try:
import cython
COMPILED = cython.compiled
except (AttributeError, ImportError):
# if cython not installed, use mock module with no-op decorators and types
from fontTools.misc import cython
COMPILED = False
from typing import (
Sequence,
Tuple,
Union,
)
from numbers import Integral, Real
_Point = Tuple[Real, Real]
_Delta = Tuple[Real, Real]
_PointSegment = Sequence[_Point]
_DeltaSegment = Sequence[_Delta]
_DeltaOrNone = Union[_Delta, None]
_DeltaOrNoneSegment = Sequence[_DeltaOrNone]
_Endpoints = Sequence[Integral]
MAX_LOOKBACK = 8
[docs]
@cython.cfunc
@cython.locals(
j=cython.int,
n=cython.int,
x1=cython.double,
x2=cython.double,
d1=cython.double,
d2=cython.double,
scale=cython.double,
x=cython.double,
d=cython.double,
)
def iup_segment(
coords: _PointSegment, rc1: _Point, rd1: _Delta, rc2: _Point, rd2: _Delta
): # -> _DeltaSegment:
"""Given two reference coordinates `rc1` & `rc2` and their respective
delta vectors `rd1` & `rd2`, returns interpolated deltas for the set of
coordinates `coords`."""
# 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:
out.extend([d1] * n)
else:
out.extend([0] * n)
continue
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
else:
# Interpolate
d = d1 + (x - x1) * scale
out.append(d)
return zip(*out_arrays)
[docs]
def iup_contour(deltas: _DeltaOrNoneSegment, coords: _PointSegment) -> _DeltaSegment:
"""For the contour given in `coords`, interpolate any missing
delta values in delta vector `deltas`.
Returns fully filled-out delta vector."""
assert len(deltas) == len(coords)
if None not in deltas:
return deltas
n = len(deltas)
# indices of points with explicit deltas
indices = [i for i, v in enumerate(deltas) 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], deltas[ri1], coords[ri2], deltas[ri2]
)
)
out.append(deltas[start])
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], deltas[ri1], coords[ri2], deltas[ri2]
)
)
out.append(deltas[end])
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], deltas[ri1], coords[ri2], deltas[ri2]
)
)
assert len(deltas) == len(out), (len(deltas), len(out))
return out
[docs]
def iup_delta(
deltas: _DeltaOrNoneSegment, coords: _PointSegment, ends: _Endpoints
) -> _DeltaSegment:
"""For the outline given in `coords`, with contour endpoints given
in sorted increasing order in `ends`, interpolate any missing
delta values in delta vector `deltas`.
Returns fully filled-out delta vector."""
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(deltas[start:end], coords[start:end])
out.extend(contour)
start = end
return out
# Optimizer
[docs]
@cython.cfunc
@cython.inline
@cython.locals(
i=cython.int,
j=cython.int,
# tolerance=cython.double, # https://github.com/fonttools/fonttools/issues/3282
x=cython.double,
y=cython.double,
p=cython.double,
q=cython.double,
)
@cython.returns(int)
def can_iup_in_between(
deltas: _DeltaSegment,
coords: _PointSegment,
i: Integral,
j: Integral,
tolerance: Real,
): # -> bool:
"""Return true if the deltas for points at `i` and `j` (`i < j`) can be
successfully used to interpolate deltas for points in between them within
provided error tolerance."""
assert j - i >= 2
interp = iup_segment(coords[i + 1 : j], coords[i], deltas[i], coords[j], deltas[j])
deltas = deltas[i + 1 : j]
return all(
abs(complex(x - p, y - q)) <= tolerance
for (x, y), (p, q) in zip(deltas, interp)
)
@cython.locals(
cj=cython.double,
dj=cython.double,
lcj=cython.double,
ldj=cython.double,
ncj=cython.double,
ndj=cython.double,
force=cython.int,
forced=set,
)
def _iup_contour_bound_forced_set(
deltas: _DeltaSegment, coords: _PointSegment, tolerance: Real = 0
) -> set:
"""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 `deltas`.
