/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;

const double MAX(3);
const double ALPHA(M_PI/6);  // alpha (demi-angle au sommet du cône)
const double SA(Sin(ALPHA)); // sin(alpha)
const double CA(Cos(ALPHA)); // cos(alpha)
const double XC(10);
const double YC(-5);


// Cône
P Cone(double x, double y) {
    return fabs(sinh(x))*P(Cos(y), Sin(y), -1/Tan(ALPHA));
}

P PolaireSurCone(double t, double r,double a) {
    return 1.5*P(r*SA*Cos(t/SA),r*SA*Sin(t/SA),-r*CA);
}


int main() {
    bounding_box(P(-MAX,-MAX),P(MAX,MAX));
    unitlength("1in");
    picture(6,6);

    begin();
	camera.at(XC,YC,4);
	clip_face(P(-XC/60,-YC/60,0),P(XC,YC,0));
	domain R(P(-1.5,0), P(0,2*M_PI), mesh(25, 36), mesh(50, 72));
	fill(White());
	surface(Cone, R);
	base(Red(0.6), "3pt");
	bold(Red());
	plot("chainette.dta",PATH,PolaireSurCone,1,2);
	clip_restore();
	pst_format();
    end();
}