* draw billiard boundary */
if (!PAINT_INT)
{
if (BLACK) glColor3f(1.0, 1.0, 1.0);
else glColor3f(0.0, 0.0, 0.0);
}
glBegin(GL_LINE_STRIP);
for (i=0; i<=NPOLY; i++)
// for (i=0; i<=1; i++)
{
for (j=0; j<NSEG; j++)
{
// s = 2.0*(((double)j/(double)NSEG)-0.5)*PI;
s = 2.0*(((double)j/(double)NSEG)-0.5)*phimax;
x1 = co + axis1*cos(s);
y1 = axis2*sin(s);
angle = i*omega + APOLY*PID;
x = cos(angle)*x1 - sin(angle)*y1;
y = sin(angle)*x1 + cos(angle)*y1;
glVertex2d(SCALING_FACTOR*x, SCALING_FACTOR*y);
}
}
glEnd ();
break;
}
case (D_ALT_REU):
{
omega = DPI/((double)NPOLY);
beta2 = asin(sin(omega*0.5)/LAMBDA);
x2plus = cos(omega*0.5) + sqrt(LAMBDA*LAMBDA - sin(omega*0.5)*sin(omega*0.5));
x2minus = cos(omega*0.5) - sqrt(LAMBDA*LAMBDA - sin(omega*0.5)*sin(omega*0.5));
glBegin(GL_LINE_STRIP);
for (i=0; i<=NPOLY; i++)
{
for (j=0; j<NSEG; j++)
{
s = 2.0*(((double)j/(double)NSEG)-0.5)*beta2;
if (i%2==0) x1 = x2plus - LAMBDA*cos(s);
else x1 = x2minus + LAMBDA*cos(s);
y1 = LAMBDA*sin(s);
angle = i*omega + APOLY*PID;
x = cos(angle)*x1 - sin(angle)*y1;
y = sin(angle)*x1 + cos(angle)*y1;
glVertex2d(x, y);
}
}
glEnd ();
break;
}
default:
{
printf("Function draw_billiard not defined for this billiard \n");
@@ -1688,57 +1876,38 @@ int color[NPARTMAX];
rangle = 2.0*(double)k*omega2 + APOLY*PID;
theta = alpha - rangle;
// if ((intb)) /* check if condition is ok */
// if ((cos(theta) > 0.0)&&(intb)) /* check if condition is ok */
ca = cos(rangle);
sa = sin(rangle);
x = pos[0]*ca + pos[1]*sa;
y = -pos[0]*sa + pos[1]*ca;
a = (x-x2)*cos(theta) + y*sin(theta);
b = (x-x2)*(x-x2) + y*y - LAMBDA*LAMBDA;
if (a*a - b > margin)
{
ca = cos(rangle);
sa = sin(rangle);
// printf("theta = %.5lg\n", theta);
// printf("rangle = %.5lg x0 = %.5lg y0 = %.5lg \n", rangle, pos[0], pos[1]);
x = pos[0]*ca + pos[1]*sa;
y = -pos[0]*sa + pos[1]*ca;
// printf("x = %.5lg\t y = %.5lg\n", x, y);
a = (x-x2)*cos(theta) + y*sin(theta);
b = (x-x2)*(x-x2) + y*y - LAMBDA*LAMBDA;
// printf("a = %.5lg\t b = %.5lg\n", a, b);
if (a*a - b > margin)
if (LAMBDA > 0.0) t = -a - sqrt(a*a - b);
else t = -a + sqrt(a*a - b);
xi = x + t*cos(theta);
yi = y + t*sin(theta);
if ((t > margin)&&(vabs(yi) <= sin(omega2)))
{
// t = vabs(a) - sqrt(a*a - b);
if (LAMBDA > 0.0) t = -a - sqrt(a*a - b);
else t = -a + sqrt(a*a - b);
xi = x + t*cos(theta);
yi = y + t*sin(theta);
// printf("t = %.5lg\t xi = %.5lg\t yi = %.5lg\n", t, xi, yi);
if ((t > margin)&&(vabs(yi) <= sin(omega2)))
{
cval[nt] = k;
tval[nt] = t;
cval[nt] = k;
tval[nt] = t;
/* rotate back */
x1[nt] = xi*ca - yi*sa;
y1[nt] = xi*sa + yi*ca;
/* rotate back */
x1[nt] = xi*ca - yi*sa;
y1[nt] = xi*sa + yi*ca;
// intb = 0;
// c = k;
tempconf[nt][0] = ((double)k + 0.5)*beta + asin(yi/LAMBDA);
tempconf[nt][1] = PID - asin(yi/LAMBDA) - theta;
// tempconf[nt][0] = ((double)k + 0.5)*beta + asin(yi/vabs(LAMBDA));
// tempconf[nt][1] = PID - asin(yi/vabs(LAMBDA)) - theta;
nt++;
}
tempconf[nt][0] = ((double)k + 0.5)*beta + asin(yi/LAMBDA);
