// Calculation Program for calculating shape of a flower with the use of a Cardioid (x3), July 28, 2012
// file name: flower_x3.c
#include< stdio.h>
#include< math.h>
void main(void)
{
double a,pi;// "a" is the constant of original Cardioid and pi=3.1415...
double r,t;// the moving radius and the phase angle of the original Cardioid respectively
double f,df;// the phase angle and its increment of heart curve respectively
double rr,ff;// the moving radius and the phase angle of a petal after contraction or expansion
double fmin,fmax;// the minimum and maximum values of the phase angle "f" respectively
double x,y;// the orthogonal coordinates of a petal (which is a heart curve itself) before contraction or expansion
int n;// desired numbers of petals of a flower
double b,c;// reformation coefficients of a petal
double d;// compression coefficient of a petal in the length direction
double e,p;// the radius and the phase angle of a center circle respectively
double dp;// the increment of "p"
double beta;// angular range to be occupied by a petal around the center circle
double dbeta;// the increment of "beta"
double k;// coefficient for to vary the bottom angle of the heart curve
double l;// magnification factor of the angular range "beta" where 0 < l
int nf;// division numbers of both phase angles "t" and "beta"
int m;// count numbers of the increment of "beta
int i,imax,j;
double xx[20001],yy[20001];// Take care of the upper limit of storage memory capacitance.
double t1, t2;// auxiliary variables to mediate "t"
FILE *fp;
// setting of the constants
pi=3.14159265;
a=1;
b=1;// b=1
c=0.2;// c=-0.2. [Caution] It is required that -1 < c < 1.
d=1;// d=1
e=0.3;// e=0.3
k=0.7;// k=0.7
l=1;// l=1
printf("Input the numbers of petals. \n n=? ");
scanf("%d",&n);
printf("n=%d\n",n);
printf("\n");
beta=2*pi/n;// fundamentally criteria value of angular range to be occupied by a petal around the center circle
beta=l*beta;// corrected value of "beta" with "l"
// setting of the other parameters
fmin=-pi/2;
fmax=3*pi/2;
nf=200;
df=(fmax-fmin)/nf;// plotting interval of "f"
dbeta=beta/nf;// increment of "beta"
dp=2*pi/n/100;// increment of "p"
i=0;
// execution of calculation
for(j=1;j<=n;j++) // sweep of n numbers of petals
{
m=0;
for(f=fmin;f< fmax;f=f+df) // sweep of phase angle "f" of the each petal
{
i++;
m++;
if(f<=-pi/2)// start of conversion of the phase from Cardioid to heart curve
{
t1=0;
}
else
{
t1=b*sqrt(f+pi/2);
}
if(f>=3*pi/2)
{
t2=0;
}
else
{
t2=b*sqrt(3*pi/2-f);
}
t=t1-t2+(1-b*sqrt(2/pi))*f+b*sqrt(pi/2);// end of conversion of the phase from Cardioid to heart curve
r=a*(1-sin(t));// relationship between the moving radius of the heart curve and the phase angle of Cardioid
x=r*(1+c*sin(f)*cos(f)*cos(f))*cos(f);// x coordinates of the fundamental (1st) petal (reformed heart curve)
y=d*r*(1+c*sin(f)*cos(f)*cos(f))*sin(f)+2*a*d;// y coordinates of the fundamental (1st) petal (reformed heart curve)
rr=sqrt(x*x+y*y);// calculation of the moving radius of the above petal (reformed heart curve)
if(x==0)// calculation of the phase angle of the above petal (reformed heart curve)
{
ff=pi/2;
}
else
{
if(x>0)
{
ff=asin(y/rr);
}
else
{
ff=pi-asin(y/rr);
}
}
ff=k*(ff-pi/2)+pi/2;// to vary the bottom angle of petal (the reformed heart curve)
ff=ff+2*pi*(j-1)/n;// the phase angle of the j-th petal
xx[i]=rr*cos(ff)+e*cos(2*pi*(j-1)/n+pi/2-beta/2+m*dbeta);
yy[i]=rr*sin(ff)+e*sin(2*pi*(j-1)/n+pi/2-beta/2+m*dbeta);
printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
}
if(l<=1) // Simply for drawing an additional circle of underlying petal.
{
for(p=2*pi*(j-1)/n+pi/2+beta/2;p<2*pi*j/n+pi/2-beta/2+0;p=p+dp)
{
i++;
xx[i]=e*cos(p);
yy[i]=e*sin(p);
printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
}
}
else
{
for(p=2*pi*(j-1)/n+pi/2+beta/2;p>2*pi*j/n+pi/2-beta/2-0;p=p-dp)
{
i++;
xx[i]=e*cos(p);
yy[i]=e*sin(p);
printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
}
}
}
i++;
xx[i]=xx[1];// for connecting the start and the end points
yy[i]=yy[1];
for(p=pi/2-beta/2;p<2*pi*(n-1)/n+pi/2+beta/2-0;p=p+dp)// drawing a center circle
{
i++;
xx[i]=e*cos(p);
yy[i]=e*sin(p);
}
imax=i;
// writing the calculated coordinates data of the curve into a textfile
fp=fopen("flower_x3.txt","w");
if(fp==NULL)
{
printf("FILE OPEN ERROR\n");
}
else
{
for(i=1;i<=imax;i++)
{
fprintf(fp,"%f,%f\n",xx[i],yy[i]);
}
fflush(fp);
fclose(fp);
}
printf("end\n");
}// the end of the program
RETURN