"""Variation fonts interpolation models."""
__all__ = [
"normalizeValue",
"normalizeLocation",
"supportScalar",
"piecewiseLinearMap",
"VariationModel",
]
from fontTools.misc.roundTools import noRound
from .errors import VariationModelError
def nonNone(lst):
return [l for l in lst if l is not None]
def allNone(lst):
return all(l is None for l in lst)
def allEqualTo(ref, lst, mapper=None):
if mapper is None:
return all(ref == item for item in lst)
mapped = mapper(ref)
return all(mapped == mapper(item) for item in lst)
def allEqual(lst, mapper=None):
if not lst:
return True
it = iter(lst)
try:
first = next(it)
except StopIteration:
return True
return allEqualTo(first, it, mapper=mapper)
def subList(truth, lst):
assert len(truth) == len(lst)
return [l for l, t in zip(lst, truth) if t]
[docs]
def normalizeValue(v, triple, extrapolate=False):
"""Normalizes value based on a min/default/max triple.
>>> normalizeValue(400, (100, 400, 900))
0.0
>>> normalizeValue(100, (100, 400, 900))
-1.0
>>> normalizeValue(650, (100, 400, 900))
0.5
"""
lower, default, upper = triple
if not (lower <= default <= upper):
raise ValueError(
f"Invalid axis values, must be minimum, default, maximum: "
f"{lower:3.3f}, {default:3.3f}, {upper:3.3f}"
)
if not extrapolate:
v = max(min(v, upper), lower)
if v == default or lower == upper:
return 0.0
if (v < default and lower != default) or (v > default and upper == default):
return (v - default) / (default - lower)
else:
assert (v > default and upper != default) or (
v < default and lower == default
), f"Ooops... v={v}, triple=({lower}, {default}, {upper})"
return (v - default) / (upper - default)
[docs]
def normalizeLocation(location, axes, extrapolate=False):
"""Normalizes location based on axis min/default/max values from axes.
>>> axes = {"wght": (100, 400, 900)}
>>> normalizeLocation({"wght": 400}, axes)
{'wght': 0.0}
>>> normalizeLocation({"wght": 100}, axes)
{'wght': -1.0}
>>> normalizeLocation({"wght": 900}, axes)
{'wght': 1.0}
>>> normalizeLocation({"wght": 650}, axes)
{'wght': 0.5}
>>> normalizeLocation({"wght": 1000}, axes)
{'wght': 1.0}
>>> normalizeLocation({"wght": 0}, axes)
{'wght': -1.0}
>>> axes = {"wght": (0, 0, 1000)}
>>> normalizeLocation({"wght": 0}, axes)
{'wght': 0.0}
>>> normalizeLocation({"wght": -1}, axes)
{'wght': 0.0}
>>> normalizeLocation({"wght": 1000}, axes)
{'wght': 1.0}
>>> normalizeLocation({"wght": 500}, axes)
{'wght': 0.5}
>>> normalizeLocation({"wght": 1001}, axes)
{'wght': 1.0}
>>> axes = {"wght": (0, 1000, 1000)}
>>> normalizeLocation({"wght": 0}, axes)
{'wght': -1.0}
>>> normalizeLocation({"wght": -1}, axes)
{'wght': -1.0}
>>> normalizeLocation({"wght": 500}, axes)
{'wght': -0.5}
>>> normalizeLocation({"wght": 1000}, axes)
{'wght': 0.0}
>>> normalizeLocation({"wght": 1001}, axes)
{'wght': 0.0}
"""
out = {}
for tag, triple in axes.items():
v = location.get(tag, triple[1])
out[tag] = normalizeValue(v, triple, extrapolate=extrapolate)
return out
[docs]
def supportScalar(location, support, ot=True, extrapolate=False, axisRanges=None):
"""Returns the scalar multiplier at location, for a master
with support. If ot is True, then a peak value of zero
for support of an axis means "axis does not participate". That
is how OpenType Variation Font technology works.
