def point(self, idx):
idx = utils.graycode(idx)
p = [0]*self.dimension
iwidth = self.bits * self.dimension
for i in range(iwidth):
b = utils.bitrange(idx, iwidth, i, i+1) << (iwidth-i-1)/self.dimension
p[i%self.dimension] |= b
return p
def hilbert_point(dimension, order, h):
"""
Convert an index on the Hilbert curve of the specified dimension and
order to a set of point coordinates.
"""
# The bit widths in this function are:
# p[*] - order
# h - order*dimension
# l - dimension
# e - dimension
hwidth = order*dimension
e, d = 0, 0
p = [0]*dimension
for i in range(order):
w = utils.bitrange(h, hwidth, i*dimension, i*dimension+dimension)
l = utils.graycode(w)
l = itransform(e, d, dimension, l)
for j in range(dimension):
b = utils.bitrange(l, dimension, j, j+1)
p[j] = utils.setbit(p[j], order, i, b)
e = e ^ utils.lrot(entry(w), d+1, dimension)
d = (d + direction(w, dimension) + 1)%dimension
return p
def hilbert_point(dimension, order, h):
"""
Convert an index on the Hilbert curve of the specified dimension and
order to a set of point coordinates.
"""
# The bit widths in this function are:
# p[*] - order
# h - order*dimension
# l - dimension
# e - dimension
hwidth = order * dimension
e, d = 0, 0
p = [0] * dimension
for i in range(order):
w = utils.bitrange(h, hwidth, i * dimension, i * dimension + dimension)
l = utils.graycode(w)
l = itransform(e, d, dimension, l)
for j in range(dimension):
b = utils.bitrange(l, dimension, j, j + 1)
p[j] = utils.setbit(p[j], order, i, b)
e = e ^ utils.lrot(entry(w), d + 1, dimension)
d = (d + direction(w, dimension) + 1) % dimension
return p
def test_transform(self):
for width in range(2, 5):
g = [utils.graycode(i) for i in range(2**width)]
# Sanity: the gray sequence should be a Hilbert cube too
self.is_hilbertcube(g)
for e in range(2**width):
for d in range(width):
x = [hilbert.transform(e, d, width, i) for i in g]
# From Lemma 2.11 of Hamilton
assert hilbert.transform(e, d, width, e) == 0
assert hilbert.itransform(e, d, width, 0) == e
# The base gray code starts at 0, and has a direction of width-1:
if e == 0 and d == width-1:
assert x == g
self.is_hilbertcube(x)
assert [hilbert.itransform(e, d, width, i) for i in x] == g
# These values are from the example on p 18 of Hamilton
assert hilbert.transform(0, 1, 2, 3) == 3
assert hilbert.transform(3, 0, 2, 2) == 2
assert hilbert.transform(3, 0, 2, 1) == 1
def test_transform(self):
for width in range(2, 5):
g = [utils.graycode(i) for i in range(2**width)]
# Sanity: the gray sequence should be a Hilbert cube too
self.is_hilbertcube(g)
for e in range(2**width):
for d in range(width):
x = [hilbert.transform(e, d, width, i) for i in g]
# From Lemma 2.11 of Hamilton
assert hilbert.transform(e, d, width, e) == 0
assert hilbert.itransform(e, d, width, 0) == e
# The base gray code starts at 0, and has a direction of width-1:
if e == 0 and d == width - 1:
assert x == g
self.is_hilbertcube(x)
assert [hilbert.itransform(e, d, width, i) for i in x] == g
# These values are from the example on p 18 of Hamilton
assert hilbert.transform(0, 1, 2, 3) == 3
assert hilbert.transform(3, 0, 2, 2) == 2
assert hilbert.transform(3, 0, 2, 1) == 1
def entry(x):
if x == 0:
return 0
else:
return utils.graycode(2 * ((x - 1) / 2))
def test_igraycode(self):
for i in range(10):
assert utils.igraycode(utils.graycode(i)) == i
assert utils.graycode(utils.igraycode(i)) == i
def test_graycode(self):
assert utils.graycode(3) == 2
assert utils.graycode(4) == 6
def entry(x):
if x == 0:
return 0
else:
return utils.graycode(2 * ((x - 1) / 2))
def test_igraycode(self):
for i in range(10):
assert utils.igraycode(utils.graycode(i)) == i
assert utils.graycode(utils.igraycode(i)) == i
def test_graycode(self):
assert utils.graycode(3) == 2
assert utils.graycode(4) == 6