class Tiling:
def __init__(self, vertex_1: Vertex, vertex_2: Vertex, vertex_3: Vertex):
self._vertices = {}
self._edges = {}
self._tiles = {}
self._edges_to_tiles = {}
self._tiles_to_colours = {}
self._vertices_to_colours = {}
self._boundary = [vertex_1, vertex_2, vertex_3]
self._colour_values = ["#eeeeee", "#111111", "#bb9977", "#99bb77"]
self._drawing = Drawing(2, 2, origin='center')
self._drawing.setRenderSize(4096)
self._populate_data()
def _populate_data(self):
for index, vertex in enumerate(self._boundary):
self._vertices[vertex] = vertex
edge = Edge(*tuple(set(self._boundary) - {vertex}))
self._edges[edge] = edge
self._vertices_to_colours[vertex] = index + 1
tile = Tile(*self._boundary)
self._tiles[tile] = tile
self._tiles_to_colours[tile] = 0
for edge in self._edges:
self._edges_to_tiles[edge] = {tile}
self._drawing.draw(
tile, fill=self._colour_values[self._tiles_to_colours[tile]])
def _build_new_tile(self, vertex_1: Vertex, vertex_2: Vertex) -> Vertex:
edge = self._edges[Edge(vertex_1, vertex_2)]
#assert len(self._edges_to_tiles[edge]) == 1
inner_tile = tuple(self._edges_to_tiles[edge])[0]
inner_vertex = tuple(inner_tile.vertices - {vertex_1, vertex_2})[0]
reflected_vertex = Line.from_points(vertex_1,
vertex_2).reflection(inner_vertex)
reflected_vertex = self._add_vertex(reflected_vertex)
self._add_edge(Edge(vertex_1, reflected_vertex))
self._add_edge(Edge(vertex_2, reflected_vertex))
new_tile = self._add_tile(Tile(vertex_1, reflected_vertex, vertex_2))
self._vertices_to_colours[
reflected_vertex] = self._vertices_to_colours[inner_vertex]
self._tiles_to_colours[new_tile] = self._vertices_to_colours[
inner_vertex] ^ self._tiles_to_colours[inner_tile]
self._drawing.draw(
new_tile,
fill=self._colour_values[self._tiles_to_colours[new_tile]])
return reflected_vertex
def _add_vertex(self, vertex: Vertex) -> Vertex:
if vertex not in self._vertices:
self._vertices[vertex] = vertex
return self._vertices[vertex]
def _add_edge(self, edge: Edge):
if edge not in self._edges:
self._edges[edge] = edge
self._edges_to_tiles[edge] = set()
def _add_tile(self, tile: Tile):
if tile not in self._tiles:
self._tiles[tile] = tile
tile = self._tiles[tile]
edge_1 = self._edges[Edge(tile.vertex_2, tile.vertex_3)]
edge_2 = self._edges[Edge(tile.vertex_3, tile.vertex_1)]
edge_3 = self._edges[Edge(tile.vertex_1, tile.vertex_2)]
self._edges_to_tiles[edge_1].add(tile)
self._edges_to_tiles[edge_2].add(tile)
self._edges_to_tiles[edge_3].add(tile)
return tile
def _draw(self, depth: int):
with open('images/logo-depth-{}-data.json'.format(depth), 'w') as f:
json.dump([path.args for path in self._drawing.elements],
f,
indent=2)
self._drawing.saveSvg('images/logo-depth-{}.svg'.format(depth))
def create_tiles(self, depth: int):
if depth == 0:
self._draw(depth)
return
self.create_tiles(depth=depth - 1)
print(f"Populating depth {depth}...")
