// Calculation Program b for calculating shape of a flower with the use of a Cardioid. 19 Feb., 2009

// file name: flower_b_E.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 t,dt;// the phase angle [radian] before the conversion and its increment [radian] of a Cardioid
	double r,z;// the moving radius anf the phase angle of a Cardioid respectively after removement of its origin point
	double f;// the phase angle of the Cardioid after the final conversion into a horned one (using as a petal of a flower)
	int n;// a desired numbers of petals of a flower
	double alpha;// the angle for the horned Cardioid (used as that alpha=2*pi/n )
	double tmin,tmax;// the minimum and maximum values of the phase angle "t" respectively
	int i,imax,j;
	double x,y;// the orthogonal coordinates of a petal before contraction or expansion
	float b;// the ratio of contraction or expansion of a petal in the length direction
	float c;// the radius of a center circle
	double rr;// the moving radius of a petal after contraction or expansion
	double ff;// the phase angle of a petal after contraction or expansion
	double xx[30001],yy[30001];// Take care of the upper limit of storage memory capacitance.

	double ff0,ffs,fs,dfs;// several variables in regard to the phase angle of the each arc connecting each two petals

	FILE *fp;

// setting of the constants
	pi=3.14159265;
	a=1.;

// setting of the other parameters
	printf("Input a desired numbers of petals of a flower in natural number. \n n=? ");
	scanf("%d",&n);
	printf("n=%d\n",n);
	printf("\n");

	alpha=2*pi/n;

	printf("Input the ratio of contraction or expansion of a petal in the length direction. \n b= ? ");
	scanf("%f",&b);
	printf("b=%f\n",b);
	printf("\n");

	printf("Input the radius of a center circle. \n c= ? ");
	scanf("%f",&c);
	printf("c=%f\n",c);
	printf("\n");

	tmin=-pi/2;
	tmax=3*pi/2;
	dt=(tmax-tmin)/1000;// plotting interval of the phase angle "t" before conversion

// execution of calculation
	i=0;

	for(j=1;j<=n;j++) // the sweeping of n numbers of petals
	{
		for(t=tmin;t<=tmax+dt;t=t+dt) // the sweeping of the phase angle t of one petal
		{
			i++;

			if(t>(3*pi/2-dt) && t<(3*pi/2+dt))
			{
				r=0.;
				z=-pi/2;
			}
			else
			{
				if(t>(-pi/2-dt) && t<(-pi/2+dt))
				{
					r=0.;
					z=pi/2;
				}
				else
				{
					r=a*sqrt((5-3*sin(t))*(1+sin(t)));
					z=asin(a*(1-sin(t))*cos(t)/r);
				}
			}
			
			f=-alpha*z/pi+pi/2;

			x=r*cos(f);
			y=b*r*sin(f);

			rr=sqrt(x*x+y*y);

			if(f< pi/2)
			{
			ff=atan(b*tan(f));
			}
			else
			{
				if(f==pi/2)
				{
					ff=pi/2;
				}
				else
				{
					ff=atan(b*tan(f))+pi;
				}
			}

			ff=ff+2*pi*(j-1)/n;

			if(i==1&&j==1)
			{
				ff0=ff;
			}

			if(t==tmin&&j>1)
			{
				if(ffs>ff)
				{
					dfs=(ffs-ff)/20;
					for(fs=ffs;fs>=ff;fs=fs-dfs)
					{
						xx[i]=c*cos(fs);
						yy[i]=c*sin(fs);
						i++;
					}
				}
				else
				{
					dfs=(ff-ffs)/20;
					for(fs=ffs;fs<=ff;fs=fs+dfs)
					{
						xx[i]=c*cos(fs);
						yy[i]=c*sin(fs);
						i++;
					}
				}
			}

			ffs=ff;

			xx[i]=(rr+c)*cos(ff);
			yy[i]=(rr+c)*sin(ff);

			printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
		}
	}

	if(ffs>2*pi)
	{
		ffs=ffs-2*pi;
	}

	if(ffs>ff0)
	{
		dfs=(ffs-ff0)/20;
		for(fs=ffs;fs>=ff0;fs=fs-dfs)
		{
			i++;
			xx[i]=c*cos(fs);
			yy[i]=c*sin(fs);
		}
	}
	else
	{
		dfs=(ff0-ffs)/20;
		for(fs=ffs;fs<=ff0;fs=fs+dfs)
		{
			i++;
			xx[i]=c*cos(fs);
			yy[i]=c*sin(fs);
		}
	}

	imax=i;

// writing the calculated coordinates data into a textfile
	fp=fopen("flower_curve_b.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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