envelope/envelope.asy

from settings access outformat;
outformat="pdf";
unitsize(1mm);
int pgw = 210;
int pgh = 297;
size(pgw, pgh);

int sqsz = pgw;

// C6: 114 x 162 mm
int envh = 114;
int envw = 162;
string envfmt = "C6";
// A6: 105 x 148 mm

// debugging tool
bool with_labels = true;


// It is unpractical to try emulating second quadrant. We will work in the
// first quadrant with the origin at the bottom-left corner of the square (not
// the whole page). Therefore, the bottom edge of the page is at y=(210-297)
int pgbot = 210-297;

//Force A4 size
//draw((0,pgbot) -- (0, sqsz) -- (sqsz, sqsz) -- (sqsz, pgbot) -- cycle, invisible);

// gimme a square?
if (with_labels) draw(box((0,0), (210,210)), p=red);

pair envc = (sqsz/2, sqsz/2);
// Write a paper type to the image?
if (with_labels) label(rotate(45)*scale(4)*Label(envfmt, envc, p=gray));

pair corn_vec = unit((1,1)) * (envw/2) + unit((1,-1)) * (envh/2);
pair flip(pair p) {
	 return p - unit((1, -1)) * envh;
}

pair[] corners = {
	envc + corn_vec,
	envc + flip(corn_vec),
	envc - corn_vec,
	envc - flip(corn_vec),
};

// Draw the base rectangle
draw(corners[0] -- corners[1] -- corners[2] -- corners[3] -- cycle, p=gray+dashed);
if (with_labels) {
	label("$E_0$", corners[0]);
	label("$E_1$", corners[1]);
	label("$E_2$", corners[2]);
	label("$E_3$", corners[3]);
}

// Enlarge the sides:
//llba: line at left bottom, A side
pair llba = (1, 1);
real llbb = dot(llba, corners[2]);
pair llta = (1, -1);
real lltb = dot(llta, corners[2]);
pair lrba = (1, -1);
real lrbb = dot(lrba, corners[0]);
pair lrta = (1, 1);
real lrtb = dot(lrta, corners[0]);

pair lineinters(pair l1a, real l1b, pair l2a, real l2b) {
	// For some reason, solve does not like having the matrices right in the
	// parameters? (Or I made a stupid error in parentheses…)
	real[][] a = {{l1a.x, l1a.y}, {l2a.x, l2a.y}};
	real[] b = {l1b, l2b};
	real[] solution = solve(a,b);
	return (solution[0], solution[1]);
}

// Cutouts at all the sides:
// Left: (cutout left first point)
// Left edge: x = 0 = 1x + 0y
pair cl1 = lineinters(llba, llbb, (1, 0), 0);
pair cl2 = lineinters(llta, lltb, (1, 0), 0);
// right
pair cr1 = lineinters(lrba, lrbb, (1, 0), sqsz);
pair cr2 = lineinters(lrta, lrtb, (1, 0), sqsz);
// bottom
pair cb1 = lineinters(llba, llbb, (0, 1), 0);
pair cb2 = lineinters(lrba, lrbb, (0, 1), 0);
// top
pair ct1 = lineinters(llta, lltb, (0, 1), sqsz);
pair ct2 = lineinters(lrta, lrtb, (0, 1), sqsz);

if (with_labels) {
	label("$CL_1$", cl1);
	label("$CL_2$", cl2);
	label("$CR_1$", cr1);
	label("$CR_2$", cr2);
	label("$CT_1$", ct1);
	label("$CT_2$", ct2);
	label("$CB_1$", cb1);
	label("$CB_2$", cb2);
}

// We do not make the envelope fully symmetric, instead we trim the side
// lobes near the cover.
cr1 = (corners[0].x, sqsz);
cb2 = (0, corners[3].y);

// Draw the cutouts
draw(cl1 -- corners[2] -- cl2);
draw(cr1 -- corners[0] -- cr2);
draw(cb1 -- corners[3] -- cb2);
draw(ct1 -- corners[1] -- ct2);

// Draw the outline of the whole template. This is handy when not printing on
// the correctly sized paper. We are lazy and draw it piecewise.
draw(cb2 -- cl2);
draw(cl1 -- (0, sqsz) -- ct2);
draw(ct1 -- cr1);
draw(cr2 -- (sqsz, 0) -- cb1);