/* Compilation  instructions */
/* gcc -Wall -ansi -pedantic -o Pi_archi_approx Pi_archi_approx.c */

/* This program generates an SVG image, showing Archimede's technique to */
/* approximate pi */
/* One argument can be provided, as the maximum number of approximations desired */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define PI 3.14159265358979

int main(int argc, char **argv)
{
    int i,j,n;
    double id,coeff;
    FILE *fpt;
    double *x, *y;
    double R = 40.0;
    /* Angle values*/
    double alpha, alpha_offset;

    int    fontsize    = 10;
    double strokewidth = 0.8;
    if (argc == 2)
        n = (int)atof(argv[1]);
    else
    {
        n = 10;
    }
    if (n<3)
    {
        printf("\n");
        fflush(stdout);
        exit(1);
    }
    /* Opening result file*/
    fpt = fopen("Pi_archi_approx.svg","w");
    fprintf(fpt,"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n");
    fprintf(fpt,"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd \">\n");
    fprintf(fpt,"<svg\n");
    fprintf(fpt,"   xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\" \n");
    fprintf(fpt,"   xmlns:svg=\"http://www.w3.org/2000/svg\" \n");
    fprintf(fpt,"   xmlns=\"http://www.w3.org/2000/svg\" \n");
    fprintf(fpt,"   width=\"%dpx\" \n",(int)(((n-2)*3+1)*R));
    fprintf(fpt,"   height=\"%dpx\" \n",(int)(4.5*R));
    fprintf(fpt,"   >\n");
    for (i=3;i<=n;i++)
    {
        id = (double) i;
        x  = (double *)malloc(i*sizeof(double));
        y  = (double *)malloc(i*sizeof(double));
        fprintf(fpt,"   <g>\n");
        fprintf(fpt,"    <circle cx=\"%f\" cy=\"%f\" r=\"%f\" ",((id-2)*3-0.75)*R,2.5*R,R);
        fprintf(fpt,"stroke=\"black\" stroke-width=\"%f\" fill=\"none\"/>\n",strokewidth);
        fprintf(fpt,"    <polygon points=\"");
        alpha_offset = -PI/2 + ((i%2)==0) * PI/id;
        for (j=0;j<i;j++)
        {
            alpha = alpha_offset + 2*j*PI/id;
            x[j]  = cos(alpha);
            y[j]  = sin(alpha);
            fprintf(fpt,"%f,%f ",R*x[j]+((id-2)*3-0.75)*R,R*(y[j]+2.5));
        }
        fprintf(fpt,"\" fill=\"none\" stroke=\"black\" stroke-width=\"%f\"/>\n",strokewidth);
        coeff = 2.0/sqrt((x[0]+x[1])*(x[0]+x[1]) + (y[0]+y[1])*(y[0]+y[1]));
        fprintf(fpt,"    <polygon points=\"");
        for (j=0;j<i;j++)
        {
            fprintf(fpt,"%f,%f ",R*coeff*x[j]+((id-2)*3-0.75)*R,R*(coeff*y[j]+2.5));
        }
        fprintf(fpt,"\" fill=\"none\" stroke=\"black\" stroke-width=\"%f\"/>\n",strokewidth);
        free(x);
        free(y);
        fprintf(fpt,"    <text x = \"%f\" y = \"%f\" text-anchor=\"middle\" fill = \"black\" font-size = \"%d\">\n",
                    ((id-2)*3-0.75)*R,4*R,fontsize);
        fprintf(fpt,"      n = %d\n",i);
        fprintf(fpt,"    </text>\n");
        fprintf(fpt,"  </g>\n");
    }
    fprintf(fpt,"</svg>\n");
    fclose(fpt);
    return (0);
}