If extrapolate is True, axisRanges must be a dict that maps axis
names to (axisMin, axisMax) tuples.
>>> supportScalar({}, {})
1.0
>>> supportScalar({'wght':.2}, {})
1.0
>>> supportScalar({'wght':.2}, {'wght':(0,2,3)})
0.1
>>> supportScalar({'wght':2.5}, {'wght':(0,2,4)})
0.75
>>> supportScalar({'wght':2.5, 'wdth':0}, {'wght':(0,2,4), 'wdth':(-1,0,+1)})
0.75
>>> supportScalar({'wght':2.5, 'wdth':.5}, {'wght':(0,2,4), 'wdth':(-1,0,+1)}, ot=False)
0.375
>>> supportScalar({'wght':2.5, 'wdth':0}, {'wght':(0,2,4), 'wdth':(-1,0,+1)})
0.75
>>> supportScalar({'wght':2.5, 'wdth':.5}, {'wght':(0,2,4), 'wdth':(-1,0,+1)})
0.75
>>> supportScalar({'wght':3}, {'wght':(0,1,2)}, extrapolate=True, axisRanges={'wght':(0, 2)})
-1.0
>>> supportScalar({'wght':-1}, {'wght':(0,1,2)}, extrapolate=True, axisRanges={'wght':(0, 2)})
-1.0
>>> supportScalar({'wght':3}, {'wght':(0,2,2)}, extrapolate=True, axisRanges={'wght':(0, 2)})
1.5
>>> supportScalar({'wght':-1}, {'wght':(0,2,2)}, extrapolate=True, axisRanges={'wght':(0, 2)})
-0.5
"""
if extrapolate and axisRanges is None:
raise TypeError("axisRanges must be passed when extrapolate is True")
scalar = 1.0
for axis, (lower, peak, upper) in support.items():
if ot:
# OpenType-specific case handling
if peak == 0.0:
continue
if lower > peak or peak > upper:
continue
if lower < 0.0 and upper > 0.0:
continue
v = location.get(axis, 0.0)
else:
assert axis in location
v = location[axis]
if v == peak:
continue
if extrapolate:
axisMin, axisMax = axisRanges[axis]
if v < axisMin and lower <= axisMin:
if peak <= axisMin and peak < upper:
scalar *= (v - upper) / (peak - upper)
continue
elif axisMin < peak:
scalar *= (v - lower) / (peak - lower)
continue
elif axisMax < v and axisMax <= upper:
if axisMax <= peak and lower < peak:
scalar *= (v - lower) / (peak - lower)
continue
elif peak < axisMax:
scalar *= (v - upper) / (peak - upper)
continue
if v <= lower or upper <= v:
scalar = 0.0
break
if v < peak:
scalar *= (v - lower) / (peak - lower)
else: # v > peak
scalar *= (v - upper) / (peak - upper)
return scalar
[docs]
class VariationModel(object):
"""Locations must have the base master at the origin (ie. 0).
If the extrapolate argument is set to True, then values are extrapolated
outside the axis range.
>>> from pprint import pprint
>>> locations = [ \
{'wght':100}, \
{'wght':-100}, \
{'wght':-180}, \
{'wdth':+.3}, \
{'wght':+120,'wdth':.3}, \
{'wght':+120,'wdth':.2}, \
{}, \
{'wght':+180,'wdth':.3}, \
{'wght':+180}, \
]
>>> model = VariationModel(locations, axisOrder=['wght'])
>>> pprint(model.locations)
[{},
{'wght': -100},
{'wght': -180},
{'wght': 100},
{'wght': 180},
{'wdth': 0.3},
{'wdth': 0.3, 'wght': 180},
{'wdth': 0.3, 'wght': 120},
{'wdth': 0.2, 'wght': 120}]
>>> pprint(model.deltaWeights)
[{},
{0: 1.0},
{0: 1.0},
{0: 1.0},
{0: 1.0},
{0: 1.0},
{0: 1.0, 4: 1.0, 5: 1.0},
{0: 1.0, 3: 0.75, 4: 0.25, 5: 1.0, 6: 0.6666666666666666},
{0: 1.0,
3: 0.75,
4: 0.25,
5: 0.6666666666666667,
6: 0.4444444444444445,
7: 0.6666666666666667}]
"""
def __init__(self, locations, axisOrder=None, extrapolate=False):
if len(set(tuple(sorted(l.items())) for l in locations)) != len(locations):
raise VariationModelError("Locations must be unique.")