tempconf[nt][1] = PID - asin(yi/LAMBDA) - theta;
nt++;
}
}
}
// printf("nt = %i\n", nt);
/* find earliest intersection */
tmin = tval[0];
@@ -1783,6 +1952,390 @@ int color[NPARTMAX];
return(c);
}
/****************************************************************************************/
/* Bunimovich flower billiard */
/****************************************************************************************/
int pos_flower(conf, pos, alpha)
/* determine position on boundary of polygon */
/* conf[0] is arclength on boundary, it belongs to [0,2*NPOLY*phimax) */
double conf[2], pos[2], *alpha;
{
double s, theta, omega, co, so, axis1, axis2, phimax, s1, x, y, angle;
int c;
s = conf[0];
theta = conf[1];
compute_flower_parameters(&omega, &co, &so, &axis1, &axis2, &phimax);
c = (int)(s/(2.0*phimax)); /* side of shape */
s1 = s - (((double)c)*2.0 + 1.0)*phimax;
x = co + axis1*cos(s1);
y = axis2*sin(s1);
angle = ((double)c)*omega + PID*APOLY;
// angle = 2.0*((double)c)*omega + PID*APOLY;
pos[0] = x*cos(angle) - y*sin(angle);
pos[1] = x*sin(angle) + y*cos(angle);
*alpha = argument(-axis1*sin(s1), axis2*cos(s1)) + theta + angle;
// printf("alpha = %.5lg\t", *alpha);
return(c);
}
int vflower_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
double config[8], alpha, pos[2];
{
double s, theta, omega, omega2, s1, rangle, x, y, x1, y1, xi, yi, t;
double ca, sa, aa, bb, cc, margin = 1.0e-14, tmin;
double co, so, co2, so2, ct, st, phimax, phi, axis1, axis2;
int k, c, intb=1, intc, i, nt = 0, ntmin, sign;
compute_flower_parameters(&omega, &co, &so, &axis1, &axis2, &phimax);
for (k=0; k<NPOLY; k++) if (intb)
{
/* rotate position so that kth side is vertical */
// rangle = (double)(2*k)*omega + APOLY*PID;
rangle = (double)k*omega + APOLY*PID;
theta = alpha - rangle;
ca = cos(rangle);
sa = sin(rangle);
ct = cos(theta);
st = sin(theta);
x = pos[0]*ca + pos[1]*sa;
y = -pos[0]*sa + pos[1]*ca;
/* find intersection with elliptical arc */
aa = ct*ct/(axis1*axis1) + st*st/(axis2*axis2);
bb = (x-co)*ct/(axis1*axis1) + y*st/(axis2*axis2);
cc = (x-co)*(x-co)/(axis1*axis1) + y*y/(axis2*axis2) - 1.0;
// if (bb*bb - aa*cc > margin)
if (bb*bb - aa*cc >= 0.0)
{
t = (-bb + sqrt(bb*bb - aa*cc))/aa;
xi = x + t*cos(theta);
yi = y + t*sin(theta);
if (yi >= 0.0) phi = argument((xi - co)/axis1, yi/axis2);
else phi = -argument((xi - co)/axis1, -yi/axis2);
if ((t > margin)&&((vabs(phi) <= phimax)||(vabs(phi-DPI) <= phimax)))
{
intb = 0;
c = k;
/* rotate back */
x1 = xi*ca - yi*sa;
y1 = xi*sa + yi*ca;
config[0] = (double)(2*k + 1)*phimax + phi;
config[1] = argument(-axis1*sin(phi), axis2*cos(phi)) - theta;
}
}
}
// if (nt == 0) printf("nt = %i\t ntmin = %i \tcmin = %i\n", nt, ntmin, c);
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 old_vflower_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
double config[8], alpha, pos[2];
{
double s, theta, omega, omega2, s1, rangle, x, y, x1[2*NPOLY], y1[2*NPOLY], xi, yi, t;
