blob: 45a7a5edfbc08468fabc3b9e639aa1188281bab0 [file] [log] [blame]
def iup_segment(coords, rc1, rd1, rc2, rd2):
# rc1 = reference coord 1
# rd1 = reference delta 1
out_arrays = [None, None]
for j in 0,1:
out_arrays[j] = out = []
x1, x2, d1, d2 = rc1[j], rc2[j], rd1[j], rd2[j]
if x1 == x2:
n = len(coords)
if d1 == d2:
if x1 > x2:
x1, x2 = x2, x1
d1, d2 = d2, d1
# x1 < x2
scale = (d2 - d1) / (x2 - x1)
for pair in coords:
x = pair[j]
if x <= x1:
d = d1
elif x >= x2:
d = d2
# Interpolate
d = d1 + (x - x1) * scale
return zip(*out_arrays)
def iup_contour(delta, coords):
assert len(delta) == len(coords)
if None not in delta:
return delta
n = len(delta)
# indices of points with explicit deltas
indices = [i for i,v in enumerate(delta) if v is not None]
if not indices:
# All deltas are None. Return 0,0 for all.
return [(0,0)]*n
out = []
it = iter(indices)
start = next(it)
if start != 0:
# Initial segment that wraps around
i1, i2, ri1, ri2 = 0, start, start, indices[-1]
out.extend(iup_segment(coords[i1:i2], coords[ri1], delta[ri1], coords[ri2], delta[ri2]))
for end in it:
if end - start > 1:
i1, i2, ri1, ri2 = start+1, end, start, end
out.extend(iup_segment(coords[i1:i2], coords[ri1], delta[ri1], coords[ri2], delta[ri2]))
start = end
if start != n-1:
# Final segment that wraps around
i1, i2, ri1, ri2 = start+1, n, start, indices[0]
out.extend(iup_segment(coords[i1:i2], coords[ri1], delta[ri1], coords[ri2], delta[ri2]))
assert len(delta) == len(out), (len(delta), len(out))
return out
def iup_delta(delta, coords, ends):
assert sorted(ends) == ends and len(coords) == (ends[-1]+1 if ends else 0) + 4
n = len(coords)
ends = ends + [n-4, n-3, n-2, n-1]
out = []
start = 0
for end in ends:
end += 1
contour = iup_contour(delta[start:end], coords[start:end])
start = end
return out
# Optimizer
def can_iup_in_between(deltas, coords, i, j, tolerance):
assert j - i >= 2
interp = list(iup_segment(coords[i+1:j], coords[i], deltas[i], coords[j], deltas[j]))
deltas = deltas[i+1:j]
assert len(deltas) == len(interp)
return all(abs(complex(x-p, y-q)) <= tolerance for (x,y),(p,q) in zip(deltas, interp))
def _iup_contour_bound_forced_set(delta, coords, tolerance=0):
"""The forced set is a conservative set of points on the contour that must be encoded
explicitly (ie. cannot be interpolated). Calculating this set allows for significantly
speeding up the dynamic-programming, as well as resolve circularity in DP.
The set is precise; that is, if an index is in the returned set, then there is no way
that IUP can generate delta for that point, given coords and delta.
assert len(delta) == len(coords)
forced = set()
# Track "last" and "next" points on the contour as we sweep.
nd, nc = delta[0], coords[0]
ld, lc = delta[-1], coords[-1]
for i in range(len(delta)-1, -1, -1):
d, c = ld, lc
ld, lc = delta[i-1], coords[i-1]
for j in (0,1): # For X and for Y
cj = c[j]
dj = d[j]
lcj = lc[j]
ldj = ld[j]
ncj = nc[j]
ndj = nd[j]
if lcj <= ncj:
