"""
Tool to find wrong contour order between different masters, and
other interpolatability (or lack thereof) issues.
Call as:
$ fonttools varLib.interpolatable font1 font2 ...
"""
from fontTools.pens.basePen import AbstractPen, BasePen
from fontTools.pens.pointPen import AbstractPointPen, SegmentToPointPen
from fontTools.pens.recordingPen import RecordingPen
from fontTools.pens.boundsPen import ControlBoundsPen
from fontTools.pens.statisticsPen import StatisticsPen, StatisticsControlPen
from fontTools.pens.momentsPen import OpenContourError
from fontTools.varLib.models import piecewiseLinearMap, normalizeLocation
from fontTools.misc.fixedTools import floatToFixedToStr
from fontTools.misc.transform import Transform
from collections import defaultdict, deque
from types import SimpleNamespace
from functools import wraps
from pprint import pformat
from math import sqrt, copysign, atan2, pi
import itertools
import logging
log = logging.getLogger("fontTools.varLib.interpolatable")
DEFAULT_TOLERANCE = 0.95
DEFAULT_KINKINESS = 0.5
DEFAULT_KINKINESS_LENGTH = 0.002 # ratio of UPEM
DEFAULT_UPEM = 1000
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."""
return l[-k:] + l[:-k]
class PerContourPen(BasePen):
def __init__(self, Pen, glyphset=None):
BasePen.__init__(self, glyphset)
self._glyphset = glyphset
self._Pen = Pen
self._pen = None
self.value = []
def _moveTo(self, p0):
self._newItem()
self._pen.moveTo(p0)
def _lineTo(self, p1):
self._pen.lineTo(p1)
def _qCurveToOne(self, p1, p2):
self._pen.qCurveTo(p1, p2)
def _curveToOne(self, p1, p2, p3):
self._pen.curveTo(p1, p2, p3)
def _closePath(self):
self._pen.closePath()
self._pen = None
def _endPath(self):
self._pen.endPath()
self._pen = None
def _newItem(self):
self._pen = pen = self._Pen()
self.value.append(pen)
class PerContourOrComponentPen(PerContourPen):
def addComponent(self, glyphName, transformation):
self._newItem()
self.value[-1].addComponent(glyphName, transformation)
class SimpleRecordingPointPen(AbstractPointPen):
def __init__(self):
self.value = []
def beginPath(self, identifier=None, **kwargs):
pass
def endPath(self) -> None:
pass
def addPoint(self, pt, segmentType=None):
self.value.append((pt, False if segmentType is None else True))
def _vdiff_hypot2(v0, v1):
s = 0
for x0, x1 in zip(v0, v1):
d = x1 - x0
s += d * d
return s
def _vdiff_hypot2_complex(v0, v1):
s = 0
for x0, x1 in zip(v0, v1):
d = x1 - x0
s += d.real * d.real + d.imag * d.imag
# This does the same but seems to be slower:
# s += (d * d.conjugate()).real
return s
def _hypot2_complex(d):
return d.real * d.real + d.imag * d.imag
def _matching_cost(G, matching):
return sum(G[i][j] for i, j in enumerate(matching))
def min_cost_perfect_bipartite_matching_scipy(G):
n = len(G)
rows, cols = linear_sum_assignment(G)
assert (rows == list(range(n))).all()
return list(cols), _matching_cost(G, cols)
def min_cost_perfect_bipartite_matching_munkres(G):
n = len(G)
cols = [None] * n
for row, col in Munkres().compute(G):
cols[row] = col
return cols, _matching_cost(G, cols)
def min_cost_perfect_bipartite_matching_bruteforce(G):
n = len(G)
if n > 6:
raise Exception("Install Python module 'munkres' or 'scipy >= 0.17.0'")
# Otherwise just brute-force
permutations = itertools.permutations(range(n))
best = list(next(permutations))
best_cost = _matching_cost(G, best)
for p in permutations:
cost = _matching_cost(G, p)
if cost < best_cost:
best, best_cost = list(p), cost
return best, best_cost
try:
from scipy.optimize import linear_sum_assignment
min_cost_perfect_bipartite_matching = min_cost_perfect_bipartite_matching_scipy
except ImportError:
try:
from munkres import Munkres
min_cost_perfect_bipartite_matching = (
min_cost_perfect_bipartite_matching_munkres
)
except ImportError:
min_cost_perfect_bipartite_matching = (
min_cost_perfect_bipartite_matching_bruteforce
)
def _contour_vector_from_stats(stats):
# Don't change the order of items here.
# It's okay to add to the end, but otherwise, other
# code depends on it. Search for "covariance".
size = sqrt(abs(stats.area))
return (
copysign((size), stats.area),
stats.meanX,
stats.meanY,
stats.stddevX * 2,
stats.stddevY * 2,
stats.correlation * size,
)
def _matching_for_vectors(m0, m1):
n = len(m0)
identity_matching = list(range(n))
costs = [[_vdiff_hypot2(v0, v1) for v1 in m1] for v0 in m0]
(
matching,
matching_cost,
) = min_cost_perfect_bipartite_matching(costs)
identity_cost = sum(costs[i][i] for i in range(n))
return matching, matching_cost, identity_cost
def _points_characteristic_bits(points):
bits = 0
for pt, b in reversed(points):
bits = (bits << 1) | b
return bits
_NUM_ITEMS_PER_POINTS_COMPLEX_VECTOR = 4
def _points_complex_vector(points):
vector = []
if not points:
return vector
points = [complex(*pt) for pt, _ in points]
n = len(points)
assert _NUM_ITEMS_PER_POINTS_COMPLEX_VECTOR == 4
points.extend(points[: _NUM_ITEMS_PER_POINTS_COMPLEX_VECTOR - 1])
while len(points) < _NUM_ITEMS_PER_POINTS_COMPLEX_VECTOR:
points.extend(points[: _NUM_ITEMS_PER_POINTS_COMPLEX_VECTOR - 1])
for i in range(n):
