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