c1, c2 = lcj, ncj
d1, d2 = ldj, ndj
c1, c2 = ncj, lcj
d1, d2 = ndj, ldj
# If coordinate for current point is between coordinate of adjacent
# points on the two sides, but the delta for current point is NOT
# between delta for those adjacent points (considering tolerance
# allowance), then there is no way that current point can be IUP-ed.
# Mark it forced.
force = False
if c1 <= cj <= c2:
if not (min(d1,d2)-tolerance <= dj <= max(d1,d2)+tolerance):
force = True
else: # cj < c1 or c2 < cj
if c1 == c2:
if d1 == d2:
if abs(dj - d1) > tolerance:
force = True
if abs(dj) > tolerance:
# Disabled the following because the "d1 == d2" does
# check does not take tolerance into consideration...
pass # force = True
elif d1 != d2:
if cj < c1:
if dj != d1 and ((dj-tolerance < d1) != (d1 < d2)):
force = True
else: # c2 < cj
if d2 != dj and ((d2 < dj+tolerance) != (d1 < d2)):
force = True
if force:
nd, nc = d, c
return forced
def _iup_contour_optimize_dp(delta, coords, forced={}, tolerance=0, lookback=None):
"""Straightforward Dynamic-Programming. For each index i, find least-costly encoding of
points 0 to i where i is explicitly encoded. We find this by considering all previous
explicit points j and check whether interpolation can fill points between j and i.
Note that solution always encodes last point explicitly. Higher-level is responsible
for removing that restriction.
As major speedup, we stop looking further whenever we see a "forced" point."""
n = len(delta)
if lookback is None:
lookback = n
costs = {-1:0}
chain = {-1:None}
for i in range(0, n):
best_cost = costs[i-1] + 1
costs[i] = best_cost
chain[i] = i - 1
if i - 1 in forced:
for j in range(i-2, max(i-lookback, -2), -1):
cost = costs[j] + 1
if cost < best_cost and can_iup_in_between(delta, coords, j, i, tolerance):
costs[i] = best_cost = cost
chain[i] = j
if j in forced:
return chain, costs
def _rot_list(l, k):
"""Rotate list by k items forward. Ie. item at position 0 will be
at position k in returned list. Negative k is allowed."""
n = len(l)
k %= n
if not k: return l
return l[n-k:] + l[:n-k]
def _rot_set(s, k, n):
k %= n
if not k: return s
return {(v + k) % n for v in s}
def iup_contour_optimize(delta, coords, tolerance=0.):
n = len(delta)
# Get the easy cases out of the way:
# If all are within tolerance distance of 0, encode nothing:
if all(abs(complex(*p)) <= tolerance for p in delta):
return [None] * n
# If there's exactly one point, return it:
if n == 1:
return delta
# If all deltas are exactly the same, return just one (the first one):
d0 = delta[0]
if all(d0 == d for d in delta):
return [d0] + [None] * (n-1)
# Else, solve the general problem using Dynamic Programming.
forced = _iup_contour_bound_forced_set(delta, coords, tolerance)
# The _iup_contour_optimize_dp() routine returns the optimal encoding
# solution given the constraint that the last point is always encoded.
# To remove this constraint, we use two different methods, depending on
# whether forced set is non-empty or not:
if forced:
# Forced set is non-empty: rotate the contour start point
# such that the last point in the list is a forced point.
k = (n-1) - max(forced)
assert k >= 0
delta = _rot_list(delta, k)
coords = _rot_list(coords, k)
forced = _rot_set(forced, k, n)
chain, costs = _iup_contour_optimize_dp(delta, coords, forced, tolerance)
# Assemble solution.
solution = set()
i = n - 1
while i is not None:
i = chain[i]
assert forced <= solution, (forced, solution)
delta = [delta[i] if i in solution else None for i in range(n)]
delta = _rot_list(delta, -k)
# Repeat the contour an extra time, solve the 2*n case, then look for solutions of the
# circular n-length problem in the solution for 2*n linear case. I cannot prove that
# this always produces the optimal solution...
chain, costs = _iup_contour_optimize_dp(delta+delta, coords+coords, forced, tolerance, n)
best_sol, best_cost = None, n+1
for start in range(n-1, 2*n-1):
# Assemble solution.
solution = set()
i = start
while i > start - n:
solution.add(i % n)
i = chain[i]
if i == start - n:
cost = costs[start] - costs[start - n]
if cost <= best_cost:
best_sol, best_cost = solution, cost
delta = [delta[i] if i in best_sol else None for i in range(n)]
return delta
def iup_delta_optimize(delta, coords, ends, tolerance=0.):
assert sorted(ends) == ends and len(coords) == (ends[-1]+1 if ends else 0) + 4
n = len(coords)
ends = ends + [n-4, n-3, n-2, n-1]
out = []
start = 0
for end in ends:
contour = iup_contour_optimize(delta[start:end+1], coords[start:end+1], tolerance)
assert len(contour) == end - start + 1
start = end+1
return out