# The weights are magic numbers.
# The point itself
p0 = points[i]
vector.append(p0)
# The vector to the next point
p1 = points[i + 1]
d0 = p1 - p0
vector.append(d0 * 3)
# The turn vector
p2 = points[i + 2]
d1 = p2 - p1
vector.append(d1 - d0)
# The angle to the next point, as a cross product;
# Square root of, to match dimentionality of distance.
cross = d0.real * d1.imag - d0.imag * d1.real
cross = copysign(sqrt(abs(cross)), cross)
vector.append(cross * 4)
return vector
def _add_isomorphisms(points, isomorphisms, reverse):
reference_bits = _points_characteristic_bits(points)
n = len(points)
# if points[0][0] == points[-1][0]:
# abort
if reverse:
points = points[::-1]
bits = _points_characteristic_bits(points)
else:
bits = reference_bits
vector = _points_complex_vector(points)
assert len(vector) % n == 0
mult = len(vector) // n
mask = (1 << n) - 1
for i in range(n):
b = ((bits << (n - i)) & mask) | (bits >> i)
if b == reference_bits:
isomorphisms.append(
(_rot_list(vector, -i * mult), n - 1 - i if reverse else i, reverse)
)
def _find_parents_and_order(glyphsets, locations):
parents = [None] + list(range(len(glyphsets) - 1))
order = list(range(len(glyphsets)))
if locations:
# Order base master first
bases = (i for i, l in enumerate(locations) if all(v == 0 for v in l.values()))
if bases:
base = next(bases)
logging.info("Base master index %s, location %s", base, locations[base])
else:
base = 0
logging.warning("No base master location found")
# Form a minimum spanning tree of the locations
try:
from scipy.sparse.csgraph import minimum_spanning_tree
graph = [[0] * len(locations) for _ in range(len(locations))]
axes = set()
for l in locations:
axes.update(l.keys())
axes = sorted(axes)
vectors = [tuple(l.get(k, 0) for k in axes) for l in locations]
for i, j in itertools.combinations(range(len(locations)), 2):
graph[i][j] = _vdiff_hypot2(vectors[i], vectors[j])
tree = minimum_spanning_tree(graph)
rows, cols = tree.nonzero()
graph = defaultdict(set)
for row, col in zip(rows, cols):
graph[row].add(col)
graph[col].add(row)
# Traverse graph from the base and assign parents
parents = [None] * len(locations)
order = []
visited = set()
queue = deque([base])
while queue:
i = queue.popleft()
visited.add(i)
order.append(i)
for j in sorted(graph[i]):
if j not in visited:
parents[j] = i
queue.append(j)
except ImportError:
pass
log.info("Parents: %s", parents)
log.info("Order: %s", order)
return parents, order
def lerp_recordings(recording1, recording2, factor=0.5):
pen = RecordingPen()
value = pen.value
for (op1, args1), (op2, args2) in zip(recording1.value, recording2.value):
if op1 != op2:
raise ValueError("Mismatched operations: %s, %s" % (op1, op2))
if op1 == "addComponent":
mid_args = args1 # XXX Interpolate transformation?
