// 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