self.origLocations = locations
self.axisOrder = axisOrder if axisOrder is not None else []
self.extrapolate = extrapolate
self.axisRanges = self.computeAxisRanges(locations) if extrapolate else None
locations = [{k: v for k, v in loc.items() if v != 0.0} for loc in locations]
keyFunc = self.getMasterLocationsSortKeyFunc(
locations, axisOrder=self.axisOrder
)
self.locations = sorted(locations, key=keyFunc)
# Mapping from user's master order to our master order
self.mapping = [self.locations.index(l) for l in locations]
self.reverseMapping = [locations.index(l) for l in self.locations]
self._computeMasterSupports()
self._subModels = {}
[docs]
def getSubModel(self, items):
"""Return a sub-model and the items that are not None.
The sub-model is necessary for working with the subset
of items when some are None.
The sub-model is cached."""
if None not in items:
return self, items
key = tuple(v is not None for v in items)
subModel = self._subModels.get(key)
if subModel is None:
subModel = VariationModel(subList(key, self.origLocations), self.axisOrder)
self._subModels[key] = subModel
return subModel, subList(key, items)
[docs]
@staticmethod
def computeAxisRanges(locations):
axisRanges = {}
allAxes = {axis for loc in locations for axis in loc.keys()}
for loc in locations:
for axis in allAxes:
value = loc.get(axis, 0)
axisMin, axisMax = axisRanges.get(axis, (value, value))
axisRanges[axis] = min(value, axisMin), max(value, axisMax)
return axisRanges
[docs]
@staticmethod
def getMasterLocationsSortKeyFunc(locations, axisOrder=[]):
if {} not in locations:
raise VariationModelError("Base master not found.")
axisPoints = {}
for loc in locations:
if len(loc) != 1:
continue
axis = next(iter(loc))
value = loc[axis]
if axis not in axisPoints:
axisPoints[axis] = {0.0}
assert (
value not in axisPoints[axis]
), 'Value "%s" in axisPoints["%s"] --> %s' % (value, axis, axisPoints)
axisPoints[axis].add(value)
def getKey(axisPoints, axisOrder):
def sign(v):
return -1 if v < 0 else +1 if v > 0 else 0
def key(loc):
rank = len(loc)
onPointAxes = [
axis
for axis, value in loc.items()
if axis in axisPoints and value in axisPoints[axis]
]
orderedAxes = [axis for axis in axisOrder if axis in loc]
orderedAxes.extend(
[axis for axis in sorted(loc.keys()) if axis not in axisOrder]
)
return (
rank, # First, order by increasing rank
-len(onPointAxes), # Next, by decreasing number of onPoint axes
tuple(
axisOrder.index(axis) if axis in axisOrder else 0x10000
for axis in orderedAxes
), # Next, by known axes
tuple(orderedAxes), # Next, by all axes
tuple(
sign(loc[axis]) for axis in orderedAxes
), # Next, by signs of axis values
tuple(
abs(loc[axis]) for axis in orderedAxes
), # Next, by absolute value of axis values
)
return key
ret = getKey(axisPoints, axisOrder)
return ret
[docs]
def reorderMasters(self, master_list, mapping):