else:
mid_args = [
(x1 + (x2 - x1) * factor, y1 + (y2 - y1) * factor)
for (x1, y1), (x2, y2) in zip(args1, args2)
]
value.append((op1, mid_args))
return pen
def test_gen(
glyphsets,
glyphs=None,
names=None,
ignore_missing=False,
*,
locations=None,
tolerance=DEFAULT_TOLERANCE,
kinkiness=DEFAULT_KINKINESS,
upem=DEFAULT_UPEM,
show_all=False,
):
if tolerance >= 10:
tolerance *= 0.01
assert 0 <= tolerance <= 1
if kinkiness >= 10:
kinkiness *= 0.01
assert 0 <= kinkiness
if names is None:
names = glyphsets
if glyphs is None:
# `glyphs = glyphsets[0].keys()` is faster, certainly, but doesn't allow for sparse TTFs/OTFs given out of order
# ... risks the sparse master being the first one, and only processing a subset of the glyphs
glyphs = {g for glyphset in glyphsets for g in glyphset.keys()}
parents, order = _find_parents_and_order(glyphsets, locations)
def grand_parent(i, glyphname):
if i is None:
return None
i = parents[i]
if i is None:
return None
while parents[i] is not None and glyphsets[i][glyphname] is None:
i = parents[i]
return i
for glyph_name in glyphs:
log.info("Testing glyph %s", glyph_name)
allGreenVectors = []
allControlVectors = []
allNodeTypes = []
allContourIsomorphisms = []
allContourPoints = []
allContourPens = []
allGlyphs = [glyphset[glyph_name] for glyphset in glyphsets]
if len([1 for glyph in allGlyphs if glyph is not None]) <= 1:
continue
for master_idx, (glyph, glyphset, name) in enumerate(
zip(allGlyphs, glyphsets, names)
):
if glyph is None:
if not ignore_missing:
yield (
glyph_name,
{"type": "missing", "master": name, "master_idx": master_idx},
)
allNodeTypes.append(None)
allControlVectors.append(None)
allGreenVectors.append(None)
allContourIsomorphisms.append(None)
allContourPoints.append(None)
allContourPens.append(None)
continue
perContourPen = PerContourOrComponentPen(RecordingPen, glyphset=glyphset)
try:
glyph.draw(perContourPen, outputImpliedClosingLine=True)
except TypeError:
glyph.draw(perContourPen)
contourPens = perContourPen.value
del perContourPen
contourControlVectors = []
contourGreenVectors = []
contourIsomorphisms = []
contourPoints = []
nodeTypes = []
allNodeTypes.append(nodeTypes)
allControlVectors.append(contourControlVectors)
allGreenVectors.append(contourGreenVectors)
allContourIsomorphisms.append(contourIsomorphisms)
allContourPoints.append(contourPoints)
allContourPens.append(contourPens)
for ix, contour in enumerate(contourPens):
contourOps = tuple(op for op, arg in contour.value)
nodeTypes.append(contourOps)
greenStats = StatisticsPen(glyphset=glyphset)
controlStats = StatisticsControlPen(glyphset=glyphset)
try:
contour.replay(greenStats)
contour.replay(controlStats)
except OpenContourError as e:
yield (
glyph_name,
{
"master": name,
"master_idx": master_idx,
"contour": ix,
"type": "open_path",
},
)
continue
contourGreenVectors.append(_contour_vector_from_stats(greenStats))
contourControlVectors.append(_contour_vector_from_stats(controlStats))
# Check starting point
if contourOps[0] == "addComponent":
continue
assert contourOps[0] == "moveTo"
assert contourOps[-1] in ("closePath", "endPath")
points = SimpleRecordingPointPen()
converter = SegmentToPointPen(points, False)
contour.replay(converter)
# points.value is a list of pt,bool where bool is true if on-curve and false if off-curve;
# now check all rotations and mirror-rotations of the contour and build list of isomorphic
# possible starting points.
isomorphisms = []
contourIsomorphisms.append(isomorphisms)
# Add rotations
_add_isomorphisms(points.value, isomorphisms, False)
# Add mirrored rotations
_add_isomorphisms(points.value, isomorphisms, True)
contourPoints.append(points.value)
matchings = [None] * len(allControlVectors)
for m1idx in order:
if allNodeTypes[m1idx] is None:
continue
m0idx = grand_parent(m1idx, glyph_name)
if m0idx is None:
continue
if allNodeTypes[m0idx] is None:
continue
#
# Basic compatibility checks
#
m1 = allNodeTypes[m1idx]
m0 = allNodeTypes[m0idx]
if len(m0) != len(m1):
yield (
glyph_name,
{
"type": "path_count",
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"value_1": len(m0),
"value_2": len(m1),
},
)
continue
if m0 != m1:
for pathIx, (nodes1, nodes2) in enumerate(zip(m0, m1)):
if nodes1 == nodes2:
continue
if len(nodes1) != len(nodes2):
yield (
glyph_name,
{
"type": "node_count",
"path": pathIx,
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"value_1": len(nodes1),
"value_2": len(nodes2),
},
)
continue
for nodeIx, (n1, n2) in enumerate(zip(nodes1, nodes2)):
if n1 != n2:
yield (
glyph_name,
{
"type": "node_incompatibility",
"path": pathIx,
"node": nodeIx,
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"value_1": n1,
"value_2": n2,
},
)
continue
#
# "contour_order" check
#
# We try matching both the StatisticsControlPen vector
# and the StatisticsPen vector.
#
# If either method found a identity matching, accept it.
# This is crucial for fonts like Kablammo[MORF].ttf and
# Nabla[EDPT,EHLT].ttf, since they really confuse the
# StatisticsPen vector because of their area=0 contours.
#
# TODO: Optimize by only computing the StatisticsPen vector
# and then checking if it is the identity vector. Only if
# not, compute the StatisticsControlPen vector and check both.
n = len(allControlVectors[m0idx])
done = n <= 1
if not done:
m1Control = allControlVectors[m1idx]
m0Control = allControlVectors[m0idx]
(
matching_control,
matching_cost_control,
identity_cost_control,
) = _matching_for_vectors(m0Control, m1Control)
done = matching_cost_control == identity_cost_control
if not done:
m1Green = allGreenVectors[m1idx]
m0Green = allGreenVectors[m0idx]
(
matching_green,
matching_cost_green,
identity_cost_green,
) = _matching_for_vectors(m0Green, m1Green)
done = matching_cost_green == identity_cost_green
if not done:
