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This commit is contained in:
nilsberglund-orleans
2021-08-15 11:49:37 +02:00
committed by GitHub
parent d227439e84
commit b1d8db471a
12 changed files with 2424 additions and 1052 deletions
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444
sub_wave.c
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@@ -67,9 +67,8 @@ void init() /* initialisation of window */
void hsl_to_rgb(h, s, l, rgb) /* color conversion from HSL to RGB */
void hsl_to_rgb(double h, double s, double l, double rgb[3]) /* color conversion from HSL to RGB */
/* h = hue, s = saturation, l = luminosity */
double h, s, l, rgb[3];
{
double c = 0.0, m = 0.0, x = 0.0;
@@ -109,19 +108,14 @@ double h, s, l, rgb[3];
double color_amplitude(value, scale, time)
double color_amplitude(double value, double scale, int time)
/* transforms the wave amplitude into a double in [-1,1] to feed into color scheme */
double value, scale;
int time;
{
return(tanh(SLOPE*value/scale)*exp(-((double)time*ATTENUATION)));
}
void color_scheme(scheme, value, scale, time, rgb) /* color scheme */
double value, scale;
int scheme, time;
double rgb[3];
void color_scheme(int scheme, double value, double scale, int time, double rgb[3]) /* color scheme */
{
double hue, y, r, amplitude;
int intpart;
@@ -182,6 +176,21 @@ void save_frame()
}
void save_frame_counter(int counter)
/* same as save_frame, but with imposed image number (for option DOUBLE_MOVIE) */
{
char *name="wave.", n2[100];
char format[6]=".%05i";
strcpy(n2, name);
sprintf(strstr(n2,"."), format, counter);
strcat(n2, ".tif");
printf(" saving frame %s \n",n2);
writetiff(n2, "Wave equation in a planar domain", 0, 0,
WINWIDTH, WINHEIGHT, COMPRESSION_LZW);
}
void write_text( double x, double y, char *st)
{
@@ -203,8 +212,7 @@ void write_text( double x, double y, char *st)
/* some basic math */
/*********************/
double vabs(x) /* absolute value */
double x;
double vabs(double x) /* absolute value */
{
double res;
@@ -213,9 +221,7 @@ void write_text( double x, double y, char *st)
return(res);
}
double module2(x, y) /* Euclidean norm */
double x, y;
double module2(double x, double y) /* Euclidean norm */
{
double m;
@@ -223,9 +229,7 @@ void write_text( double x, double y, char *st)
return(m);
}
double argument(x, y)
double x, y;
double argument(double x, double y)
{
double alph;
@@ -257,10 +261,8 @@ void write_text( double x, double y, char *st)
/* sets of coordinates decreases number of double computations when */
/* drawing the field */
void xy_to_ij(x, y, ij)
void xy_to_ij(double x, double y, int ij[2])
/* convert (x,y) position to (i,j) in table representing wave */
double x, y;
int ij[2];
{
double x1, y1;
@@ -272,9 +274,8 @@ int ij[2];
}
void xy_to_pos(x, y, pos)
void xy_to_pos(double x, double y, double pos[2])
/* convert (x,y) position to double-valued position in table representing wave */
double x, y, pos[2];
{
double x1, y1;
@@ -286,10 +287,8 @@ double x, y, pos[2];
}
void ij_to_xy(i, j, xy)
void ij_to_xy(int i, int j, double xy[2])
/* convert (i,j) position in table representing wave to (x,y) */
int i, j;
double xy[2];
{
double x1, y1;
@@ -297,8 +296,26 @@ double xy[2];
xy[1] = YMIN + ((double)j)*(YMAX-YMIN)/((double)NY);
}
void draw_rectangle(x1, y1, x2, y2)
double x1, y1, x2, y2;
void erase_area(double x, double y, double dx, double dy)
{
double pos[2], rgb[3];
