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/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;
const P VIEWPT(20, 0, 8);
const double tmin(2/sqrt(3));
const Color light(Blue(1.6));
const Color dark(Red(0.8));
const Color lt_gray(Black(0.2));
const Color net_color(Yellow(0.1));
void label_tag(P loc, P head, std::string txt, epix_label_posn align)
{
dart(loc, head);
masklabel(loc, P(0,0), txt, align);
}
domain R(P(-2,-2), P(2,2), mesh(20, 20), mesh(40,40));
domain edge(P(-2,-2), P(2,2), mesh(1,1), mesh(40,40));
// surface
P Phi(double u, double v)
{
return P(4*v, 0.75*(u*u-2*v)*u, 2*u);
}
P cubic(double t) { return Phi(t, 1.5*t*t); }
// cubic projections to background planes
P Phi12(double t)
{
P temp(cubic(t));
return P(temp.x1(), temp.x2(), -8);
}
P Phi13(double t)
{
P temp(cubic(t));
return P(temp.x1(), -8, temp.x3());
}
P Phi23(double t)
{
P temp(cubic(t));
return P(-8, temp.x2(), temp.x3());
}
int main() {
picture(P(-14,-15), P(10,9), "6x6in");
begin();
set_crop();
camera.at(VIEWPT);
// background grids
pen(lt_gray);
grid(P(-8, -8, -8), P(8, 8, -8), 8,8);
grid(P(-8, -8, -8), P(8, -8, 6), 7,8); // n.b. (z,x) divisions
grid(P(-8, -8, -8), P(-8, 8, 6), 8,7);
// background coordinate axes
pen(Black());
line(P(0, -8, -8), P(0, 8, -8));
line(P(-8, 0, -8), P(8, 0, -8));
line(P(0, -8, -8), P(0, -8, 6));
line(P(-8, -8, 0), P(8, -8, 0));
line(P(-8, 0, -8), P(-8, 0, 6));
line(P(-8, -8, 0), P(-8, 8, 0));
// projections of cubic
bold(dark);
plot(Phi12, -tmin, tmin, 80);
plot(Phi13, -tmin, tmin, 80);
plot(Phi23, -tmin, tmin, 80);
// surface
plain(net_color);
fill(lt_gray);
surface(Phi, R.resize1(-2,0)); // bottom half
// and cubic curve
bold(dark);
plot(cubic, -tmin, 0, 80);
plain(net_color);
surface(Phi, R.resize1(0,2)); // top half
bold(dark);
plot(cubic, 0, tmin, 80);
// surface boundary
bold(Yellow());
plot(Phi, edge);
// guide lines to cusp projection
plain(light);
dashed();
line(cubic( tmin), Phi12( tmin));
line(cubic(-tmin), Phi12(-tmin));
/*
// guide lines to other projections
line(cubic( tmin), Phi13( tmin));
line(cubic(-tmin), Phi13(-tmin));
line(cubic( tmin), Phi23( tmin));
line(cubic(-tmin), Phi23(-tmin));
*/
// fake transparency
plain(dark);
plot(Phi12, -tmin, tmin, 20); // cusp
// plot(Phi13, -tmin, tmin, 20);
// plot(Phi23, -tmin, tmin, 20);
label_color(Black());
label(P(8,0,-8), P(0,-4), "$x$", b);
label(P(0,8,-8), P(4,0), "$y$", r);
pen(light);
label_border(light, "0.4pt");
solid();
label_tag(Phi(-2,-2)+P(0,2,6), Phi(-1.75,-1.75),
"$y=\\frac{3}{32}(z^3-2xz)$", t);
label_tag(cubic(-1)+P(0,2,3), cubic(-1),
"$(x,y,z)=(6t^2, -\\frac{3}{2}t^3, 2t)$", t);
pst_format();
end();
}
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