# See if reversing contours in one master helps.
# That's a common problem. Then the wrong_start_point
# test will fix them.
#
# Reverse the sign of the area (0); the rest stay the same.
if not done:
m1ControlReversed = [(-m[0],) + m[1:] for m in m1Control]
(
matching_control_reversed,
matching_cost_control_reversed,
identity_cost_control_reversed,
) = _matching_for_vectors(m0Control, m1ControlReversed)
done = (
matching_cost_control_reversed == identity_cost_control_reversed
)
if not done:
m1GreenReversed = [(-m[0],) + m[1:] for m in m1Green]
(
matching_control_reversed,
matching_cost_control_reversed,
identity_cost_control_reversed,
) = _matching_for_vectors(m0Control, m1ControlReversed)
done = (
matching_cost_control_reversed == identity_cost_control_reversed
)
if not done:
# Otherwise, use the worst of the two matchings.
if (
matching_cost_control / identity_cost_control
< matching_cost_green / identity_cost_green
):
matching = matching_control
matching_cost = matching_cost_control
identity_cost = identity_cost_control
else:
matching = matching_green
matching_cost = matching_cost_green
identity_cost = identity_cost_green
if matching_cost < identity_cost * tolerance:
log.debug(
"matching_control_ratio %g; matching_green_ratio %g.",
matching_cost_control / identity_cost_control,
matching_cost_green / identity_cost_green,
)
this_tolerance = matching_cost / identity_cost
log.debug("tolerance: %g", this_tolerance)
yield (
glyph_name,
{
"type": "contour_order",
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"value_1": list(range(n)),
"value_2": matching,
"tolerance": this_tolerance,
},
)
matchings[m1idx] = matching
#
# "wrong_start_point" / weight check
#
m1 = allContourIsomorphisms[m1idx]
m0 = allContourIsomorphisms[m0idx]
m1Vectors = allGreenVectors[m1idx]
m0Vectors = allGreenVectors[m0idx]
recording0 = allContourPens[m0idx]
recording1 = allContourPens[m1idx]
# If contour-order is wrong, adjust it
if matchings[m1idx] is not None and m1: # m1 is empty for composite glyphs
m1 = [m1[i] for i in matchings[m1idx]]
m1Vectors = [m1Vectors[i] for i in matchings[m1idx]]
recording1 = [recording1[i] for i in matchings[m1idx]]
midRecording = []
for c0, c1 in zip(recording0, recording1):
try:
midRecording.append(lerp_recordings(c0, c1))
except ValueError:
# Mismatch because of the reordering above
midRecording.append(None)
for ix, (contour0, contour1) in enumerate(zip(m0, m1)):
if len(contour0) == 0 or len(contour0) != len(contour1):
# We already reported this; or nothing to do; or not compatible
# after reordering above.
continue
c0 = contour0[0]
# Next few lines duplicated below.
costs = [_vdiff_hypot2_complex(c0[0], c1[0]) for c1 in contour1]
min_cost_idx, min_cost = min(enumerate(costs), key=lambda x: x[1])
first_cost = costs[0]
if min_cost < first_cost * tolerance:
this_tolerance = min_cost / first_cost
# c0 is the first isomorphism of the m0 master
# contour1 is list of all isomorphisms of the m1 master
#
# If the two shapes are both circle-ish and slightly
# rotated, we detect wrong start point. This is for
# example the case hundreds of times in
# RobotoSerif-Italic[GRAD,opsz,wdth,wght].ttf
#
# If the proposed point is only one off from the first
# point (and not reversed), try harder:
#
# Find the major eigenvector of the covariance matrix,
# and rotate the contours by that angle. Then find the
# closest point again. If it matches this time, let it
# pass.
proposed_point = contour1[min_cost_idx][1]
reverse = contour1[min_cost_idx][2]
num_points = len(allContourPoints[m1idx][ix])
leeway = 3
okay = False
if not reverse and (
proposed_point <= leeway
or proposed_point >= num_points - leeway
):
# Try harder
# Recover the covariance matrix from the GreenVectors.
# This is a 2x2 matrix.
transforms = []
for vector in (m0Vectors[ix], m1Vectors[ix]):
meanX = vector[1]
meanY = vector[2]
stddevX = vector[3] * 0.5
stddevY = vector[4] * 0.5
correlation = vector[5] / abs(vector[0])
# https://cookierobotics.com/007/
a = stddevX * stddevX # VarianceX
c = stddevY * stddevY # VarianceY
b = correlation * stddevX * stddevY # Covariance
delta = (((a - c) * 0.5) ** 2 + b * b) ** 0.5
lambda1 = (a + c) * 0.5 + delta # Major eigenvalue
lambda2 = (a + c) * 0.5 - delta # Minor eigenvalue
theta = (
atan2(lambda1 - a, b)
if b != 0
else (pi * 0.5 if a < c else 0)
)
trans = Transform()
# Don't translate here. We are working on the complex-vector
# that includes more than just the points. It's horrible what
# we are doing anyway...
# trans = trans.translate(meanX, meanY)
trans = trans.rotate(theta)
trans = trans.scale(sqrt(lambda1), sqrt(lambda2))
transforms.append(trans)
trans = transforms[0]
new_c0 = (
[
complex(*trans.transformPoint((pt.real, pt.imag)))
for pt in c0[0]
],
) + c0[1:]
trans = transforms[1]
new_contour1 = []
for c1 in contour1:
new_c1 = (
[
complex(*trans.transformPoint((pt.real, pt.imag)))
for pt in c1[0]
],
) + c1[1:]
new_contour1.append(new_c1)
# Next few lines duplicate from above.
costs = [
_vdiff_hypot2_complex(new_c0[0], new_c1[0])
for new_c1 in new_contour1
]
min_cost_idx, min_cost = min(
enumerate(costs), key=lambda x: x[1]
)
first_cost = costs[0]
if min_cost < first_cost * tolerance:
pass
# this_tolerance = min_cost / first_cost
# proposed_point = new_contour1[min_cost_idx][1]
else:
okay = True
if not okay:
yield (
glyph_name,
{
"type": "wrong_start_point",
"contour": ix,
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"value_1": 0,
"value_2": proposed_point,
"reversed": reverse,
"tolerance": this_tolerance,
},
)
else:
