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/* -*-ePiX-*- */
/*
* ePiX surface demo image, June 08, 2006
*
* This file illustrates the use of pstricks (for color-filled
* arrowheads), manual layering of figure elements (for hidden-surface
* removal), and simulated transparency.
*/
#include "epix.h"
using namespace ePiX;
// Style parameters
// camera location (in spherical coordinates); must be in first orthant
const P VIEWPT=sph(4, M_PI/6, M_PI/6);
// colors
void color_coord(void) { rgb(0.7, 0.9, 0.5); }
void color_axis(void) { rgb(0.8, 0.2, 0.9); }
void color_xslice(void) { red(); }
void color_yslice(void) { blue(); }
void ps_axis_color(void)
{
std::cout << "\n\\newrgbcolor{axis_color}{0.8 0.2 0.9}%";
}
const int MESH(12); // number of coordinate grid squares
// location of tangency point
const double x_0=7.0/MESH;
const double y_0=6.0/MESH;
const double z_0=0.25; // height of top of slicing planes
const int MAX=1; // maximum coordinate
// function to be graphed
P f(double x, double y) { return P(x, y, 0.75*y*(y*y-3*x*x)); }
// constant y slice of the graph of f
P Df_x(double t) { return f(t+x_0, y_0); }
// constant x slice of the graph of f
P Df_y(double t) { return f(x_0, t+y_0); }
int main()
{
bounding_box(P(-2,-2), P(2,1));
picture(2,1.5);
unitlength("1.25in");
use_pstricks();
begin();
viewpoint(VIEWPT);
use_pstricks(false);
clip_box(P(-2, -2, -1), P(2, 2, 0.75));
// front and back halves
domain R1(P(-1,-1), P(0, 1), mesh(MESH, 2*MESH), mesh(MESH, 2*MESH));
domain R2(P( 0,-1), P(1, 1), mesh(MESH, 2*MESH), mesh(MESH, 2*MESH));
// coordinate grids
color_coord();
grid(P(-MAX,-MAX,-MAX), P(-MAX, MAX, MAX), MESH, MESH);
grid(P(-MAX,-MAX,-MAX), P( MAX,-MAX, MAX), MESH, MESH);
grid(P(-MAX,-MAX,-MAX), P( MAX, MAX,-MAX), MESH, MESH);
color_axis();
label(P(0,0.25+MAX,0), P(4,0), "$y$", r);
label(P(0,0,0.25+MAX), P(0,4), "$z$", t);
clip();
fill();
surface(f, R1);
fill(false);
clip(false);
// coordinate axes
bold();
use_pstricks();
ps_axis_color();
psset("linecolor=axis_color,fillcolor=axis_color");
// color_axis();
dart(P(0,-MAX,0), P(0,0.25+MAX,0));
dart(P(0,0,0), P(0,0,0.25+MAX));
use_pstricks(false);
// vertices of slicing planes
P pt1(x_0, 0, z_0), pt2(x_0, 0, -MAX), pt3(x_0, MAX, -MAX);
P pt4(0, y_0, z_0), pt5(0, y_0, -MAX), pt6(MAX, y_0, -MAX);
P pt7(x_0, 0, 0), pt8(x_0, MAX, z_0), pt9=f(0,y_0);
P pt10(MAX, y_0, z_0);
// lower outlines of slicing planes (partially hidden by surface)
color_xslice();
polyline(3, &pt1, &pt2, &pt3).draw();
color_yslice();
polyline(3, &pt4, &pt5, &pt6).draw();
plain();
clip();
fill();
// front 1/2 of surface (x>0)
surface(f, R2);
fill(false);
clip(false);
// last coordinate axis
bold();
use_pstricks();
psset("linecolor=axis_color, fillcolor=axis_color");
dart(P(-MAX,0,0), P(0.25+MAX,0,0));
use_pstricks(false);
color_axis();
label(P(0.25+MAX,0,0), P(-2,-2), "$x$", bl);
font_size("scriptsize");
// slices of the graph and labels
pen(1);
color_yslice();
plot(Df_x, -x_0, MAX-x_0, 20);
label(Df_x(MAX-x_0), P(-4,0),
"$\\displaystyle\\frac{\\partial f}{\\partial x}$: $y$ constant", l);
clip();
color_xslice();
plot(Df_y, -y_0, MAX-y_0, 20);
clip(false);
label(Df_y(MAX-y_0), P(4,0),
"$\\displaystyle\\frac{\\partial f}{\\partial y}$: $x$ constant", br);
// overall label
black();
label(P(-MAX, 0, MAX), P(2,2),
"$z=\\displaystyle\\frac{1}{2}(y^3-3x^2y)$", tr);
// fake transparency: redraw slicing planes thinly
// clip();
pen(0.15);
color_xslice();
rect(P(x_0, 0, -MAX), P(x_0, 1, z_0));
color_yslice();
rect(P(0, y_0, -MAX), P(1, y_0, z_0));
// upper outlines of slicing planes (not hidden by surface)
bold();
color_xslice();
polyline(4, &pt7, &pt1, &pt8, &pt3).draw();
color_yslice();
polyline(4, &pt9, &pt4, &pt10, &pt6).draw();
end();
}
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