#include <stdio.h>
#include <stdlib.h>
#include <math.h>

void usage() {
    fprintf(stderr, "Usage: paraboloid <segments> <radius> <fraction>\n");
    fprintf(stderr, "  segments: the number of segments that "
		    "must be attached to make the paraboloid\n");
    fprintf(stderr, "  radius: the radius in inches of the final shape\n");
    fprintf(stderr, "  fraction: the height as a fraction of the radius;\n");
    fprintf(stderr, "            A height of 0.5 puts the focal point "
                    "in the plane of the top.\n");
    exit(1);
}

#define PTS 100

void lineto(double x, double y) {
    printf("%g %g lineto %% %g, %g\n", x*72, y*72, x, y);
}

int main(int argc, char **argv) {
    if (argc != 4) {
	usage();
    } else {
    double n = atof(argv[1]);
    double R0 = atof(argv[2]);
    double f = atof(argv[3]);
    double th2 = M_PI / n; /* theta / 2 */
    double a = f/R0; /* paraboloid: z = ar^2 */
    double TOL = 1.0e-7 * R0;
    double cth2 = cos(th2);
    double sth2 = sin(th2);
    double csq = cth2 * cth2;

    puts("%!PS-Adobe-2.0");
    puts("%%Creator: paraboloid");
    puts("%%Pages: 1");
    puts("%%PageOrder: Ascend");
    puts("%%BoundingBox: 0 0 612 792");
    puts("%%EndComments");
    puts("%%BeginSetup");
    puts("%%EndSetup");

    puts("%%Page: 1 1");

    double pts[PTS][2];
    int i;
    for (i = 0; i < PTS; i++) {
	double r = i * R0 / (PTS - 1);
	double h = r * sth2;
	double d = 0.5 * r * cth2 * sqrt(1. + 4.*a*a*r*r/csq) + csq * asinh(2.*a*r/cth2) / (4.*a);
	pts[i][0] = h;
	pts[i][1] = d;
    }
    printf("%g %g translate\n", 4.25*72, 0.5*72);
    puts("0 0 moveto");
    for (i = 0; i < PTS; i++) {
	lineto(pts[i][0], pts[i][1]);
    }
    puts("stroke");
    puts("0 0 moveto");
    for (i = 0; i < PTS; i++) {
	lineto(-pts[i][0], pts[i][1]);
    }
    lineto(pts[PTS-1][0], pts[PTS-1][1]);
    puts("stroke");

    puts("0 0 moveto");
    for (i = 20; i < PTS; i++) {
	lineto(pts[i][0] + 0.25, pts[i][1] - 0.25);
    }
    lineto(pts[PTS-1][0], pts[PTS-1][1]);
    puts("stroke");

    puts("showpage");
    puts("%%EOF");
    }
}