# Weight check.
#
# If contour could be mid-interpolated, and the two
# contours have the same area sign, proceeed.
#
# The sign difference can happen if it's a werido
# self-intersecting contour; ignore it.
contour = midRecording[ix]
if contour and (m0Vectors[ix][0] < 0) == (m1Vectors[ix][0] < 0):
midStats = StatisticsPen(glyphset=glyphset)
contour.replay(midStats)
midVector = _contour_vector_from_stats(midStats)
size0 = m0Vectors[ix][0] * m0Vectors[ix][0]
size1 = m1Vectors[ix][0] * m1Vectors[ix][0]
midSize = midVector[0] * midVector[0]
bounds0Pen = ControlBoundsPen(glyphsets[m0idx])
bounds1Pen = ControlBoundsPen(glyphsets[m1idx])
recording0[ix].replay(bounds0Pen)
recording1[ix].replay(bounds1Pen)
bounds0 = bounds0Pen.bounds or (0, 0, 0, 0)
bounds1 = bounds1Pen.bounds or (0, 0, 0, 0)
width0, height0 = bounds0[2] - bounds0[0], bounds0[3] - bounds0[1]
width1, height1 = bounds1[2] - bounds1[0], bounds1[3] - bounds1[1]
try:
size0 /= width0 * height0
size1 /= width1 * height1
midSize /= (width0 + width1) * .5 * (height0 + height1) * .5
except ZeroDivisionError:
continue
size0, size1 = sorted((size0, size1))
for overweight, problem_type in enumerate(
("underweight", "overweight")
):
if overweight:
expectedSize = (size0 * size1) ** 0.5
expectedSize = (size0 + size1) - expectedSize
#expectedSize = (size0 + size1) * .5
else:
expectedSize = (size0 * size1) ** 0.5
log.debug(
"%s: actual size %g; threshold size %g, master sizes: %g, %g",
problem_type,
midSize,
expectedSize,
size0,
size1,
)
if (
not overweight
and expectedSize * tolerance > midSize + 1e-5
) or (
overweight and 1e-5 + expectedSize < midSize * tolerance
):
try:
if overweight:
this_tolerance = expectedSize / midSize
else:
this_tolerance = midSize / expectedSize
except ZeroDivisionError:
this_tolerance = 0
log.debug("tolerance %g", this_tolerance)
yield (
glyph_name,
{
"type": problem_type,
"contour": ix,
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"tolerance": this_tolerance,
},
)
#
# "kink" detector
#
m1 = allContourPoints[m1idx]
m0 = allContourPoints[m0idx]
# If contour-order is wrong, adjust it
if matchings[m1idx] is not None and m1: # m1 is empty for composite glyphs
m1 = [m1[i] for i in matchings[m1idx]]
t = 0.1 # ~sin(radian(6)) for tolerance 0.95
deviation_threshold = (
upem * DEFAULT_KINKINESS_LENGTH * DEFAULT_KINKINESS / kinkiness
)
for ix, (contour0, contour1) in enumerate(zip(m0, m1)):
if len(contour0) == 0 or len(contour0) != len(contour1):
# We already reported this; or nothing to do; or not compatible
# after reordering above.
continue
# Walk the contour, keeping track of three consecutive points, with
# middle one being an on-curve. If the three are co-linear then
# check for kinky-ness.
for i in range(len(contour0)):
pt0 = contour0[i]
pt1 = contour1[i]
if not pt0[1] or not pt1[1]:
# Skip off-curves
continue
pt0_prev = contour0[i - 1]
pt1_prev = contour1[i - 1]
pt0_next = contour0[(i + 1) % len(contour0)]
pt1_next = contour1[(i + 1) % len(contour1)]
if pt0_prev[1] and pt1_prev[1]:
# At least one off-curve is required
continue
if pt0_prev[1] and pt1_prev[1]:
# At least one off-curve is required
continue
pt0 = complex(*pt0[0])
pt1 = complex(*pt1[0])
pt0_prev = complex(*pt0_prev[0])
pt1_prev = complex(*pt1_prev[0])
pt0_next = complex(*pt0_next[0])
pt1_next = complex(*pt1_next[0])
# We have three consecutive points. Check whether
# they are colinear.
d0_prev = pt0 - pt0_prev
d0_next = pt0_next - pt0
d1_prev = pt1 - pt1_prev
d1_next = pt1_next - pt1
sin0 = d0_prev.real * d0_next.imag - d0_prev.imag * d0_next.real
sin1 = d1_prev.real * d1_next.imag - d1_prev.imag * d1_next.real
try:
sin0 /= abs(d0_prev) * abs(d0_next)
sin1 /= abs(d1_prev) * abs(d1_next)
except ZeroDivisionError:
continue
if abs(sin0) > t or abs(sin1) > t:
