logari81
commented
1 year ago and here a dictionary-free version of the same code
#!/usr/bin/python3
import numpy as np
from time import time
import matplotlib.pyplot as plt
PI = np.pi
# increase this number for larger tilings.
N_ITERATIONS = 0
IDENTITY = np.array([[1,0,0],
[0,1,0]], 'float32')
COLOR_MAP = (np.array((211, 95, 95),'f')/255., # 0: Gamma
np.array(( 0, 255, 255),'f')/255., # 1: Delta
np.array((255, 170, 238),'f')/255., # 2: Theta
np.array((128, 128, 128),'f')/255., # 3: Lambda
np.array((145, 95, 211),'f')/255., # 4: Xi
np.array(( 95, 95, 211),'f')/255., # 5: Pi
np.array(( 85, 212, 0),'f')/255., # 6: Sigma
np.array((255, 179, 128),'f')/255., # 7: Phi
np.array((255, 221, 85),'f')/255., # 8: Psi
np.array((200, 55, 55),'f')/255., # 9: Gamma1
np.array((222, 135, 135),'f')/255.) #10: Gamma2
SPECTRE_POINTS = np.array([(0.0, 0.0),
(1.0, 0.0),
(1.5, -np.sqrt(3)/2),
(1.5+np.sqrt(3)/2, 0.5-np.sqrt(3)/2),
(1.5+np.sqrt(3)/2, 1.5-np.sqrt(3)/2),
(2.5+np.sqrt(3)/2, 1.5-np.sqrt(3)/2),
(3+np.sqrt(3)/2, 1.5),
(3.0, 2.0),
(3-np.sqrt(3)/2, 1.5),
(2.5-np.sqrt(3)/2, 1.5+np.sqrt(3)/2),
(1.5-np.sqrt(3)/2, 1.5+np.sqrt(3)/2),
(0.5-np.sqrt(3)/2, 1.5+np.sqrt(3)/2),
(-np.sqrt(3)/2, 1.5),
(0.0, 1.0)], 'float32')
SPECTRE_QUAD = SPECTRE_POINTS[[3,5,7,11],:]
def mul(A, B):
AB = A.copy()
AB[:,:2] = A[:,:2].dot(B[:,:2])
AB[:,2] += A[:,:2].dot(B[:,2])
return AB
class Tile:
def __init__(self, tile_type):
self.type = tile_type
self.quad = SPECTRE_QUAD.copy()
def add_to_cluster(self, cluster, tile_transformation=IDENTITY.copy()):
cluster.append((self.type, tile_transformation))
def draw(self, polygons, tile_transformation=IDENTITY.copy()):
vertices = SPECTRE_POINTS.dot(tile_transformation[:,:2].T) + tile_transformation[:,2]
polygons.append((vertices, COLOR_MAP[self.type]))
class MetaTile:
def __init__(self, tiles=[], transformations=[], quad=SPECTRE_QUAD.copy()):
self.tiles = tiles
self.transformations = transformations
self.quad = quad
def add_to_cluster(self, cluster, transformation=IDENTITY.copy()):
for tile, trsf in zip(self.tiles, self.transformations):
tile.add_to_cluster(cluster, mul(transformation, trsf))
def draw(self, polygons, transformation=IDENTITY.copy()):
for tile, trsf in zip(self.tiles, self.transformations):
tile.draw(polygons, mul(transformation, trsf))
def buildSpectreBase():
ttrans = np.array([[1,0,SPECTRE_POINTS[8,0]],
[0,1,SPECTRE_POINTS[8,1]]])
trot = np.array([[np.cos(PI/6),-np.sin(PI/6),0.],
[np.sin(PI/6), np.cos(PI/6),0.]],'float32')
trsf = mul(ttrans, trot)
tiles = [MetaTile(tiles=[Tile(9),Tile(10)],
transformations=[IDENTITY.copy(),trsf],
quad=SPECTRE_QUAD.copy())]
tiles += [Tile(i) for i in range(1,9)]
return tiles
def buildSupertiles(input_tiles):
# First, use any of the nine-unit tiles in "tiles" to obtain a
# list of transformation matrices for placing tiles within supertiles.
quad = input_tiles[1].quad
transformations = [IDENTITY.copy()]
total_angle = 0
trot = IDENTITY.copy()
transformed_quad = quad
for _angle, _from, _to in (( PI/3, 3, 1),
( 0., 2, 0),
( PI/3, 3, 1),
( PI/3, 3, 1),
( 0., 2, 0),
( PI/3, 3, 1),
(-2*PI/3, 3, 3)):
if _angle != 0:
total_angle += _angle
trot = np.array([[1, 0,0],[0,1,0]])*np.cos(total_angle) \
+np.array([[0,-1,0],[1,0,0]])*np.sin(total_angle)
transformed_quad = quad.dot(trot[:,:2].T) # + trot[:,2]
last_trsf = transformations[-1]
ttrans = IDENTITY.copy()
ttrans[:,2] = last_trsf[:,:2].dot(quad[_from,:]) + last_trsf[:,2] \
-transformed_quad[_to,:]
transformations.append(mul(ttrans, trot))
R = np.array([[-1,0,0],[ 0,1,0]], 'float32')
transformations = [ mul(R, trsf) for trsf in transformations ]
# Now build the actual supertiles, labeling appropriately.
super_quad = quad[[2,1,2,1],:]
for i,itrsf in enumerate([6,5,3,0]):
trsf = transformations[itrsf]
super_quad[i,:] = trsf[:,:2].dot(super_quad[i,:]) + trsf[:,2]
tiles = []
for substitutions in ((5, 1, -1, 2, 6, 4, 7, 0),
(4, 1, 4, 7, 6, 5, 7, 0),
(8, 1, 5, 7, 6, 5, 7, 0),
(8, 1, 4, 7, 6, 5, 7, 0),
(8, 1, 5, 7, 6, 8, 7, 0),
(8, 1, 4, 7, 6, 8, 7, 0),
(4, 1, 4, 7, 6, 5, 3, 0),
(8, 1, 8, 7, 6, 5, 7, 0),
(8, 1, 8, 7, 6, 8, 7, 0)):
tiles.append(MetaTile(tiles=[input_tiles[subst] for subst in substitutions if subst >= 0],
transformations=[trsf for subst, trsf in zip(substitutions, transformations) if subst >= 0],
quad=super_quad))
return tiles
start = time()
tiles = buildSpectreBase()
for _ in range(N_ITERATIONS):
tiles = buildSupertiles(tiles)
time1 = time()-start
print(f"supertiling loop took {round(time1, 4)} seconds")
start = time()
polygons = []
tiles[1].draw(polygons)
time2 = time()-start
print(f"tile recursion loop took {round(time2, 4)} seconds, generated {len(polygons)} tiles")
plt.figure(figsize=(8, 8))
plt.axis('equal')
for pts,color in polygons:
plt.fill(pts[:,0],pts[:,1],facecolor=color)
plt.show()
shrx
reversi-fun
Thanks for this nice port to python, here there is a version of your code ported to numpy and using matplotlib for plotting