"""
assert len(deltas) == len(coords)
n = len(deltas)
forced = set()
# Track "last" and "next" points on the contour as we sweep.
for i in range(len(deltas) - 1, -1, -1):
ld, lc = deltas[i - 1], coords[i - 1]
d, c = deltas[i], coords[i]
nd, nc = deltas[i - n + 1], coords[i - n + 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
else:
c1, c2 = ncj, lcj
d1, d2 = ndj, ldj
force = False
# If the two coordinates are the same, then the interpolation
# algorithm produces the same delta if both deltas are equal,
# and zero if they differ.
#
# This test has to be before the next one.
if c1 == c2:
if abs(d1 - d2) > tolerance and abs(dj) > tolerance:
force = True
# 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.
elif c1 <= cj <= c2: # and c1 != c2
if not (min(d1, d2) - tolerance <= dj <= max(d1, d2) + tolerance):
force = True
# Otherwise, the delta should either match the closest, or have the
# same sign as the interpolation of the two deltas.
else: # cj < c1 or c2 < cj
if d1 != d2:
if cj < c1:
if (
abs(dj) > tolerance
and abs(dj - d1) > tolerance
and ((dj - tolerance < d1) != (d1 < d2))
):
force = True
else: # c2 < cj
if (
abs(dj) > tolerance
and abs(dj - d2) > tolerance
and ((d2 < dj + tolerance) != (d1 < d2))
):
force = True
if force:
forced.add(i)
break
return forced
@cython.locals(
i=cython.int,
j=cython.int,
best_cost=cython.double,
best_j=cython.int,
cost=cython.double,
forced=set,
tolerance=cython.double,
)
def _iup_contour_optimize_dp(
deltas: _DeltaSegment,
coords: _PointSegment,
forced=set(),
tolerance: Real = 0,
lookback: Integral = 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(deltas)
if lookback is None:
lookback = n
lookback = min(lookback, MAX_LOOKBACK)
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:
continue
for j in range(i - 2, max(i - lookback, -2), -1):
cost = costs[j] + 1
if cost < best_cost and can_iup_in_between(deltas, coords, j, i, tolerance):
costs[i] = best_cost = cost
chain[i] = j
if j in forced:
break
return chain, costs
def _rot_list(l: list, k: int):
"""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: set, k: int, n: int):
k %= n
if not k:
return s
return {(v + k) % n for v in s}
[docs]
def iup_contour_optimize(
deltas: _DeltaSegment, coords: _PointSegment, tolerance: Real = 0.0
) -> _DeltaOrNoneSegment:
"""For contour with coordinates `coords`, optimize a set of delta
values `deltas` within error `tolerance`.
Returns delta vector that has most number of None items instead of
the input delta.
"""
n = len(deltas)
# 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 deltas):
return [None] * n
# If there's exactly one point, return it:
if n == 1:
return deltas
# If all deltas are exactly the same, return just one (the first one):
d0 = deltas[0]
if all(d0 == d for d in deltas):
return [d0] + [None] * (n - 1)
# Else, solve the general problem using Dynamic Programming.
forced = _iup_contour_bound_forced_set(deltas, 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:
# Debugging: Make the next if always take the second branch and observe
# if the font size changes (reduced); that would mean the forced-set
# has members it should not have.
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
deltas = _rot_list(deltas, k)
coords = _rot_list(coords, k)
forced = _rot_set(forced, k, n)
# Debugging: Pass a set() instead of forced variable to the next call
# to exercise forced-set computation for under-counting.
chain, costs = _iup_contour_optimize_dp(deltas, coords, forced, tolerance)
# Assemble solution.
solution = set()
i = n - 1
while i is not None:
solution.add(i)
i = chain[i]
solution.remove(-1)
# if not forced <= solution:
# print("coord", coords)
# print("deltas", deltas)
# print("len", len(deltas))
assert forced <= solution, (forced, solution)
deltas = [deltas[i] if i in solution else None for i in range(n)]
deltas = _rot_list(deltas, -k)
else:
# Repeat the contour an extra time, solve the new case, then look for solutions of the
# circular n-length problem in the solution for new linear case. I cannot prove that
# this always produces the optimal solution...
chain, costs = _iup_contour_optimize_dp(
deltas + deltas, coords + coords, forced, tolerance, n
)
best_sol, best_cost = None, n + 1
for start in range(n - 1, len(costs) - 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
# if not forced <= best_sol:
# print("coord", coords)
# print("deltas", deltas)
# print("len", len(deltas))
assert forced <= best_sol, (forced, best_sol)
deltas = [deltas[i] if i in best_sol else None for i in range(n)]
return deltas
[docs]
def iup_delta_optimize(
deltas: _DeltaSegment,
coords: _PointSegment,
ends: _Endpoints,
tolerance: Real = 0.0,
) -> _DeltaOrNoneSegment:
"""For the outline given in `coords`, with contour endpoints given
in sorted increasing order in `ends`, optimize a set of delta
values `deltas` within error `tolerance`.
Returns delta vector that has most number of None items instead of
the input delta.
"""
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(
deltas[start : end + 1], coords[start : end + 1], tolerance
)
assert len(contour) == end - start + 1
out.extend(contour)
start = end + 1
return out