/******************************************************************************
* LICENSE *
******************************************************************************
* This file is part of Mathematics-and-Physics. *
* *
* Mathematics-and-Physics is free software: you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as published *
* by the Free Software Foundation, either version 3 of the License, or *
* (at your option) any later version. *
* *
* Mathematics-and-Physics is distributed in the hope that it will be useful *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with Mathematics-and-Physics. If not, see *
* <https://www.gnu.org/licenses/>. *
******************************************************************************
* Purpose: *
* Draws the intersection of a plane with a cube, revealing a hexagon. *
* This is what you'd get if you dipped a cube into water with one of *
* vertices of the cube facing down. *
******************************************************************************/
/* PDF is easiest to use in LaTeX, so output this. */
import settings;
settings.outformat = "pdf";
/* Size of the figure. */
size(128);
/* Default pen for drawings. */
defaultpen(black + linewidth(0.5pt));
/* Other pens used. */
pen dashp = defaultpen + linetype("4 4");
pen thinp = black + linewidth(0.1pt);
pen bluep = blue + linewidth(0.5pt);
pen thindashp = thinp + linetype("4 4");
pen bluedashp = bluep + linetype("4 4");
pen greendashp = green + linewidth(0.4pt) + linetype("4 4");
/* Function for making 3D drawings with 2D points. */
pair xyzpoint(real x, real y, real z)
{
pair X = (-0.4*x, -0.4*x);
pair Y = (y, 0.0);
pair Z = (0.0, z);
return X + Y + Z;
}
/* End of xyzpoint. */
/* Coordinates for all of the points in the cube. */
pair O = xyzpoint(0, 0, 0);
pair x = xyzpoint(6, 0, 0);
pair y = xyzpoint(0, 6, 0);
pair z = xyzpoint(0, 0, 6);
pair xy = xyzpoint(6, 6, 0);
pair xz = xyzpoint(6, 0, 6);
pair yz = xyzpoint(0, 6, 6);
pair xyz = xyzpoint(6, 6, 6);
pair MID = xyzpoint(3, 3, 3);
pair a1 = xyzpoint(3, 0, 6);
pair a2 = xyzpoint(3, 6, 6);
pair a3 = xyzpoint(0, 3, 6);
pair a4 = xyzpoint(6, 3, 6);
pair b1 = xyzpoint(0, 0, 3);
pair b2 = xyzpoint(6, 0, 3);
pair b3 = a1;
pair b4 = xyzpoint(3, 0, 0);
pair c1 = b2;
pair c2 = xyzpoint(6, 6, 3);
pair c3 = a4;
pair c4 = xyzpoint(6, 3, 0);
pair d1 = xyzpoint(0, 6, 3);
pair d2 = c2;
pair d3 = a2;
pair d4 = xyzpoint(3, 6, 0);
pair e1 = a3;
pair e2 = xyzpoint(0, 3, 0);
pair e3 = b1;
pair e4 = d1;
pair f1 = e2;
pair f2 = c4;
pair f3 = b4;
pair f4 = d4;
pair A = xyzpoint(3, 3, 6);
pair B = xyzpoint(3, 0, 3);
pair C = xyzpoint(6, 3, 3);
pair D = xyzpoint(3, 6, 3);
pair E = xyzpoint(0, 3, 3);
pair F = xyzpoint(3, 3, 0);
/* Draw the back of the cube. */
draw(O -- x, dashp);
draw(O -- y, dashp);
draw(O -- z, dashp);
/* Dashed lines inside of the cube. */
draw(a1 -- a2, thinp);
draw(a3 -- a4, thinp);
draw(b1 -- b2, thindashp);
draw(b3 -- b4, thindashp);
draw(c1 -- c2, thinp);
draw(c3 -- c4, thinp);
draw(d1 -- d2, thinp);
draw(d3 -- d4, thinp);
draw(e1 -- e2, thindashp);
draw(e3 -- e4, thindashp);
draw(f1 -- f2, thindashp);
draw(f3 -- f4, thindashp);
draw(A -- MID, thindashp);
draw(B -- MID, thindashp);
draw(C -- MID, thindashp);
draw(D -- MID, thindashp);
draw(E -- MID, thindashp);
draw(F -- MID, thindashp);
/* Draw the hexagon. */
draw(a1 -- a3, bluep);
draw(a3 -- d1, bluedashp);
draw(d1 -- d4, bluep);
draw(d4 -- c4, bluedashp);
draw(c4 -- b2, bluep);
draw(b2 -- a1, bluedashp);
/* Draw the spokes of the hexagon. */
draw(a1 -- MID, greendashp);
draw(a3 -- MID, greendashp);
draw(d1 -- MID, greendashp);
draw(c4 -- MID, greendashp);
draw(d4 -- MID, greendashp);
draw(b2 -- MID, greendashp);
/* Draw the front of the cube. */
draw(x -- xy);
draw(y -- xy);
draw(x -- xz);
draw(z -- xz);
draw(y -- yz);
draw(z -- yz);
draw(xy -- xyz);
draw(yz -- xyz);
draw(xz -- xyz);