new_boundary = [
self._build_new_tile(self._boundary[0], self._boundary[-1])
]
index = 0
counter = 0
num_tiles = (3 * sqrt(3) * ((2 + sqrt(3))**depth -
(2 - sqrt(3))**depth)).as_int()
while True:
new_vertex = self._build_new_tile(new_boundary[-1],
self._boundary[index])
counter += 1
print(f"created {counter} / {num_tiles} tiles...", end="\r")
if new_vertex in self._boundary:
index += 1
elif new_vertex in new_boundary:
break
else:
new_boundary.append(new_vertex)
self._boundary = new_boundary
self._draw(depth)
print(f"Populated, found {len(self._tiles)} tiles")
theta1, theta2 = math.pi * 2 / p1, math.pi * 2 / p2
phiSum = math.pi * 2 / q
r1 = triangleSideForAngles(theta1 / 2, phiSum / 2, theta2 / 2)
r2 = triangleSideForAngles(theta2 / 2, phiSum / 2, theta1 / 2)
tGen1 = htiles.TileGen.makeRegular(p1, hr=r1, skip=1)
tGen2 = htiles.TileGen.makeRegular(p2, hr=r2, skip=1)
decorator1 = TileDecoratorFish(p1, p2, q)
tLayout = TileLayoutFish()
tLayout.addGenerator(tGen1, ((0, 1) * 10)[:p1], decorator1)
tLayout.addGenerator(tGen2, ((0, 1, 2) * 10)[:p2], htiles.TileDecoratorNull())
startTile = tLayout.startTile(code=0, rotateDeg=rotate)
tiles = tLayout.tilePlane(startTile, depth=depth)
d = Drawing(2, 2, origin='center')
d.draw(euclid.shapes.Circle(0, 0, 1), fill='silver')
for tile in tiles:
d.draw(tile, layer=0)
for tile in tiles:
d.draw(tile, layer=1)
for tile in tiles:
d.draw(tile, layer=2)
d.setRenderSize(w=400)
d.saveSvg('Tess02.svg')
#Rest of code I already commented in Tess01
theta1, theta2 = math.pi * 2 / p1, math.pi * 2 / p2
phiSum = math.pi * 2 / q
# above values of p1, p2, q will set angles of each triangle in the tessellation by dividing pi/2 over each
# specified value
r1 = triangleSideForAngles(theta1 / 2, phiSum / 2, theta2 / 2)
r2 = triangleSideForAngles(theta2 / 2, phiSum / 2, theta1 / 2)
#solves for the last side of each triange given input parameters of such
tGen1 = htiles.TileGen.makeRegular(p1, hr=r1, skip=1)
tGen2 = htiles.TileGen.makeRegular(p2, hr=r2, skip=1)
tLayout = htiles.TileLayout()
tLayout.addGenerator(tGen1, (1, ) * p1)
tLayout.addGenerator(tGen2, (0, ) * p2)
#Generates the iterations of tiles
startTile = tLayout.defaultStartTile(rotateDeg=10)
#draws tiles with 360/rotateDeg sides
tiles = tLayout.tilePlane(startTile, depth=4)
#depth specifies how many iterations tessellation will repeat
d = Drawing(2, 2, origin='center')
d.draw(euclid.shapes.Circle(0, 0, 1), fill='silver')
drawTiles(d, tiles)
#draws disk where tessllation will be contained within
d.setRenderSize(w=400)
d.saveSvg('Tess01.svg')
#will save in an image file called Tess01 in same project file
for tile in tiles:
d.draw(tile, hwidth=0.2, fill="white")
for tile in tiles:
d.draw(tile, drawVerts=True, hradius=0.3, hwidth=0.2, fill="black", opacity=0.6)
t1 = 4
t2 = 3
s = 3
theta1, theta2 = math.pi*2/t1, math.pi*2/t2
phiSum = math.pi*2/s
r1 = triangleSideForAngles((1/2)*(theta1, phiSum, theta2)
r2 = triangleSideForAngles((1/2)*(theta2, phiSum, theta1)
tile_generator1 = htiles.TileGen.makeRegular(t1, hr=r1, skip=1)
tile_generator2 = htiles.TileGen.makeRegular(t2, hr=r2, skip=1)
tile_layout = htiles.TileLayout()
tile_layout.addGenerator(tile_generator1, (1,)*t1)
tile_layout.addGenerator(tile_generator2, (0,)*t2)
starting_tile = tile_layout.defaultStartTile(rotateDeg=45)
tiles = tile_layout.tilePlane(starting_tile, depth=5)
d = Drawing(4, 4, origin='center')
d.draw(euclid.shapes.Circle(0,0,4), fill='blue')
drawTiles(d, tiles)
d.setRenderSize=(w=400)
d.saveSvg('images/tileTriangleSquare.svg')
edges = []
for i, point in enumerate(points):
v1 = vertices[i]
v2 = vertices[(i + 1) % p1]
edge = Hypercycle.fromPoints(*v1,
*v2,
*point,
segment=True,
excludeMid=True)
edges.append(edge)
decoratePoly = Polygon(edges=edges, vertices=vertices)
decorator1 = htiles.TileDecoratorPolygons(decoratePoly)
tLayout.setDecorator(decorator1, 0)
startTile = tLayout.defaultStartTile(rotateDeg=rotate)
tiles = tLayout.tilePlane(startTile, depth=6)
d = Drawing(2, 2, origin='center')
#d.draw(euclid.shapes.Circle(0, 0, 1), fill='silver')
for tile in tiles:
d.draw(tile, hwidth=0.05, fill='green')
tiles[0].decorator = None
d.draw(Hypercycle.fromPoints(*tiles[0].vertices[0], *tiles[0].vertices[1],
*pointBase),
hwidth=0.05,
fill='black')
d.setRenderSize(w=300)
d.saveSvg('Tess03.svg')
d