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"""Variation fonts interpolation models."""
from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *
__all__ = ['normalizeValue', 'normalizeLocation', 'supportScalar', 'VariationModel']
def normalizeValue(v, triple):
"""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
assert lower <= default <= upper, "invalid axis values: %3.3f, %3.3f %3.3f"%(lower, default, upper)
v = max(min(v, upper), lower)
if v == default:
v = 0.
elif v < default:
v = (v - default) / (default - lower)
else:
v = (v - default) / (upper - default)
return v
def normalizeLocation(location, axes):
"""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)
return out
def supportScalar(location, support, ot=True):
"""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.
>>> 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
"""
scalar = 1.
for axis,(lower,peak,upper) in support.items():
if ot:
# OpenType-specific case handling
if peak == 0.:
continue
if lower > peak or peak > upper:
continue
if lower < 0. and upper > 0.:
continue
v = location.get(axis, 0.)
else:
assert axis in location
v = location[axis]
if v == peak:
continue
if v <= lower or upper <= v:
scalar = 0.
break;
if v < peak:
scalar *= (v - lower) / (peak - lower)
else: # v > peak
scalar *= (v - upper) / (peak - upper)
return scalar
class VariationModel(object):
"""
Locations must be in normalized space. Ie. base master
is at origin (0).
>>> 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=[]):
locations = [{k:v for k,v in loc.items() if v != 0.} for loc in locations]
keyFunc = self.getMasterLocationsSortKeyFunc(locations, axisOrder=axisOrder)
axisPoints = keyFunc.axisPoints
self.locations = sorted(locations, key=keyFunc)
# TODO Assert that locations are unique.
self.mapping = [self.locations.index(l) for l in locations] # Mapping from user's master order to our master order
self.reverseMapping = [locations.index(l) for l in self.locations] # Reverse of above
self._computeMasterSupports(axisPoints, axisOrder)
@staticmethod
def getMasterLocationsSortKeyFunc(locations, axisOrder=[]):
assert {} in locations, "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.}
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 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)
ret.axisPoints = axisPoints
return ret
@staticmethod
def lowerBound(value, lst):
if any(v < value for v in lst):
return max(v for v in lst if v < value)
else:
return value
@staticmethod
def upperBound(value, lst):
if any(v > value for v in lst):
return min(v for v in lst if v > value)
else:
return value
def _computeMasterSupports(self, axisPoints, axisOrder):
supports = []
deltaWeights = []
locations = self.locations
for i,loc in enumerate(locations):
box = {}
# Account for axisPoints first
# TODO Use axis min/max instead? Isn't that always -1/+1?
for axis,values in axisPoints.items():
if not axis in loc:
continue
locV = loc[axis]
if locV > 0:
box[axis] = (0, locV, max({locV}|values))
else:
box[axis] = (min({locV}|values), locV, 0)
locAxes = set(loc.keys())
# Walk over previous masters now
for j,m in enumerate(locations[:i]):
# Master with extra axes do not participte
if not set(m.keys()).issubset(locAxes):
continue
# If it's NOT in the current box, it does not participate
relevant = True
for axis, (lower,peak,upper) in box.items():
if axis not in m or not (m[axis] == peak or lower < m[axis] < upper):
relevant = False
break
if not relevant:
continue
# Split the box for new master; split in whatever direction
# that has largest range ratio. See commit for details.
orderedAxes = [axis for axis in axisOrder if axis in m.keys()]
orderedAxes.extend([axis for axis in sorted(m.keys()) if axis not in axisOrder])
bestAxis = None
bestRatio = -1
for axis in orderedAxes:
val = m[axis]
assert axis in box
lower,locV,upper = box[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:
bestRatio = ratio
bestAxis = axis
bestLower = newLower
bestUpper = newUpper
bestLocV = locV
if bestAxis:
box[bestAxis] = (bestLower,bestLocV,bestUpper)
supports.append(box)
deltaWeight = {}
# Walk over previous masters now, populate deltaWeight
for j,m in enumerate(locations[:i]):
scalar = supportScalar(loc, supports[j])
if scalar:
deltaWeight[j] = scalar
deltaWeights.append(deltaWeight)
self.supports = supports
self.deltaWeights = deltaWeights
def getDeltas(self, masterValues):
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():
delta -= out[j] * weight
out.append(delta)
return out
def getScalars(self, loc):
return [supportScalar(loc, support) for support in self.supports]
@staticmethod
def interpolateFromDeltasAndScalars(deltas, scalars):
v = None
assert len(deltas) == len(scalars)
for i,(delta,scalar) in enumerate(zip(deltas, scalars)):
if not scalar: continue
contribution = delta * scalar
if v is None:
v = contribution
else:
v += contribution
return v
def interpolateFromDeltas(self, loc, deltas):
scalars = self.getScalars(loc)
return self.interpolateFromDeltasAndScalars(deltas, scalars)
def interpolateFromMasters(self, loc, masterValues):
deltas = self.getDeltas(masterValues)
return self.interpolateFromDeltas(loc, deltas)
def interpolateFromMastersAndScalars(self, masterValues, scalars):
deltas = self.getDeltas(masterValues)
return self.interpolateFromDeltasAndScalars(deltas, scalars)
def main(args):
from fontTools import configLogger
args = args[1:]
# TODO: allow user to configure logging via command-line options
configLogger(level="INFO")
if len(args) < 1:
print("usage: fonttools varLib.models source.designspace", file=sys.stderr)
print(" or")
print("usage: fonttools varLib.models location1 location2 ...", file=sys.stderr)
sys.exit(1)
from pprint import pprint
if len(args) == 1 and args[0].endswith('.designspace'):
from fontTools.designspaceLib import DesignSpaceDocument
doc = DesignSpaceDocument()
doc.read(args[0])
locs = [s.location for s in doc.sources]
print("Original locations:")
pprint(locs)
doc.normalize()
print("Normalized locations:")
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]
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.argv))
sys.exit(doctest.testmod().failed)
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