/* coil.c */
#include <math.h>

#define PI M_PI
#define MAX_JUMP 0.025

double theta = PI/6;
double scale = 100;
double x_origin = 2.5;
double y_origin = 2.0;
double t_start = 0;
double t_end = 3;

/* parameteric eqns */

double X(t)
double t;
{
	return cos(2*PI*t);
}

double Y(t)
double t;
{
	return sin(2*PI*t);
}

double Z(t)
double t;
{
	return t;
}

/* transformation 3-space to user space */
transform (x, y, z)
double x, y, z;
{
	double X = y - x * cos( theta );
	double Y = z - x * sin( theta );

	printf ( "%f %f lineto\n", X, Y );
}

start_graph (x, y, z)
double x, y, z;
{
	double X = y - x * cos( theta );
	double Y = z - x * sin( theta );

	printf ( "newpath\n" );
	printf ( "%f %f moveto\n", X, Y );
}

/* draw the parametric curve */

draw ( t_1, x_1, y_1, z_1, t_2, x_2, y_2, z_2 )
double t_1, x_1, y_1, z_1, t_2, x_2, y_2, z_2;
{
	double t_mid = (t_2 + t_1)/2;
	double x_mid = X(t_mid);
	double y_mid = Y(t_mid);
	double z_mid = Z(t_mid);

	double dist_sq = (t_2 - t_1) * (t_2 - t_1) +
		(x_2 - x_mid) * (x_2 - x_mid) +
		(x_1 - x_mid) * (x_1 - x_mid) +
		(y_2 - y_mid) * (y_2 - y_mid) +
		(y_1 - y_mid) * (y_1 - y_mid) +
		(z_2 - z_mid) * (z_2 - z_mid) +
		(z_1 - z_mid) * (z_1 - z_mid);
	
	if ( dist_sq < MAX_JUMP)
	{
		transform ( x_2, y_2, z_2 );
	}
	else
	{
		draw ( t_1, x_1, y_1, z_1, t_mid, x_mid, y_mid, z_mid );
		draw ( t_mid, x_mid, y_mid, z_mid, t_2, x_2, y_2, z_2 );
	}
}

/* main routine */
main()
{
	double t_1 = t_start; double t_2 = t_end;
	double x_1 = X(t_1); double y_1 = Y(t_1); double z_1 = Z(t_1);
	double x_2 = X(t_2); double y_2 = Y(t_2); double z_2 = Z(t_2);
	printf ( "%%!-PostScript\n" );
	printf ( "%%%% The Good Doctors Coil.c\n" );
	printf ( "%%%% not EPS\n" );

	printf ( "%f %f scale\n", scale, scale );
	printf ( "%f %f translate\n", x_origin, y_origin );
	printf ( "0 setlinewidth\n" );

	printf ( "0 0 moveto\n" );
	transform (1.5, 0.0, 0.0 );
	printf ( "stroke\n" );

	printf ( "0 0 moveto\n" );
	transform (0.0, 1.5, 0.0 );
	printf ( "stroke\n" );

	printf ( "0 0 moveto\n" );
	transform (0.0, 0.0, 3.5 );
	printf ( "stroke\n" );

	start_graph ( x_1, y_1, z_1 );
	draw ( t_1, x_1, y_1, z_1, t_2, x_2, y_2, z_2 );

	printf ( "stroke\nshowpage\n" );
}