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/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;
const double MAX(3);
// hyperboloid of one sheet/spacelike cone
P Fp(double x, double y, double z)
{
return P(z*cosh(x)*Cos(y), z*cosh(x)*Sin(y), z*sinh(x));
}
// hyperboloid of two sheets/timelike cone
P Fm(double x, double y, double z)
{
return P(z*sinh(x)*Cos(y), z*sinh(x)*Sin(y), z*cosh(x));
}
// light cone
P Fz(double x, double y)
{
return fabs(sinh(x))*P(Cos(y), Sin(y), sgn(x));
}
// hyperbolic lines
P hl1(double t)
{
return cosh(t)*P(-sqrt(1.25),0,1.5) + sinh(t)*E_2;
}
P hl2(double t)
{
return cosh(t)*P(-1,0.5,1.5) + (sqrt(0.4)*sinh(t))*P(0.5, 1, 0);
}
int main()
{
bounding_box(P(-MAX,-MAX),P(MAX,MAX));
unitlength("1in");
picture(6,6);
begin();
camera.at(10,-3,4);
// camera.range(40);
revolutions();
domain R(P(-1.5,0.25,-1), P(1.5,0.75,1), mesh(18, 12, 4), mesh(36, 48, 12));
fill(White());
// assemble surfaces as a single object
scenery hyp(Fp, R.slice3(1));
hyp.add(Fm, R.resize1(0,1.5).slice3(1));
hyp.add(Fm, R.resize1(-1.5,0).slice3(-1));
hyp.add(Fz, R.slice3(1));
hyp.draw();
nofill();
// Draw cuts of intersection with (y,z)-plane.
// Simulated 3-D/tube pen: light color drawn over darker shade
base(Red(0.6), "3pt");
bold(Red());
plot(Fp, R.slice2(0.25).slice3(1));
plot(Fp, R.slice2(0.25).slice3(-1));
plot(Fm, R.slice2(0.25).slice3(1));
plot(Fm, R.slice2(0.25).slice3(-1));
plot(Fz, R.slice2(0.25).slice3(1));
plot(Fz, R.slice2(0.75).slice3(-1));
// to clip lines
clip_box(P(-10,-10,-cosh(1.5)), P(10,10,cosh(1.5)));
base(Green(0.6), "3pt");
bold(Green());
plot(hl1, -1.5, 1.5, 120);
plot(hl2, -1.5, 1.5, 120);
// Labels with "overlay" arrows
font_size("scriptsize");
black();
camera.at(P(0,0,10000));
label(P(1.5,0), P(4,16), "Future timelike unit vectors", r);
label(P(1.5,0), P(4,0), "Unit spacelike vectors", r);
label(P(1.5,0), P(4,-16), "Lightlike vectors", r);
label(P(1.5,0), P(4,-32), "Past timelike unit vectors", r);
base(White(), "2pt");
bold(Black());
arrow(P(1.5,0), P(1,0), 0.5);
arrow(P(1.5, 0.25), P(1,1.35), 0.5);
arrow(P(1.5,-0.25), P(1,-0.75), 0.5);
arrow(P(1.5,-0.5), P(1,-1.05), 0.5);
pst_format();
end();
}
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