double ca, sa, aa, bb, cc, margin = 1.0e-14, tmin, tval[2*NPOLY], tempconf[2*NPOLY][2];
double co, so, co2, so2, ct, st, phimax, phi, axis1, axis2;
int k, c, intb=1, intc, i, nt = 0, cval[2*NPOLY], ntmin, sign;
compute_flower_parameters(&omega, &co, &so, &axis1, &axis2, &phimax);
for (k=0; k<NPOLY; k++)
{
/* rotate position so that kth side is vertical */
// rangle = (double)(2*k)*omega + APOLY*PID;
rangle = (double)k*omega + APOLY*PID;
theta = alpha - rangle;
ca = cos(rangle);
sa = sin(rangle);
ct = cos(theta);
st = sin(theta);
x = pos[0]*ca + pos[1]*sa;
y = -pos[0]*sa + pos[1]*ca;
/* find intersection with elliptical arc */
aa = ct*ct/(axis1*axis1) + st*st/(axis2*axis2);
bb = (x-co)*ct/(axis1*axis1) + y*st/(axis2*axis2);
cc = (x-co)*(x-co)/(axis1*axis1) + y*y/(axis2*axis2) - 1.0;
// if (bb*bb - aa*cc > margin)
if (bb*bb - aa*cc >= 0.0)
{
t = (-bb + sqrt(bb*bb - aa*cc))/aa;
xi = x + t*cos(theta);
yi = y + t*sin(theta);
if (yi >= 0.0) phi = argument((xi - co)/axis1, yi/axis2);
else phi = -argument((xi - co)/axis1, -yi/axis2);
// phi = argument((xi - co)/axis1, yi/axis2);
// if (phi > PI) phi += -DPI;
if ((t > margin)&&((vabs(phi) <= phimax)||(vabs(phi-DPI) <= phimax)))
// if (((vabs(phi) <= phimax)||(vabs(phi-DPI) <= phimax)))
// if ((t > margin))
{
cval[nt] = k;
// cval[nt] = 2*k;
tval[nt] = t;
/* rotate back */
x1[nt] = xi*ca - yi*sa;
y1[nt] = xi*sa + yi*ca;
tempconf[nt][0] = (double)(2*k + 1)*phimax + phi;
tempconf[nt][1] = argument(-axis1*sin(phi), axis2*cos(phi)) - theta;
nt++;
}
}
}
/* find earliest intersection */
tmin = tval[0];
ntmin = 0;
for (i=1; i<nt; i++)
if (tval[i] < tmin)
{
tmin = tval[i];
ntmin = i;
}
config[0] = tempconf[ntmin][0];
config[1] = tempconf[ntmin][1];
c = cval[ntmin];
if (nt == 0) printf("nt = %i\t ntmin = %i \tcmin = %i\n", nt, ntmin, c);
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]); /* distance to collision */
config[4] = pos[0]; /* start position */
config[5] = pos[1];
config[6] = x1[ntmin]; /* position of collision */
config[7] = y1[ntmin];
return(c);
}
int vflower(config)
/* determine initial configuration when starting from boundary */
double config[8];
{
double pos[2], alpha;
int c;
c = pos_flower(config, pos, &alpha);
vflower_xy(config, alpha, pos);
return(c);
}
/****************************************************************************************/
/* Alternating between Reuleaux-type and star-shaped billiard */
/****************************************************************************************/
int pos_alt_reuleaux(conf, pos, alpha)
/* determine position on boundary of polygon */
/* conf[0] is arclength on boundary */
double conf[2], pos[2], *alpha;
{
double s, theta, omega2, beta2, beta, s1, angle, x2plus, x2minus, x, y;
int c;
s = conf[0];
theta = conf[1];
omega2 = PI/((double)NPOLY);
beta2 = asin(sin(omega2)/vabs(LAMBDA));
beta = beta2*2.0;
c = (int)(s/beta); /* side of shape */
s1 = s - ((double)c)*beta;
