def point(self, 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 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 index(self, p):
idx = 0
iwidth = self.bits * self.dimension
for i in range(iwidth):
bitoff = self.bits-(i/self.dimension)-1
poff = self.dimension-(i%self.dimension)-1
b = utils.bitrange(p[poff], self.bits, bitoff, bitoff+1) << i
idx |= b
return utils.igraycode(idx)
def point(self, 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
p.reverse()
return p
def hilbert_index(dimension, order, p):
h, e, d = 0, 0, 0
for i in range(order):
l = 0
for x in range(dimension):
b = utils.bitrange(p[dimension - x - 1], order, i, i + 1)
l |= b << x
l = transform(e, d, dimension, l)
w = utils.igraycode(l)
e = e ^ utils.lrot(entry(w), d + 1, dimension)
d = (d + direction(w, dimension) + 1) % dimension
h = (h << dimension) | w
return h
def hilbert_index(dimension, order, p):
h, e, d = 0, 0, 0
for i in range(order):
l = 0
for x in range(dimension):
b = utils.bitrange(p[dimension - x - 1], order, i, i + 1)
l |= b << x
l = transform(e, d, dimension, l)
w = utils.igraycode(l)
e = e ^ utils.lrot(entry(w), d + 1, dimension)
d = (d + direction(w, dimension) + 1) % dimension
h = (h << dimension) | w
return h
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 hilbert_index(dimension, order, p):
# Hamilton's paper initialises d to 0, which appears to be an error.
h, e, d = 0, 0, 1
for i in range(order):
l = 0
for x in range(dimension):
b = utils.bitrange(p[x], order, i, i+1)
l |= b<<x
l = transform(e, d, dimension, l)
w = utils.igraycode(l)
e = e ^ utils.lrot(entry(w), d+1, dimension)
d = (d + direction(w, dimension) + 1)%dimension
h = (h<<dimension)|w
return h
def checkbit(i, width, start, end, expected):
e = utils.bitrange(i, width, start, end)
assert e == expected
assert e == utils.bits2int(utils.bits(i, width)[start:end])
def checkbit(i, width, start, end, expected):
e = utils.bitrange(i, width, start, end)
assert e == expected
assert e == utils.bits2int(utils.bits(i, width)[start:end])