hsl_to_rgb(220.0, 0.8, 0.7, rgb);
glColor3f(rgb[0], rgb[1], rgb[2]);
glBegin(GL_QUADS);
xy_to_pos(x - dx, y - dy, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(x + dx, y - dy, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(x + dx, y + dy, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(x - dx, y + dy, pos);
glVertex2d(pos[0], pos[1]);
glEnd();
}
void draw_rectangle(double x1, double y1, double x2, double y2)
{
double pos[2];
@@ -314,9 +331,7 @@ double x1, y1, x2, y2;
glEnd();
}
void draw_rotated_rectangle(x1, y1, x2, y2)
double x1, y1, x2, y2;
void draw_rotated_rectangle(double x1, double y1, double x2, double y2)
{
double pos[2];
double xa, ya, xb, yb, xc, yc;
@@ -340,12 +355,51 @@ double x1, y1, x2, y2;
glEnd();
}
void draw_circle(double x, double y, double r, int nseg)
{
int i;
double pos[2], alpha, dalpha;
dalpha = DPI/(double)nseg;
glBegin(GL_LINE_LOOP);
for (i=0; i<=nseg; i++)
{
alpha = (double)i*dalpha;
xy_to_pos(x + r*cos(alpha), y + r*sin(alpha), pos);
glVertex2d(pos[0], pos[1]);
}
glEnd();
}
void draw_colored_circle(double x, double y, double r, int nseg, double rgb[3])
{
int i;
double pos[2], alpha, dalpha;
dalpha = DPI/(double)nseg;
glColor3f(rgb[0], rgb[1], rgb[2]);
glBegin(GL_TRIANGLE_FAN);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
for (i=0; i<=nseg; i++)
{
alpha = (double)i*dalpha;
xy_to_pos(x + r*cos(alpha), y + r*sin(alpha), pos);
glVertex2d(pos[0], pos[1]);
}
glEnd();
}
void init_circle_config()
/* initialise the arrays circlex, circley, circlerad and circleactive */
/* for billiard shape D_CIRCLES */
{
int i, j, n;
double dx, dy, p, phi, r, ra[5], sa[5];
int i, j, n, ncirc0;
double dx, dy, p, phi, r, r0, ra[5], sa[5], height, x, y = 0.0, gamma;
switch (CIRCLE_PATTERN) {
case (C_SQUARE):
@@ -372,11 +426,13 @@ void init_circle_config()
for (j = 0; j < NGRIDY+1; j++)
{
n = (NGRIDY+1)*i + j;
circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy;
circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy; /* is +0.5 needed? */
circley[n] = YMIN + ((double)j - 0.5)*dy;
if ((i+NGRIDX)%2 == 1) circley[n] += 0.5*dy;
circlerad[n] = MU;
circleactive[n] = 1;
/* activate only circles that intersect the domain */
if ((circley[n] < YMAX + MU)&&(circley[n] > YMIN - MU)) circleactive[n] = 1;
else circleactive[n] = 0;
}
break;
}
@@ -388,9 +444,9 @@ void init_circle_config()
for (j = 0; j < NGRIDY; j++)
{
n = NGRIDY*i + j;
circlex[n] = ((double)(i-NGRIDX/2) + 0.5 + 0.5*(double)rand()/RAND_MAX)*dy;
circley[n] = YMIN + ((double)j + 0.5 + 0.5*(double)rand()/RAND_MAX)*dy;
circlerad[n] = MU*(1.0 + 0.35*(double)rand()/RAND_MAX);
circlex[n] = ((double)(i-NGRIDX/2) + 0.5*((double)rand()/RAND_MAX - 0.5))*dy;
circley[n] = YMIN + ((double)j + 0.5 + 0.5*((double)rand()/RAND_MAX - 0.5))*dy;
circlerad[n] = MU*sqrt(1.0 + 0.8*((double)rand()/RAND_MAX - 0.5));
circleactive[n] = 1;
}
break;
@@ -461,6 +517,129 @@ void init_circle_config()
}
break;
}
case (C_GOLDEN_MEAN):
{
ncircles = 300;
gamma = (sqrt(5.0) - 1.0)*0.5; /* golden mean */
height = YMAX - YMIN;
dx = 2.0*LAMBDA/((double)ncircles);
for (n = 0; n < ncircles; n++)
{
circlex[n] = -LAMBDA + n*dx;
circley[n] = y;
y += height*gamma;
if (y > YMAX) y -= height;
circlerad[n] = MU;
circleactive[n] = 1;
}
/* test for circles that overlap top or bottom boundary */
ncirc0 = ncircles;
for (n=0; n < ncirc0; n++)
{
if (circley[n] + circlerad[n] > YMAX)
