// Calculation Program for calculating shape of a flower with the use of a Cardioid_c1_overlap, Sep. 20, 2012
// file name: flower_c1_overlap.c
#include< stdio.h>
#include< math.h>
void main(void)
{
double a,pi;// "a" is the constant of the original Cardioid, "pi" is the pi
double r,f;// the moving radius and the phase angle [radian] of a heart curve respectively
double fmin,fmax,df;
double x,y;
double rr,ff;
double ffmin,ffmax;
int n;
double t;
double b,c;
double d;
double e;
double k;
double p;// the index of overlap of petals
int i,imax,j;
double xx[20001],yy[20001];
double t1, t2,fff,fs,dfs,fff0,fffs;
FILE *fp;
// setting of the constants [Caution: Some combination of conrtants b, c, d and e may yields a calculation error. But, the cause of this error is unknown yet.]
pi=3.14159265;
a=1;
b=2;
c=0.5;
d=1;
e=0.5;
k=1;
p=2;// 0< p< 1 in the case of no overlap of petals, and 1< p in the case of overlap of petals
printf("Input of the numbers of petals. \n n=? ");
scanf("%d",&n);
printf("n=%d\n",n);
printf("\n");
// setting of the other parameters
fmin=-pi/2;
fmax=3*pi/2;
df=(fmax-fmin)/400;
fmin=fmin+df;
fmax=fmax-df;
ffmin=pi/2;
ffmax=pi/2;
// pre-calculation (obtaining the maximum and the minimum angles of the shape of heart curve)
for(f=fmin;f<=fmax;f=f+df)
{
if(f<=-pi/2)
{
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);
r=a*(1-sin(t));
x=r*(1+c*sin(f))*cos(f);
y=d*r*(1+c*sin(f))*sin(f)+2*a*d*(1-c);
rr=sqrt(x*x+y*y);
if(x==0)
{
ff=pi/2;
}
else
{
if(x>0)
{
ff=asin(y/rr);
}
else
{
ff=pi-asin(y/rr);
}
}
if(ff>ffmax){ffmax=ff;}
if(ff< ffmin){ffmin=ff;}
}
ffmax=k*(ffmax-pi/2)+pi/2;
ffmin=k*(ffmin-pi/2)+pi/2;
i=0;
// main calculation
for(j=1;j<=n;j++)
{
for(f=fmin;f<=fmax;f=f+df)
{
i++;
if(f<=-pi/2)
{
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);
r=a*(1-sin(t));
x=r*(1+c*sin(f))*cos(f);
y=d*r*(1+c*sin(f))*sin(f)+2*a*d*(1-c);
rr=sqrt(x*x+y*y);
if(x==0)
{
ff=pi/2;
}
else
{
if(x>0)
{
ff=asin(y/rr);
}
else
{
ff=pi-asin(y/rr);
}
}
fff=(p*2*pi/(n*(ffmax-ffmin)))*ff+pi/2+2*(j-1)*pi/n-p*pi*pi/(n*(ffmax-ffmin));
if(i==1&&j==1) // connecting by an arc curve to fill a gap between adjacent petals (start)
{
fff0=fff;
}
if(fabs(fff-fffs)> 0.00001)
{
if(f==fmin&&j>1&&fffs>fff)
{
dfs=(fffs-fff)/20;
for(fs=fffs;fs>=fff;fs=fs-dfs)
{
xx[i]=e*cos(fs);
yy[i]=e*sin(fs);
i++;
}
}
if(f==fmin&&j>1&&fffs< fff)
{
dfs=(fff-fffs)/20;
for(fs=fffs;fs<=fff;fs=fs+dfs)
{
xx[i]=e*cos(fs);
yy[i]=e*sin(fs);
i++;
}
}
} // connecting by an arc curve to fill a gap between adjacent petals (the end)
fffs=fff;
xx[i]=(rr+e)*cos(fff);
yy[i]=(rr+e)*sin(fff);
printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
}
}
if(fffs>2*pi) // connecting by an arc curve to fill a gap between adjacent petals (start)
{
fffs=fffs-2*pi;
}
if(fabs(fff-fffs)> 0.00001)
{
if(fffs>fff0)
{
dfs=(fffs-fff0)/20;
for(fs=fffs;fs>=fff0;fs=fs-dfs)
{
i++;
xx[i]=e*cos(fs);
yy[i]=e*sin(fs);
}
}
else
{
dfs=(fff0-fffs)/20;
for(fs=fffs;fs<=fff0;fs=fs+dfs)
{
i++;
xx[i]=e*cos(fs);
yy[i]=e*sin(fs);
}
}
} // connecting by an arc curve to fill a gap between adjacent petals (the end)
i++;
xx[i]=xx[1];
yy[i]=yy[1];
imax=i;
// writing the calculated coordinates data of the curve into a textfile
fp=fopen("flower_c1_overlap.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