Layered island

Source 87 lines

// Layered island: a made-up mountain as a stack of contour layers, like a
// topographic map you can touch. The height of the land is a formula, and
// each layer is traced where the land crosses its height. Every layer is
// scored with the outline of the one above, so gluing up is easy.
 
/* [Island] */
// Width of the base plate
size = 200; // [120:10:400]
// Contour layers above the sea
layers = 8; // [3:1:14]
// How rough the land is
roughness = 1; // [0:0.1:2]
// Different seeds raise different islands
seed = 9; // [1:1:999]
// Engraved on the base plate, leave empty for none
name = "ISLA KERF"; // 20
 
/* [Material] */
// Sheet thickness
$thickness = 3; // [2:0.5:6]
// Beam width
$kerf = 0.15; // [0:0.01:0.3]
 
/* [Hidden] */
$material = "plywood";
plate = [size, size * 0.75];
peak = [size * 0.45, plate[1] * 0.5];
reach = plate[1] * 0.48;
rnd = rands(0, 1, 16, seed);
 
// Two smaller hills, somewhere around the main peak
hills = [for (i = [0:1]) let (a = rnd[0] * 360 + i * (110 + rnd[1] * 100), d = reach * (0.55 + rnd[i + 2] * 0.25))
  [peak + d * [cos(a), sin(a)], reach * (0.2 + rnd[i + 4] * 0.08), 0.5 + rnd[i + 6] * 0.25]];
 
function bump(p, c, w) = exp(-((p - c) * (p - c)) / (2 * w * w));
 
// Height of the land at point p
function land(p) = bump(p, peak, reach * 0.26)
  + hills[0][2] * bump(p, hills[0][0], hills[0][1])
  + hills[1][2] * bump(p, hills[1][0], hills[1][1])
  + roughness * (0.07 * sin(p.x * 360 / (reach * 0.9) + rnd[8] * 360) * sin(p.y * 360 / (reach * 1.1) + rnd[9] * 360)
      + 0.03 * sin((p.x + p.y) * 360 / (reach * 0.45) + rnd[10] * 360)
      + 0.01 * sin((p.x - 2 * p.y) * 360 / (reach * 0.22) + rnd[11] * 360));
 
// Sample the land along rays from the peak once; every layer reuses them
rays = 144;
samples = 48;
dr = reach / samples;
profiles = [for (i = [0:rays - 1]) let (a = i * 360 / rays)
  [for (j = [0:samples]) land(peak + j * dr * [cos(a), sin(a)])]];
 
coast = 0.08;
top = land(peak);
function level(k) = coast + (top - coast) * k / (layers + 1);
 
// Distance along a ray where the land first drops below height h
function crossing(prof, h, j = 1) =
  j > samples ? reach :
  prof[j] < h ? dr * (j - 1 + (prof[j - 1] - h) / (prof[j - 1] - prof[j])) :
  crossing(prof, h, j + 1);
 
function contour(k) = [for (i = [0:rays - 1]) let (a = i * 360 / rays)
  peak + max(crossing(profiles[i], level(k)), 3) * [cos(a), sin(a)]];
 
// Smooth the traced outline and keep it free of slivers
module contour_layer(k) offset(r = 1.2) offset(r = -1.2) polygon(contour(k));
 
// Assembled: the layers stacked on the base, lowest first
part("Base", at = [0, 0, 0]) {
  rect(plate, r = 4);
  score() contour_layer(1);
  engrave() if (name != "") translate([plate[0] - 10, 10])
    text(name, size = plate[1] * 0.045, halign = "right", spacing = 1.2);
  score() translate([plate[0] - 18, plate[1] - 20]) {
    for (a = [0:90:270]) rotate(a) polygon([[0, 10], [2, 0], [-2, 0]]);
    circle(r = 4, $fn = 32);
  }
}
 
for (k = [1:layers]) step(str("Glue layer ", k, " on its scored outline")) part(str("Layer ", k), at = [0, 0, k * $thickness]) {
  contour_layer(k);
  if (k < layers) {
    score() contour_layer(k + 1);
    // The number hides under the next layer
    engrave() translate(peak) text(str(k), size = 4, halign = "center", valign = "center");
  }
}