{
circlex[ncircles] = circlex[n];
circley[ncircles] = circley[n] - height;
circlerad[ncircles] = MU;
circleactive[ncircles] = 1;
ncircles ++;
}
else if (circley[n] - circlerad[n] < YMIN)
{
circlex[ncircles] = circlex[n];
circley[ncircles] = circley[n] + height;
circlerad[ncircles] = MU;
circleactive[ncircles] = 1;
ncircles ++;
}
}
break;
}
case (C_GOLDEN_SPIRAL):
{
ncircles = 1;
circlex[0] = 0.0;
circley[0] = 0.0;
gamma = (sqrt(5.0) - 1.0)*PI; /* golden mean times 2Pi */
phi = 0.0;
r0 = 2.0*MU;
r = r0 + MU;
for (i=0; i<1000; i++)
{
x = r*cos(phi);
y = r*sin(phi);
phi += gamma;
r += MU*r0/r;
if ((vabs(x) < LAMBDA)&&(vabs(y) < YMAX + MU))
{
circlex[ncircles] = x;
circley[ncircles] = y;
ncircles++;
}
}
for (i=0; i<ncircles; i++)
{
circlerad[i] = MU;
/* inactivate circles outside the domain */
if ((circley[i] < YMAX + MU)&&(circley[i] > YMIN - MU)) circleactive[i] = 1;
// printf("i = %i, circlex = %.3lg, circley = %.3lg\n", i, circlex[i], circley[i]);
}
break;
}
case (C_SQUARE_HEX):
{
ncircles = NGRIDX*(NGRIDY+1);
dy = (YMAX - YMIN)/((double)NGRIDY);
dx = dy*0.5*sqrt(3.0);
for (i = 0; i < NGRIDX; i++)
for (j = 0; j < NGRIDY+1; j++)
{
n = (NGRIDY+1)*i + j;
circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy; /* is +0.5 needed? */
circley[n] = YMIN + ((double)j - 0.5)*dy;
if (((i+NGRIDX)%4 == 2)||((i+NGRIDX)%4 == 3)) circley[n] += 0.5*dy;
circlerad[n] = MU;
/* activate only circles that intersect the domain */
if ((circley[n] < YMAX + MU)&&(circley[n] > YMIN - MU)) circleactive[n] = 1;
else circleactive[n] = 0;
}
break;
}
case (C_ONE):
{
circlex[ncircles] = 0.0;
circley[ncircles] = 0.0;
circlerad[ncircles] = MU;
circleactive[ncircles] = 1;
ncircles += 1;
break;
}
case (C_TWO): /* used for comparison with cloak */
{
circlex[ncircles] = 0.0;
circley[ncircles] = 0.0;
circlerad[ncircles] = MU;
circleactive[ncircles] = 2;
ncircles += 1;
circlex[ncircles] = 0.0;
circley[ncircles] = 0.0;
circlerad[ncircles] = 2.0*MU;
circleactive[ncircles] = 1;
ncircles += 1;
break;
}
case (C_NOTHING):
{
ncircles += 0;
break;
}
default:
{
printf("Function init_circle_config not defined for this pattern \n");
@@ -477,19 +656,19 @@ double x, y;
int i, j, k, k1, k2, condition;
switch (B_DOMAIN) {
case D_RECTANGLE:
case (D_RECTANGLE):
{
if ((vabs(x) <LAMBDA)&&(vabs(y) < 1.0)) return(1);
else return(0);
break;
}
case D_ELLIPSE:
case (D_ELLIPSE):
{
if (x*x/(LAMBDA*LAMBDA) + y*y < 1.0) return(1);
else return(0);
break;
}
case D_STADIUM:
case (D_STADIUM):
{
if ((x > -0.5*LAMBDA)&&(x < 0.5*LAMBDA)&&(y > -1.0)&&(y < 1.0)) return(1);
else if (module2(x+0.5*LAMBDA, y) < 1.0) return(1);
@@ -497,13 +676,13 @@ double x, y;
else return(0);
break;
}
case D_SINAI:
case (D_SINAI):
{
if (x*x + y*y > LAMBDA*LAMBDA) return(1);
else return(0);
break;
}
case D_DIAMOND:
case (D_DIAMOND):
{
l2 = LAMBDA*LAMBDA;
r2 = l2 + (LAMBDA-1.0)*(LAMBDA-1.0);
@@ -514,26 +693,26 @@ double x, y;
else return(0);
break;
}
case D_TRIANGLE:
case (D_TRIANGLE):
{
if ((x>-LAMBDA)&&(y>-1.0)&&(LAMBDA*y+x<0.0)) return(1);
else return(0);
break;
}
case D_FLAT:
case (D_FLAT):
{
if (y > -LAMBDA) return(1);
else return(0);
break;
}
case D_ANNULUS:
case (D_ANNULUS):
{
l2 = LAMBDA*LAMBDA;
r2 = x*x + y*y;
if ((r2 > l2)&&(r2 < 1.0)) return(1);
else return(0);
}
case D_POLYGON:
case (D_POLYGON):
{
condition = 1;
omega = DPI/((double)NPOLY);
@@ -546,13 +725,13 @@ double x, y;