# Not colinear / not smooth.
continue
# Check the mid-point is actually, well, in the middle.
dot0 = d0_prev.real * d0_next.real + d0_prev.imag * d0_next.imag
dot1 = d1_prev.real * d1_next.real + d1_prev.imag * d1_next.imag
if dot0 < 0 or dot1 < 0:
# Sharp corner.
continue
# Fine, if handle ratios are similar...
r0 = abs(d0_prev) / (abs(d0_prev) + abs(d0_next))
r1 = abs(d1_prev) / (abs(d1_prev) + abs(d1_next))
r_diff = abs(r0 - r1)
if abs(r_diff) < t:
# Smooth enough.
continue
mid = (pt0 + pt1) / 2
mid_prev = (pt0_prev + pt1_prev) / 2
mid_next = (pt0_next + pt1_next) / 2
mid_d0 = mid - mid_prev
mid_d1 = mid_next - mid
sin_mid = mid_d0.real * mid_d1.imag - mid_d0.imag * mid_d1.real
try:
sin_mid /= abs(mid_d0) * abs(mid_d1)
except ZeroDivisionError:
continue
# ...or if the angles are similar.
if abs(sin_mid) * (tolerance * kinkiness) <= t:
# Smooth enough.
continue
# How visible is the kink?
cross = sin_mid * abs(mid_d0) * abs(mid_d1)
arc_len = abs(mid_d0 + mid_d1)
deviation = abs(cross / arc_len)
if deviation < deviation_threshold:
continue
deviation_ratio = deviation / arc_len
if deviation_ratio > t:
continue
this_tolerance = t / (abs(sin_mid) * kinkiness)
log.debug(
"deviation %g; deviation_ratio %g; sin_mid %g; r_diff %g",
deviation,
deviation_ratio,
sin_mid,
r_diff,
)
log.debug("tolerance %g", this_tolerance)
yield (
glyph_name,
{
"type": "kink",
"contour": ix,
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
"value": i,
"tolerance": this_tolerance,
},
)
#
# --show-all
#
if show_all:
yield (
glyph_name,
{
"type": "nothing",
"master_1": names[m0idx],
"master_2": names[m1idx],
"master_1_idx": m0idx,
"master_2_idx": m1idx,
},
)
@wraps(test_gen)
def test(*args, **kwargs):
problems = defaultdict(list)
for glyphname, problem in test_gen(*args, **kwargs):
problems[glyphname].append(problem)
return problems
def recursivelyAddGlyph(glyphname, glyphset, ttGlyphSet, glyf):
if glyphname in glyphset:
return
glyphset[glyphname] = ttGlyphSet[glyphname]
for component in getattr(glyf[glyphname], "components", []):
recursivelyAddGlyph(component.glyphName, glyphset, ttGlyphSet, glyf)
def main(args=None):
"""Test for interpolatability issues between fonts"""
import argparse
import sys
parser = argparse.ArgumentParser(
"fonttools varLib.interpolatable",
description=main.__doc__,
)
parser.add_argument(
"--glyphs",
action="store",
help="Space-separate name of glyphs to check",
)
parser.add_argument(
"--show-all",
action="store_true",
help="Show all glyph pairs, even if no problems are found",
)
parser.add_argument(
"--tolerance",
action="store",
type=float,
help="Error tolerance. Between 0 and 1. Default %s" % DEFAULT_TOLERANCE,
)
parser.add_argument(
"--kinkiness",
action="store",
type=float,
help="How aggressively report kinks. Default %s" % DEFAULT_KINKINESS,
)
parser.add_argument(
"--json",
action="store_true",
help="Output report in JSON format",
)
parser.add_argument(
"--pdf",
action="store",
help="Output report in PDF format",
)
parser.add_argument(
"--ps",
action="store",
help="Output report in PostScript format",
)
parser.add_argument(
"--html",
action="store",
help="Output report in HTML format",
)
parser.add_argument(
"--quiet",
action="store_true",
help="Only exit with code 1 or 0, no output",
)
parser.add_argument(
"--output",
action="store",
help="Output file for the problem report; Default: stdout",
)
parser.add_argument(
"--ignore-missing",
action="store_true",
help="Will not report glyphs missing from sparse masters as errors",
)
parser.add_argument(
"inputs",
metavar="FILE",
type=str,
nargs="+",
help="Input a single variable font / DesignSpace / Glyphs file, or multiple TTF/UFO files",
)
parser.add_argument(
"--name",
metavar="NAME",
type=str,
action="append",
help="Name of the master to use in the report. If not provided, all are used.",
)
parser.add_argument("-v", "--verbose", action="store_true", help="Run verbosely.")
parser.add_argument("--debug", action="store_true", help="Run with debug output.")
