def circulate(p0, r0, p1, r1, p2, r2, p3, r3, depth):
pointList = [p0, p1, p2]
radiiList = [r0, r1, r2]
if depth == 0:
return [p3], [r3]
else:
newPL = []
newRL = []
for indxs in itertools.combinations(range(3), 2):
i0, i1 = indxs
pI, rI, pO, rO = circit(pointList[i0], radiiList[i0],
pointList[i1], radiiList[i1],
p3, r3)
if radiiList[i0]*radiiList[i1]*r3 > 0:
pNew, rNew = pI, rI
else:
pNew, rNew = pO, rO
result = circulate(pointList[i0], radiiList[i0],
pointList[i1], radiiList[i1],
p3, r3, pNew, rNew, depth-1)
newPL += result[0]
newRL += result[1]
return [p3]+newPL, [r3]+newRL
def circulate(c0, c1, c2, c3, depth):
cList = [c0, c1, c2]
if depth == 0:
return [c3]
else:
new = []
for indxs in itertools.combinations(range(3), 2):
i0, i1 = indxs
cI, cO = circit(cList[i0], cList[i1], c3)
if cList[i0][0] * cList[i1][0] * c3[0] > 0:
cNew = cI
else:
cNew = cO
new += circulate(cList[i0], cList[i1], c3, cNew, depth - 1)
return [c3] + new
def circulate(c0, c1, c2, depth):
cList = [c0, c1, c2]
if depth == 0:
return c3
new = []
for circleA, circleB in itertools.combinations(cList, 2):
cInner, cOuter = circit(circleA, circleB, c2)
if circleA[0] * circleB[0] > 0:
cNew = cInner
else:
cNew = cOuter
result = circulate(circleA, circleB, cNew, depth-1)
new += result
return c3 + new
def circulate(c0, c1, c2, c3, depth):
cList = [c0, c1, c2]
if depth == 0:
return [c3]
else:
new = []
for indxs in itertools.combinations(range(3), 2):
i0, i1 = indxs
cI, cO = circit(cList[i0], cList[i1], c3)
if cList[i0][0] * cList[i1][0] * c3[0] > 0:
cNew = cI
else:
cNew = cO
result = circulate(cList[i0], cList[i1], c3, cNew, depth - 1)
new += result
return [c3] + new
def make_one(shift=[0., 0.]):
""" original """
# startPoints = list(range(3))
# for i in startPoints:
# x = 2.5*cos(2.0 * pi * i / 3)
# y = 2.5*sin(2.0 * pi * i / 3)
# startPoints[i] = [x, y]
""" anomalus """
# startPoints = [[-2, 2], [0, 0], [2, 2]]
""" earhoops """
# startPoints = [[-1, -2], [0, 1], [1, -2]]
""" random """
# startPoints = (np.random.rand(3, 2) * 4. - 2.).tolist()
""" random angles """
# startPoints = [[np.cos(2. * np.pi * t), np.sin(2. * np.pi * t)] for t in np.random.rand(3)]
# all circles are defined as c = [r, px, py] with
# radius = c[0] and x, y coordinates of the center
# c[1] and c[2] (latter adding c[3] to make a 3d
# gasket with spheres)
def rand_init():
points = np.random.rand(3, 2) - .5
return points.tolist()
def circulate(c0, c1, c2, c3, depth):
cList = [c0, c1, c2]
if depth == 0:
return [c3]
else:
new = []
for indxs in itertools.combinations(range(3), 2):
i0, i1 = indxs
cI, cO = circit(cList[i0], cList[i1], c3)
if cList[i0][0] * cList[i1][0] * c3[0] > 0:
cNew = cI
else:
cNew = cO
new += circulate(cList[i0], cList[i1], c3, cNew, depth - 1)
return [c3] + new
def sign(p1, p2, p3):
return (p1[1] - p3[1]) * (p2[2] - p3[2]) - (p2[1] - p3[1]) * (p1[2] -
p3[2])
def PointInTriangle(pt, v1, v2, v3):
b1 = sign(pt, v1, v2) < 0.
b2 = sign(pt, v2, v3) < 0.
b3 = sign(pt, v3, v1) < 0.
return ((b1 == b2) and (b2 == b3))
loops = 4
good3 = False
while not good3:
startPoints = rand_init()
[c0, c1, c2] = radii(*startPoints)
c3, c4 = circit(c0, c1, c2)
if c4[0] > 0: continue
if not PointInTriangle(c4, c1, c2, c3): continue
good3 = True
clot = [c0, c1, c2] + circulate(c0, c1, c2, c4, loops) + circulate(
c0, c1, c2, c3, loops)
biggestR = max(abs(np.array(clot)[:, 0]))
scale = 1.4 / biggestR
annuli = []
for c in clot:
r, x, y = c
if abs(r) < 0.05: continue
annuli.append(
makeShapelyCircle(scale * (x - c4[1]) + (shift[0] - 1) * 3,
scale * (y - c4[2]) + (shift[1] - 1) * 3,
scale * abs(r),
thickness=0.05))
testUnion = cascaded_union(annuli)
return testUnion
if radiiList[i0]*radiiList[i1]*r3 > 0:
pNew, rNew = pI, rI
else:
pNew, rNew = pO, rO
result = circulate(pointList[i0], radiiList[i0],
pointList[i1], radiiList[i1],
p3, r3, pNew, rNew, depth-1)
newPL += result[0]
newRL += result[1]
return [p3]+newPL, [r3]+newRL
loops = 9
p0, p1, p2 = startPointList
r0, r1, r2 = startRadiiList
p3, r3, p4, r4 = circit(p0, r0, p1, r1, p2, r2)
plot = [p0, p1, p2] + circulate(p0, r0, p1, r1, p2, r2, p4, r4, loops)[0] + circulate(p0, r0, p1, r1, p2, r2, p3, r3, loops)[0]
rlot = [r0, r1, r2] + circulate(p0, r0, p1, r1, p2, r2, p4, r4, loops)[1] + circulate(p0, r0, p1, r1, p2, r2, p3, r3, loops)[1]
# Make a pdf surface
surf = cairo.PDFSurface(open("test.pdf", "w"), 512, 512)
# Make a svg surface
# surf = cairo.SVGSurface(open("test.svg", "w"), 512, 512)
# Get a context object
ctx = cairo.Context(surf)
width = 0.005
ctx.set_line_width(width)
cI, cO = circit(cList[i0], cList[i1], c3)
if cList[i0][0] * cList[i1][0] * c3[0] > 0:
cNew = cI
else:
cNew = cO
result = circulate(cList[i0], cList[i1], c3, cNew, depth - 1)
new += result
return [c3] + new
loops = 8
[c0, c1, c2] = radii(*startPoints)
c3, c4 = circit(c0, c1, c2)
clot = [c0, c1, c2] + circulate(c0, c1, c2, c4, loops) + circulate(c0, c1, c2, c3, loops)
w = 512
h = 512
# Make a pdf surface
surf = cairo.PDFSurface(open("test.pdf", "w"), w, h)
# Make a svg surface
# surf = cairo.SVGSurface(open("test.svg", "w"), w, h)
# Get a context object
ctx = cairo.Context(surf)
lineWidth = 0.001