# For changing the master data order without
# recomputing supports and deltaWeights.
new_list = [master_list[idx] for idx in mapping]
self.origLocations = [self.origLocations[idx] for idx in mapping]
locations = [
{k: v for k, v in loc.items() if v != 0.0} for loc in self.origLocations
]
self.mapping = [self.locations.index(l) for l in locations]
self.reverseMapping = [locations.index(l) for l in self.locations]
self._subModels = {}
return new_list
def _computeMasterSupports(self):
self.supports = []
regions = self._locationsToRegions()
for i, region in enumerate(regions):
locAxes = set(region.keys())
# Walk over previous masters now
for prev_region in regions[:i]:
# Master with extra axes do not participte
if set(prev_region.keys()) != locAxes:
continue
# If it's NOT in the current box, it does not participate
relevant = True
for axis, (lower, peak, upper) in region.items():
if not (
prev_region[axis][1] == peak
or lower < prev_region[axis][1] < upper
):
relevant = False
break
if not relevant:
continue
# Split the box for new master; split in whatever direction
# that has largest range ratio.
#
# For symmetry, we actually cut across multiple axes
# if they have the largest, equal, ratio.
# https://github.com/fonttools/fonttools/commit/7ee81c8821671157968b097f3e55309a1faa511e#commitcomment-31054804
bestAxes = {}
bestRatio = -1
for axis in prev_region.keys():
val = prev_region[axis][1]
assert axis in region
lower, locV, upper = region[axis]
newLower, newUpper = lower, upper
if val < locV:
newLower = val
ratio = (val - locV) / (lower - locV)
elif locV < val:
newUpper = val
ratio = (val - locV) / (upper - locV)
else: # val == locV
# Can't split box in this direction.
continue
if ratio > bestRatio:
bestAxes = {}
bestRatio = ratio
if ratio == bestRatio:
bestAxes[axis] = (newLower, locV, newUpper)
for axis, triple in bestAxes.items():
region[axis] = triple
self.supports.append(region)
self._computeDeltaWeights()
def _locationsToRegions(self):
locations = self.locations
# Compute min/max across each axis, use it as total range.
# TODO Take this as input from outside?
minV = {}
maxV = {}
for l in locations:
for k, v in l.items():
minV[k] = min(v, minV.get(k, v))
maxV[k] = max(v, maxV.get(k, v))
regions = []
for loc in locations:
region = {}
for axis, locV in loc.items():
if locV > 0:
region[axis] = (0, locV, maxV[axis])
else:
region[axis] = (minV[axis], locV, 0)
regions.append(region)
return regions
def _computeDeltaWeights(self):
self.deltaWeights = []
for i, loc in enumerate(self.locations):
deltaWeight = {}
# Walk over previous masters now, populate deltaWeight
for j, support in enumerate(self.supports[:i]):
scalar = supportScalar(loc, support)
if scalar:
deltaWeight[j] = scalar
self.deltaWeights.append(deltaWeight)
[docs]
def getDeltas(self, masterValues, *, round=noRound):
assert len(masterValues) == len(self.deltaWeights)
mapping = self.reverseMapping
out = []
for i, weights in enumerate(self.deltaWeights):
delta = masterValues[mapping[i]]
for j, weight in weights.items():
if weight == 1:
delta -= out[j]
else:
delta -= out[j] * weight
out.append(round(delta))
return out
[docs]
def getDeltasAndSupports(self, items, *, round=noRound):
model, items = self.getSubModel(items)
return model.getDeltas(items, round=round), model.supports
[docs]
def getScalars(self, loc):
"""Return scalars for each delta, for the given location.
If interpolating many master-values at the same location,
this function allows speed up by fetching the scalars once
and using them with interpolateFromMastersAndScalars()."""
return [
supportScalar(
loc, support, extrapolate=self.extrapolate, axisRanges=self.axisRanges
)
for support in self.supports
]
[docs]
def getMasterScalars(self, targetLocation):
"""Return multipliers for each master, for the given location.
If interpolating many master-values at the same location,
this function allows speed up by fetching the scalars once
and using them with interpolateFromValuesAndScalars().