args = parser.parse_args(args)
from fontTools import configLogger
configLogger(level=("INFO" if args.verbose else "ERROR"))
if args.debug:
configLogger(level="DEBUG")
glyphs = args.glyphs.split() if args.glyphs else None
from os.path import basename
fonts = []
names = []
locations = []
upem = DEFAULT_UPEM
original_args_inputs = tuple(args.inputs)
if len(args.inputs) == 1:
designspace = None
if args.inputs[0].endswith(".designspace"):
from fontTools.designspaceLib import DesignSpaceDocument
designspace = DesignSpaceDocument.fromfile(args.inputs[0])
args.inputs = [master.path for master in designspace.sources]
locations = [master.location for master in designspace.sources]
axis_triples = {
a.name: (a.minimum, a.default, a.maximum) for a in designspace.axes
}
axis_mappings = {a.name: a.map for a in designspace.axes}
axis_triples = {
k: tuple(piecewiseLinearMap(v, dict(axis_mappings[k])) for v in vv)
for k, vv in axis_triples.items()
}
elif args.inputs[0].endswith(".glyphs"):
from glyphsLib import GSFont, to_designspace
gsfont = GSFont(args.inputs[0])
upem = gsfont.upm
designspace = to_designspace(gsfont)
fonts = [source.font for source in designspace.sources]
names = ["%s-%s" % (f.info.familyName, f.info.styleName) for f in fonts]
args.inputs = []
locations = [master.location for master in designspace.sources]
axis_triples = {
a.name: (a.minimum, a.default, a.maximum) for a in designspace.axes
}
axis_mappings = {a.name: a.map for a in designspace.axes}
axis_triples = {
k: tuple(piecewiseLinearMap(v, dict(axis_mappings[k])) for v in vv)
for k, vv in axis_triples.items()
}
elif args.inputs[0].endswith(".ttf"):
from fontTools.ttLib import TTFont
font = TTFont(args.inputs[0])
upem = font["head"].unitsPerEm
if "gvar" in font:
# Is variable font
axisMapping = {}
fvar = font["fvar"]
for axis in fvar.axes:
axisMapping[axis.axisTag] = {
-1: axis.minValue,
0: axis.defaultValue,
1: axis.maxValue,
}
if "avar" in font:
avar = font["avar"]
for axisTag, segments in avar.segments.items():
fvarMapping = axisMapping[axisTag].copy()
for location, value in segments.items():
axisMapping[axisTag][value] = piecewiseLinearMap(
location, fvarMapping
)
gvar = font["gvar"]
glyf = font["glyf"]
# Gather all glyphs at their "master" locations
ttGlyphSets = {}
glyphsets = defaultdict(dict)
if glyphs is None:
glyphs = sorted(gvar.variations.keys())
for glyphname in glyphs:
for var in gvar.variations[glyphname]:
locDict = {}
loc = []
for tag, val in sorted(var.axes.items()):
locDict[tag] = val[1]
loc.append((tag, val[1]))
locTuple = tuple(loc)
if locTuple not in ttGlyphSets:
ttGlyphSets[locTuple] = font.getGlyphSet(
location=locDict, normalized=True, recalcBounds=False
)
recursivelyAddGlyph(
glyphname, glyphsets[locTuple], ttGlyphSets[locTuple], glyf
)
names = ["''"]
fonts = [font.getGlyphSet()]
locations = [{}]
axis_triples = {a: (-1, 0, +1) for a in sorted(axisMapping.keys())}
for locTuple in sorted(glyphsets.keys(), key=lambda v: (len(v), v)):
name = (
"'"
+ " ".join(
"%s=%s"
% (
k,
floatToFixedToStr(
piecewiseLinearMap(v, axisMapping[k]), 14
),
)
for k, v in locTuple
)
+ "'"
)
names.append(name)
fonts.append(glyphsets[locTuple])
locations.append(dict(locTuple))
args.ignore_missing = True
args.inputs = []
if not locations:
locations = [{} for _ in fonts]
for filename in args.inputs:
if filename.endswith(".ufo"):
from fontTools.ufoLib import UFOReader
font = UFOReader(filename)
info = SimpleNamespace()
font.readInfo(info)
upem = info.unitsPerEm
fonts.append(font)
else:
from fontTools.ttLib import TTFont
font = TTFont(filename)
upem = font["head"].unitsPerEm
fonts.append(font)
names.append(basename(filename).rsplit(".", 1)[0])
glyphsets = []
for font in fonts:
if hasattr(font, "getGlyphSet"):
glyphset = font.getGlyphSet()
else:
glyphset = font
glyphsets.append({k: glyphset[k] for k in glyphset.keys()})
if args.name:
accepted_names = set(args.name)
glyphsets = [
glyphset
for name, glyphset in zip(names, glyphsets)
if name in accepted_names
]
locations = [
location
for name, location in zip(names, locations)
if name in accepted_names
]
names = [name for name in names if name in accepted_names]
if not glyphs:
glyphs = sorted(set([gn for glyphset in glyphsets for gn in glyphset.keys()]))
glyphsSet = set(glyphs)
for glyphset in glyphsets:
glyphSetGlyphNames = set(glyphset.keys())
diff = glyphsSet - glyphSetGlyphNames
if diff:
for gn in diff:
glyphset[gn] = None
# Normalize locations
locations = [normalizeLocation(loc, axis_triples) for loc in locations]
tolerance = args.tolerance or DEFAULT_TOLERANCE
kinkiness = args.kinkiness if args.kinkiness is not None else DEFAULT_KINKINESS
