// Calculation Program for calculating shape of a flower with the use of a Cardioid (3), July 19, 2012

// file name: flower_i.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=1.3;// d=1.3
	e=0.2;// e=0.2
	k=0.75;// k=0.75
	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=100;

	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)*fabs(cos(f)))*cos(f);// x coordinates of the fundamental (1st) petal (reformed heart curve)
			y=d*r*(1+c*sin(f))*sin(f)+2*a*d*(1-c);// 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 named "flower_i.txt"
	fp=fopen("flower_i.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

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