add tile_penrose2

src/experimental/tile_penrose2.scad

@@ -0,0 +1,151 @@
+use <hull_polyline2d.scad>;
+use <util/dedup.scad>;
+
+// tile type
+KITE = 0;
+DART = 1;
+
+function tile(type, x, y, angle, size) = [type, x, y, angle, size];
+function tile_type(t) = t[0];
+function tile_x(t) = t[1];
+function tile_y(t) = t[2];
+function tile_angle(t) = t[3];
+function tile_size(t) = t[4];
+
+tile_eq = function(t1, t2, epsilon = 0.0001) 
+    abs(tile_x(t1) - tile_x(t2)) < epsilon && 
+	abs(tile_y(t1) - tile_y(t2)) < epsilon && 
+	tile_angle(t1) == tile_angle(t2);
+	
+tile_hash = function(t) tile_type(t) + tile_angle(t);
+
+function between_360(a) = 
+    a >= 360 ? a - 360 :
+	a < 0 ? a + 360 :
+	a;
+
+
+function sub_kite(tile) = 
+	let(
+	    PHI = 1.618033988749895,
+	    x = tile_x(tile),
+		y = tile_y(tile),
+		angle = tile_angle(tile),
+		size = tile_size(tile),
+		n_size = tile_size(tile) / PHI,
+		r = PHI * size
+	)
+	[
+		for(i = 0, sign = 1; i < 2; i = i + 1, sign = -sign)
+		let(a = angle - 36 * sign)
+		each [
+			tile(
+				DART,
+				x,
+				y,
+				between_360(angle - 4 * 36 * sign),
+				n_size
+			),
+			tile(
+				KITE,
+				x + r * cos(a),
+				y + r * sin(a),
+				between_360(angle + 3 * 36 * sign),
+				n_size
+			)
+		]
+	];
+	
+function sub_dart(tile) = 
+	let(
+	    PHI = 1.618033988749895,
+	    x = tile_x(tile),
+		y = tile_y(tile),
+		angle = tile_angle(tile),
+		size = tile_size(tile),
+		n_size = tile_size(tile) / PHI,
+		r = PHI * size
+	)
+	concat(
+		[tile(KITE, x, y, between_360(angle + 5 * 36), n_size)],
+		[
+			for(i = 0, sign = 1; i < 2; i = i + 1, sign = -sign)
+			let(a = between_360(angle - 4 * 36 * sign))
+			tile(
+			    DART,
+				x + r * cos(a),
+				y + r * sin(a),
+				a,
+				n_size
+			)
+		]
+	);
+
+function subdivide(tiles) = [
+    for(tile = tiles)
+	each (tile_type(tile) == DART ? sub_dart(tile) : sub_kite(tile))
+];
+
+function _penrose2(tiles, n, i = 0) = 
+	i == n ? tiles :
+			_penrose2(dedup(subdivide(tiles), eq = tile_eq, hash = tile_hash), n, i + 1);
+			
+function tile_penrose2(n) = 
+    let(
+	    tiles = _penrose2([for(i = [0:4]) tile(KITE, 0, 0, 36 * (1 + 2 * i), 1)], n),
+		PHI = 1.618033988749895,
+	    dist = [[PHI, PHI, PHI], [-PHI, -1, -PHI]]
+	)
+	[
+	    for(tile = tiles)
+		let(
+			angle = tile_angle(tile) - 36,
+			type = tile_type(tile),
+			size = tile_size(tile),
+			shape = concat(
+				[[tile_x(tile), tile_y(tile)]],
+				[
+					for(i = [0:2])
+					let(
+						r = dist[type][i] * size,
+						a = angle + i * 36
+					)
+					[tile_x(tile) + r * cos(a), tile_y(tile) + r * sin(a)]
+				]
+			)
+		)
+		each [
+		    [type, [shape[0], shape[1], shape[2]]], 
+			[type, [shape[0], shape[3], shape[2]]]
+		]
+	];
+	
+module draw(tris, radius) {
+	for(tri = tris) {
+		color(tri[0] == KITE ? "black" : "white")
+	    polygon(tri[1] * radius);
+	}
+
+	for(tri = tris) {
+	    hull_polyline2d(tri[1] * radius, .1);
+	}
+}
+
+radius = 7;
+
+draw(tile_penrose2(0), radius);
+
+translate([30, 0])
+    draw(tile_penrose2(1), radius);
+
+translate([60, 0])
+    draw(tile_penrose2(2), radius);
+
+translate([0, -30])
+    draw(tile_penrose2(3), radius);
+
+translate([30, -30])
+    draw(tile_penrose2(4), radius);
+
+translate([60, -30])
+    draw(tile_penrose2(5), radius);