// for (k=0; k<NPOLY; k++) condition = condition*(-x*sin((k+0.5)*omega) + y*cos((k+0.5)*omega) < c);
return(condition);
}
case D_YOUNG:
case (D_YOUNG):
{
if ((x < -MU)||(x > MU)) return(1);
else if ((vabs(y-LAMBDA) < MU)||(vabs(y+LAMBDA) < MU)) return (1);
else return(0);
}
case D_GRATING:
case (D_GRATING):
{
k1 = -(int)((-YMIN)/LAMBDA);
k2 = (int)(YMAX/LAMBDA);
@@ -565,11 +744,11 @@ double x, y;
// printf("x = %.3lg, y = %.3lg, k1 = %i, k2 = %i, condition = %i\n", x, y, k1, k2, condition);
return(condition);
}
case D_EHRENFEST:
case (D_EHRENFEST):
{
return(((x-1.0)*(x-1.0) + y*y < LAMBDA*LAMBDA)||((x+1.0)*(x+1.0) + y*y < LAMBDA*LAMBDA)||((vabs(x) < 1.0)&&(vabs(y) < MU)));
}
case D_DISK_GRID:
case (D_DISK_GRID):
{
dy = (YMAX - YMIN)/((double)NGRIDY);
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
@@ -581,7 +760,7 @@ double x, y;
}
return(1);
}
case D_DISK_HEX:
case (D_DISK_HEX):
{
dy = (YMAX - YMIN)/((double)NGRIDY);
dx = dy*0.5*sqrt(3.0);
@@ -595,7 +774,7 @@ double x, y;
}
return(1);
}
case D_CIRCLES:
case (D_CIRCLES):
{
for (i = 0; i < ncircles; i++)
if (circleactive[i])
@@ -607,7 +786,7 @@ double x, y;
}
return(1);
}
case D_MENGER:
case (D_MENGER):
{
x1 = 0.5*(x+1.0);
y1 = 0.5*(y+1.0);
@@ -619,7 +798,7 @@ double x, y;
}
return(1);
}
case D_JULIA_INT:
case (D_JULIA_INT):
{
u = x/JULIA_SCALE;
v = y/JULIA_SCALE;
@@ -634,7 +813,7 @@ double x, y;
if (u*u + v*v < MANDELLIMIT) return(1);
else return(0);
}
case D_MENGER_ROTATED:
case (D_MENGER_ROTATED):
{
x2 = 1.0*(x + y);
y2 = 1.0*(x - y);
@@ -651,7 +830,7 @@ double x, y;
}
return(1);
}
case D_ANNULUS_HEATED: /* returns 2 if in inner circle */
case (D_ANNULUS_HEATED): /* returns 2 if in inner circle */
{
l2 = LAMBDA*LAMBDA;
r2 = x*x + y*y;
@@ -660,7 +839,7 @@ double x, y;
else if (r2mu <= l2) return(2);
else return (0);
}
case D_MENGER_HEATED:
case (D_MENGER_HEATED):
{
if ((vabs(x) >= 1.0)||(vabs(y) >= 1.0)) return(0);
else
@@ -676,7 +855,7 @@ double x, y;
return(1);
}
}
case D_MENGER_H_OPEN: /* returns 2 if in inner circle */
case (D_MENGER_H_OPEN): /* returns 2 if in inner circle */
{
x1 = 0.5*(x+1.0);
y1 = 0.5*(y+1.0);
@@ -688,7 +867,7 @@ double x, y;
}
return(1);
}
case D_MANDELBROT:
case (D_MANDELBROT):
{
u = 0.0;
v = 0.0;
@@ -707,7 +886,7 @@ double x, y;
else if ((x-0.5)*(x-0.5)/3.0 + y*y/1.0 > 1.2) return(2);
else return(1);
}
case D_MANDELBROT_CIRCLE:
case (D_MANDELBROT_CIRCLE):
{
u = 0.0;
v = 0.0;
@@ -723,7 +902,7 @@ double x, y;
else if ((x-LAMBDA)*(x-LAMBDA) + (y-0.5)*(y-0.5) < MU*MU) return(2);
else return(1);
}
case D_JULIA:
case (D_JULIA):
{
u = x/JULIA_SCALE;
v = y/JULIA_SCALE;
@@ -750,9 +929,8 @@ double x, y;
}
}
int ij_in_billiard(i, j)
int ij_in_billiard(int i, int j)
/* returns 1 if (i,j) represents a point in the billiard */
int i, j;
{
double xy[2];
@@ -811,31 +989,13 @@ void draw_billiard() /* draws the billiard boundary */
glLineWidth(2);
glEnable(GL_LINE_SMOOTH);
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = x0 + r*cos(phi);
y = r*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd();
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = -x0 + r*cos(phi);
y = r*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd();
draw_circle(x0, 0.0, r, NSEG);
draw_circle(-x0, 0.0, r, NSEG);
}
break;
}
case D_STADIUM:
case (D_STADIUM):
{
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
@@ -857,21 +1017,12 @@ void draw_billiard() /* draws the billiard boundary */