try:
log.info("Running on %d glyphsets", len(glyphsets))
log.info("Locations: %s", pformat(locations))
problems_gen = test_gen(
glyphsets,
glyphs=glyphs,
names=names,
locations=locations,
upem=upem,
ignore_missing=args.ignore_missing,
tolerance=tolerance,
kinkiness=kinkiness,
show_all=args.show_all,
)
problems = defaultdict(list)
f = sys.stdout if args.output is None else open(args.output, "w")
if not args.quiet:
if args.json:
import json
for glyphname, problem in problems_gen:
problems[glyphname].append(problem)
print(json.dumps(problems), file=f)
else:
last_glyphname = None
for glyphname, p in problems_gen:
problems[glyphname].append(p)
if glyphname != last_glyphname:
print(f"Glyph {glyphname} was not compatible:", file=f)
last_glyphname = glyphname
last_master_idxs = None
master_idxs = (
(p["master_idx"])
if "master_idx" in p
else (p["master_1_idx"], p["master_2_idx"])
)
if master_idxs != last_master_idxs:
master_names = (
(p["master"])
if "master" in p
else (p["master_1"], p["master_2"])
)
print(f" Masters: %s:" % ", ".join(master_names), file=f)
last_master_idxs = master_idxs
if p["type"] == "missing":
print(
" Glyph was missing in master %s" % p["master"], file=f
)
elif p["type"] == "open_path":
print(
" Glyph has an open path in master %s" % p["master"],
file=f,
)
elif p["type"] == "path_count":
print(
" Path count differs: %i in %s, %i in %s"
% (
p["value_1"],
p["master_1"],
p["value_2"],
p["master_2"],
),
file=f,
)
elif p["type"] == "node_count":
print(
" Node count differs in path %i: %i in %s, %i in %s"
% (
p["path"],
p["value_1"],
p["master_1"],
p["value_2"],
p["master_2"],
),
file=f,
)
elif p["type"] == "node_incompatibility":
print(
" Node %o incompatible in path %i: %s in %s, %s in %s"
% (
p["node"],
p["path"],
p["value_1"],
p["master_1"],
p["value_2"],
p["master_2"],
),
file=f,
)
elif p["type"] == "contour_order":
print(
" Contour order differs: %s in %s, %s in %s"
% (
p["value_1"],
p["master_1"],
p["value_2"],
p["master_2"],
),
file=f,
)
elif p["type"] == "wrong_start_point":
print(
" Contour %d start point differs: %s in %s, %s in %s; reversed: %s"
% (
p["contour"],
p["value_1"],
p["master_1"],
p["value_2"],
p["master_2"],
p["reversed"],
),
file=f,
)
elif p["type"] == "underweight":
print(
" Contour %d interpolation is underweight: %s, %s"
% (
p["contour"],
p["master_1"],
p["master_2"],
),
file=f,
)
elif p["type"] == "overweight":
print(
" Contour %d interpolation is overweight: %s, %s"
% (
p["contour"],
p["master_1"],
p["master_2"],
),
file=f,
)
elif p["type"] == "kink":
print(
" Contour %d has a kink at %s: %s, %s"
% (
p["contour"],
p["value"],
p["master_1"],
p["master_2"],
),
file=f,
)
elif p["type"] == "nothing":
print(
" Showing %s and %s"
% (
p["master_1"],
p["master_2"],
),
file=f,
)
else:
for glyphname, problem in problems_gen:
problems[glyphname].append(problem)
if args.pdf:
log.info("Writing PDF to %s", args.pdf)
from .interpolatablePlot import InterpolatablePDF
with InterpolatablePDF(args.pdf, glyphsets=glyphsets, names=names) as pdf:
pdf.add_title_page(
original_args_inputs, tolerance=tolerance, kinkiness=kinkiness
)
pdf.add_problems(problems)
if not problems and not args.quiet:
pdf.draw_cupcake()
if args.ps:
log.info("Writing PS to %s", args.pdf)
from .interpolatablePlot import InterpolatablePS
with InterpolatablePS(args.ps, glyphsets=glyphsets, names=names) as ps:
ps.add_title_page(
original_args_inputs, tolerance=tolerance, kinkiness=kinkiness
)
ps.add_problems(problems)
if not problems and not args.quiet:
ps.draw_cupcake()
if args.html:
log.info("Writing HTML to %s", args.html)
from .interpolatablePlot import InterpolatableSVG
svgs = []
glyph_starts = {}
with InterpolatableSVG(svgs, glyphsets=glyphsets, names=names) as svg:
svg.add_title_page(
original_args_inputs,
show_tolerance=False,
tolerance=tolerance,
kinkiness=kinkiness,
)
for glyph, glyph_problems in problems.items():
glyph_starts[len(svgs)] = glyph
svg.add_problems(
{glyph: glyph_problems},
show_tolerance=False,
show_page_number=False,
)
if not problems and not args.quiet:
svg.draw_cupcake()
import base64
with open(args.html, "wb") as f:
f.write(b"\n")
f.write(
b'\n'
)
f.write(b"fonttools varLib.interpolatable report\n")
for i, svg in enumerate(svgs):
if i in glyph_starts:
f.write(f"Glyph {glyph_starts[i]}
\n".encode("utf-8"))
f.write("![](data:image/svg+xml;base64,".encode("utf-8"))
f.write(base64.b64encode(svg))
f.write(b")
\n")
f.write(b"
\n")
f.write(b"\n")
except Exception as e:
e.args += original_args_inputs
log.error(e)
raise
if problems:
return problems
if __name__ == "__main__":
import sys
problems = main()
sys.exit(int(bool(problems)))