x2plus = cos(omega2) + sqrt(LAMBDA*LAMBDA - sin(omega2)*sin(omega2));
x2minus = cos(omega2) - sqrt(LAMBDA*LAMBDA - sin(omega2)*sin(omega2));
if (c%2 == 0) x = x2plus - LAMBDA*cos(s1 - beta2);
else x = x2minus + LAMBDA*cos(s1 - beta2);
if (c%2 == 0) y = LAMBDA*sin(s1 - beta2);
else y = -LAMBDA*sin(s1 - beta2);
/* test, to be removed */
// x = x2plus - LAMBDA*cos(s1 - beta2);
// y = LAMBDA*sin(s1 - beta2);
angle = 2.0*((double)c)*omega2 + PID*APOLY;
pos[0] = x*cos(angle) - y*sin(angle);
pos[1] = x*sin(angle) + y*cos(angle);
*alpha = PID - s1 + beta2 + theta + 2.0*(double)c*omega2 + APOLY*PID;
// printf("alpha = %.5lg\t", *alpha);
return(c);
}
int valt_reuleaux_xy(config, alpha, pos)
/* determine initial configuration for start at point pos = (x,y) */
double config[8], alpha, pos[2];
{
double s, theta, omega2, beta, s1, rangle, x, y, x1[NPOLY], y1[NPOLY], xi, yi, t, x2plus, x2minus, arcsine;
double ca, sa, a, b, margin = 1.0e-14, tmin, tval[NPOLY], tempconf[NPOLY][2];
int k, c, intb=1, intc, i, nt = 0, cval[NPOLY], ntmin;
/* dimensions/angles of polygon */
omega2 = PI/((double)NPOLY);
beta = 2.0*asin(sin(omega2)/vabs(LAMBDA));
// printf("beta = %.5lg\n", beta);
x2plus = cos(omega2) + sqrt(LAMBDA*LAMBDA - sin(omega2)*sin(omega2));
x2minus = cos(omega2) - sqrt(LAMBDA*LAMBDA - sin(omega2)*sin(omega2));
// printf("x2 = %.5lg\n", x2);
for (k=0; k<NPOLY; k++)
{
/* rotate position so that kth side is vertical */
rangle = 2.0*(double)k*omega2 + APOLY*PID;
theta = alpha - rangle;
ca = cos(rangle);
sa = sin(rangle);
x = pos[0]*ca + pos[1]*sa;
y = -pos[0]*sa + pos[1]*ca;
if (k%2==0)
{
a = (x-x2plus)*cos(theta) + y*sin(theta);
b = (x-x2plus)*(x-x2plus) + y*y - LAMBDA*LAMBDA;
}
else
{
a = (x-x2minus)*cos(theta) + y*sin(theta);
b = (x-x2minus)*(x-x2minus) + y*y - LAMBDA*LAMBDA;
}
if (a*a - b > margin)
{
if (k%2==0) t = -a - sqrt(a*a - b);
else t = -a + sqrt(a*a - b);
xi = x + t*cos(theta);
yi = y + t*sin(theta);
if ((t > margin)&&(vabs(yi) <= sin(omega2)))
{
cval[nt] = k;
tval[nt] = t;
/* rotate back */
x1[nt] = xi*ca - yi*sa;
y1[nt] = xi*sa + yi*ca;
if (k%2==0) arcsine = asin(yi/LAMBDA);
else arcsine = -asin(yi/LAMBDA);
tempconf[nt][0] = ((double)k + 0.5)*beta + arcsine;
tempconf[nt][1] = PID - arcsine - theta;
nt++;
}
}
}
/* find earliest intersection */
tmin = tval[0];
ntmin = 0;
for (i=1; i<nt; i++)
if (tval[i] < tmin)
{
tmin = tval[i];
ntmin = i;
}
config[0] = tempconf[ntmin][0];
config[1] = tempconf[ntmin][1];
c = cval[ntmin];
// printf("nt = %i\t ntmin = %i \tcmin = %i\n", nt, ntmin, c);
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]); /* distance to collision */
config[4] = pos[0]; /* start position */
config[5] = pos[1];
config[6] = x1[ntmin]; /* position of collision */
config[7] = y1[ntmin];
return(c);
}
int valt_reuleaux(config)
/* determine initial configuration when starting from boundary */
double config[8];
{
double pos[2], alpha;
int c;
c = pos_alt_reuleaux(config, pos, &alpha);