glEnd();
break;
}
case D_SINAI:
case (D_SINAI):
{
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = LAMBDA*cos(phi);
y = LAMBDA*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd();
draw_circle(0.0, 0.0, LAMBDA, NSEG);
break;
}
case D_DIAMOND:
case (D_DIAMOND):
{
alpha = atan(1.0 - 1.0/LAMBDA);
dphi = (PID - 2.0*alpha)/(double)NSEG;
@@ -936,26 +1087,8 @@ void draw_billiard() /* draws the billiard boundary */
}
case (D_ANNULUS):
{
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = LAMBDA*cos(phi);
y = LAMBDA*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = cos(phi);
y = sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
draw_circle(0.0, 0.0, LAMBDA, NSEG);
draw_circle(0.0, 0.0, 1.0, NSEG);
break;
}
case (D_POLYGON):
@@ -1008,27 +1141,18 @@ void draw_billiard() /* draws the billiard boundary */
glEnd();
break;
}
case D_GRATING:
case (D_GRATING):
{
k1 = -(int)(-YMIN/LAMBDA);
k2 = (int)(YMAX/LAMBDA);
for (i=k1; i<= k2; i++)
{
z = (double)i*LAMBDA;
glBegin(GL_LINE_LOOP);
for (j=0; j<=NSEG; j++)
{
phi = (double)j*DPI/(double)NSEG;
x = MU*cos(phi);
y = z + MU*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
draw_circle(0.0, z, MU, NSEG);
}
break;
}
case D_EHRENFEST:
case (D_EHRENFEST):
{
alpha = asin(MU/LAMBDA);
x0 = 1.0 - sqrt(LAMBDA*LAMBDA - MU*MU);
@@ -1053,7 +1177,7 @@ void draw_billiard() /* draws the billiard boundary */
glEnd ();
break;
}
case D_DISK_GRID:
case (D_DISK_GRID):
{
glLineWidth(2);
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
@@ -1063,20 +1187,11 @@ void draw_billiard() /* draws the billiard boundary */
dx = dy*0.5*sqrt(3.0);
x1 = ((double)i + 0.5)*dy;
y1 = YMIN + ((double)j + 0.5)*dy;
glBegin(GL_LINE_LOOP);
for (k=0; k<=NSEG; k++)
{
phi = (double)k*DPI/(double)NSEG;
x = x1 + MU*cos(phi);
y = y1 + MU*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
draw_circle(x1, y1, MU, NSEG);
}
break;
}
case D_DISK_HEX:
case (D_DISK_HEX):
{
glLineWidth(2);
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
@@ -1086,16 +1201,7 @@ void draw_billiard() /* draws the billiard boundary */
x1 = ((double)i + 0.5)*dy;
y1 = YMIN + ((double)j + 0.5)*dy;
if ((i+NGRIDX)%2 == 1) y1 += 0.5*dy;
glBegin(GL_LINE_LOOP);
for (k=0; k<=NSEG; k++)
{
phi = (double)k*DPI/(double)NSEG;
x = x1 + MU*cos(phi);
y = y1 + MU*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
draw_circle(x1, y1, MU, NSEG);
}
break;
}
@@ -1103,19 +1209,7 @@ void draw_billiard() /* draws the billiard boundary */
{
glLineWidth(BOUNDARY_WIDTH);
for (i = 0; i < ncircles; i++)
if (circleactive[i])
{
glBegin(GL_LINE_LOOP);
for (k=0; k<=NSEG; k++)
{
phi = (double)k*DPI/(double)NSEG;
x = circlex[i] + circlerad[i]*cos(phi);
y = circley[i] + circlerad[i]*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
}
if (circleactive[i]) draw_circle(circlex[i], circley[i], circlerad[i], NSEG);
break;
}
case (D_MENGER):
@@ -1221,26 +1315,8 @@ void draw_billiard() /* draws the billiard boundary */
}
case (D_ANNULUS_HEATED):
{
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = MU + LAMBDA*cos(phi);
y = LAMBDA*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
glBegin(GL_LINE_LOOP);
for (i=0; i<=NSEG; i++)
{
phi = (double)i*DPI/(double)NSEG;
x = cos(phi);
y = sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
draw_circle(MU, 0.0, LAMBDA, NSEG);
draw_circle(0.0, 0.0, 1.0, NSEG);
break;
}
case (D_MENGER_HEATED):