// Calculation Program for calculating shape of a flower with the use of a Cardioid d_overlap, Sep. 23, 2023



// file name: flower_d_overlap.c



#include< stdio.h>

#include< math.h>



void main(void)

{

	double a,pi;

	double r,f;

	double fmin,fmax,df;

	double x,y;

	double rr,ff;



	int n;

	double t;

	double b,c;

	double d;

	double e;

	double p;// the index of overlap of petals

	int i,imax,j;

	double xx[20001],yy[20001];

	double t1, t2;

	double fs,dfs,ff0,ffs;



	FILE *fp;



// setting of the constants

	pi=3.14159265;

	a=1;



	b=2.;

	c=0.1;

	d=1;

	e=0.;

	p=3;// 0< p< 1 in the case of no overlap of petals, and 1< p in the case of overlap of petals



	printf("Input of 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;



	i=0;



// execution of 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);



                        ff=(f+(2*pi*j/p+((n/p)-5)*pi/2))/(n/p);



			if(fabs(p-1.)>0.00001) // connecting by an arc curve to fill a gap between adjacent petals (start)

			{



				if(i==1&&j==1)

				{

					ff0=ff;

				}



				if(f==fmin&&j>1)

				{

					if(ffs>ff)

					{

						dfs=(ffs-ff)/20;

						for(fs=ffs;fs>=ff;fs=fs-dfs)

						{

							xx[i]=e*cos(fs);

							yy[i]=e*sin(fs);

							i++;

						}

					}

					else

					{

						dfs=(ff-ffs)/20;

						for(fs=ffs;fs<=ff;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)



			ffs=ff;



			xx[i]=(rr+e)*cos(ff);

			yy[i]=(rr+e)*sin(ff);



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

		}

	}



	if(fabs(p-1.)>0.00001) // connecting by an arc curve to fill a gap between adjacent petals (start)

	{

		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]=e*cos(fs);

				yy[i]=e*sin(fs);

			}

		}

		else

		{

			dfs=(ff0-ffs)/20;

			for(fs=ffs;fs<=ff0;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)



	imax=i;



// writing the calculated coordinates data of the curve into a textfile

	fp=fopen("flower_d_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