valt_reuleaux_xy(config, alpha, pos);
return(c);
}
/****************************************************************************************/
/* general billiard */
@@ -1833,6 +2386,16 @@ int color[NPARTMAX];
return(pos_reuleaux(conf, pos, &alpha));
break;
}
case (D_FLOWER):
{
return(pos_flower(conf, pos, &alpha));
break;
}
case (D_ALT_REU):
{
return(pos_alt_reuleaux(conf, pos, &alpha));
break;
}
default:
{
printf("Function pos_billiard not defined for this billiard \n");
@@ -1887,6 +2450,16 @@ int color[NPARTMAX];
return(vreuleaux_xy(config, alpha, pos));
break;
}
case (D_FLOWER):
{
return(vflower_xy(config, alpha, pos));
break;
}
case (D_ALT_REU):
{
return(valt_reuleaux_xy(config, alpha, pos));
break;
}
default:
{
printf("Function vbilliard_xy not defined for this billiard \n");
@@ -1960,6 +2533,20 @@ int color[NPARTMAX];
return(vreuleaux(config, alpha, pos));
break;
}
case (D_FLOWER):
{
c = pos_flower(config, pos, &alpha);
return(vflower(config, alpha, pos));
break;
}
case (D_ALT_REU):
{
c = pos_alt_reuleaux(config, pos, &alpha);
return(valt_reuleaux(config, alpha, pos));
break;
}
default:
{
printf("Function vbilliard not defined for this billiard \n");
@@ -1971,7 +2558,7 @@ int color[NPARTMAX];
/* returns 1 if (x,y) represents a point in the billiard */
double x, y;
{
double l2, r2, omega, omega2, c, angle, x1, y1, x2, co, so;
double l2, r1, r2, omega, omega2, c, angle, x1, y1, x2, co, so, x2plus, x2minus;
int condition, k;
switch (B_DOMAIN) {
@@ -2021,8 +2608,9 @@ int color[NPARTMAX];
case D_ANNULUS:
{
l2 = LAMBDA*LAMBDA;
r2 = x*x + y*y;
if ((r2 > l2)&&(r2 < 1.0)) return(1);
r1 = x*x + y*y;
r2 = (x-MU)*(x-MU) + y*y;
if ((r2 > l2)&&(r1 < 1.0)) return(1);
else return(0);
break;
}
@@ -2056,22 +2644,42 @@ int color[NPARTMAX];
y1 = -x*sin(angle) + y*cos(angle);
if (LAMBDA > 0.0) condition = condition*((x1-x2)*(x1-x2) + y1*y1 > LAMBDA*LAMBDA);
else condition = condition*((x1-x2)*(x1-x2) + y1*y1 < LAMBDA*LAMBDA);
// if (!condition)
// {
// printf("x = %.5lg \t y = %.5lg \t x1 = %.5lg \t y1 = %.5lg \t angle = %.5lg \n", x, y, x1, y1, angle);
// printf("k = %i \t condition = %i\n", k, condition);
// sleep(1);
// }
}
return(condition);
break;
}
/* D_REULEAUX : distance to all centers of arcs should be larger than LAMBDA */
case D_FLOWER:
{
/* TO DO */
return(1);
break;
}
case D_ALT_REU:
{
condition = 1;
omega2 = PI/((double)NPOLY);
co = cos(omega2);
so = sin(omega2);
x2plus = co + sqrt(LAMBDA*LAMBDA - so*so);
x2minus = co - sqrt(LAMBDA*LAMBDA - so*so);
for (k=0; k<NPOLY; k++)
{
angle = 2.0*(double)k*omega2 + APOLY*PID;
x1 = x*cos(angle) + y*sin(angle);
y1 = -x*sin(angle) + y*cos(angle);
if (k%2==0) condition = condition*((x1-x2plus)*(x1-x2plus) + y1*y1 > LAMBDA*LAMBDA);
else condition = condition*((x1-x2minus)*(x1-x2minus) + y1*y1 < LAMBDA*LAMBDA);
}
return(condition);
break;
}
default:
{
printf("Function ij_in_billiard not defined for this billiard \n");
return(0);
return(1);
}
}
}