Note that the scalars used in interpolateFromMastersAndScalars(),
are *not* the same as the ones returned here. They are the result
of getScalars()."""
out = self.getScalars(targetLocation)
for i, weights in reversed(list(enumerate(self.deltaWeights))):
for j, weight in weights.items():
out[j] -= out[i] * weight
out = [out[self.mapping[i]] for i in range(len(out))]
return out
[docs]
@staticmethod
def interpolateFromValuesAndScalars(values, scalars):
"""Interpolate from values and scalars coefficients.
If the values are master-values, then the scalars should be
fetched from getMasterScalars().
If the values are deltas, then the scalars should be fetched
from getScalars(); in which case this is the same as
interpolateFromDeltasAndScalars().
"""
v = None
assert len(values) == len(scalars)
for value, scalar in zip(values, scalars):
if not scalar:
continue
contribution = value * scalar
if v is None:
v = contribution
else:
v += contribution
return v
[docs]
@staticmethod
def interpolateFromDeltasAndScalars(deltas, scalars):
"""Interpolate from deltas and scalars fetched from getScalars()."""
return VariationModel.interpolateFromValuesAndScalars(deltas, scalars)
[docs]
def interpolateFromDeltas(self, loc, deltas):
"""Interpolate from deltas, at location loc."""
scalars = self.getScalars(loc)
return self.interpolateFromDeltasAndScalars(deltas, scalars)
[docs]
def interpolateFromMasters(self, loc, masterValues, *, round=noRound):
"""Interpolate from master-values, at location loc."""
scalars = self.getMasterScalars(loc)
return self.interpolateFromValuesAndScalars(masterValues, scalars)
[docs]
def interpolateFromMastersAndScalars(self, masterValues, scalars, *, round=noRound):
"""Interpolate from master-values, and scalars fetched from
getScalars(), which is useful when you want to interpolate
multiple master-values with the same location."""
deltas = self.getDeltas(masterValues, round=round)
return self.interpolateFromDeltasAndScalars(deltas, scalars)
[docs]
def piecewiseLinearMap(v, mapping):
keys = mapping.keys()
if not keys:
return v
if v in keys:
return mapping[v]
k = min(keys)
if v < k:
return v + mapping[k] - k
k = max(keys)
if v > k:
return v + mapping[k] - k
# Interpolate
a = max(k for k in keys if k < v)
b = min(k for k in keys if k > v)
va = mapping[a]
vb = mapping[b]
return va + (vb - va) * (v - a) / (b - a)
def main(args=None):
"""Normalize locations on a given designspace"""
from fontTools import configLogger
import argparse
parser = argparse.ArgumentParser(
"fonttools varLib.models",
description=main.__doc__,
)
parser.add_argument(
"--loglevel",
metavar="LEVEL",
default="INFO",
help="Logging level (defaults to INFO)",
)
group = parser.add_mutually_exclusive_group(required=True)
group.add_argument("-d", "--designspace", metavar="DESIGNSPACE", type=str)
group.add_argument(
"-l",
"--locations",
metavar="LOCATION",
nargs="+",
help="Master locations as comma-separate coordinates. One must be all zeros.",
)
args = parser.parse_args(args)
configLogger(level=args.loglevel)
from pprint import pprint
if args.designspace:
from fontTools.designspaceLib import DesignSpaceDocument
doc = DesignSpaceDocument()
doc.read(args.designspace)
locs = [s.location for s in doc.sources]
print("Original locations:")
pprint(locs)
doc.normalize()
print("Normalized locations:")
locs = [s.location for s in doc.sources]
pprint(locs)
else:
axes = [chr(c) for c in range(ord("A"), ord("Z") + 1)]
locs = [
dict(zip(axes, (float(v) for v in s.split(",")))) for s in args.locations
]
model = VariationModel(locs)
print("Sorted locations:")
pprint(model.locations)
print("Supports:")
pprint(model.supports)
if __name__ == "__main__":
import doctest, sys
if len(sys.argv) > 1:
sys.exit(main())
sys.exit(doctest.testmod().failed)