310 lines
11 KiB
Python
310 lines
11 KiB
Python
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from fontTools.varLib.models import supportScalar
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from fontTools.misc.fixedTools import MAX_F2DOT14
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from functools import lru_cache
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__all__ = ["rebaseTent"]
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EPSILON = 1 / (1 << 14)
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def _reverse_negate(v):
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return (-v[2], -v[1], -v[0])
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def _solve(tent, axisLimit, negative=False):
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axisMin, axisDef, axisMax, _distanceNegative, _distancePositive = axisLimit
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lower, peak, upper = tent
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# Mirror the problem such that axisDef <= peak
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if axisDef > peak:
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return [
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(scalar, _reverse_negate(t) if t is not None else None)
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for scalar, t in _solve(
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_reverse_negate(tent),
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axisLimit.reverse_negate(),
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not negative,
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)
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]
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# axisDef <= peak
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# case 1: The whole deltaset falls outside the new limit; we can drop it
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#
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# peak
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# 1.........................................o..........
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# / \
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# / \
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# / \
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# / \
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# 0---|-----------|----------|-------- o o----1
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# axisMin axisDef axisMax lower upper
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#
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if axisMax <= lower and axisMax < peak:
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return [] # No overlap
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# case 2: Only the peak and outermost bound fall outside the new limit;
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# we keep the deltaset, update peak and outermost bound and and scale deltas
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# by the scalar value for the restricted axis at the new limit, and solve
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# recursively.
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#
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# |peak
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# 1...............................|.o..........
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# |/ \
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# / \
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# /| \
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# / | \
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# 0--------------------------- o | o----1
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# lower | upper
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# |
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# axisMax
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#
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# Convert to:
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#
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# 1............................................
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# |
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# o peak
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# /|
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# /x|
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# 0--------------------------- o o upper ----1
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# lower |
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# |
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# axisMax
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if axisMax < peak:
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mult = supportScalar({"tag": axisMax}, {"tag": tent})
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tent = (lower, axisMax, axisMax)
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return [(scalar * mult, t) for scalar, t in _solve(tent, axisLimit)]
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# lower <= axisDef <= peak <= axisMax
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gain = supportScalar({"tag": axisDef}, {"tag": tent})
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out = [(gain, None)]
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# First, the positive side
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# outGain is the scalar of axisMax at the tent.
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outGain = supportScalar({"tag": axisMax}, {"tag": tent})
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# Case 3a: Gain is more than outGain. The tent down-slope crosses
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# the axis into negative. We have to split it into multiples.
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#
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# | peak |
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# 1...................|.o.....|..............
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# |/x\_ |
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# gain................+....+_.|..............
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# /| |y\|
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# ................../.|....|..+_......outGain
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# / | | | \
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# 0---|-----------o | | | o----------1
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# axisMin lower | | | upper
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# | | |
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# axisDef | axisMax
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# |
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# crossing
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if gain >= outGain:
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# Note that this is the branch taken if both gain and outGain are 0.
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# Crossing point on the axis.
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crossing = peak + (1 - gain) * (upper - peak)
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loc = (max(lower, axisDef), peak, crossing)
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scalar = 1
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# The part before the crossing point.
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out.append((scalar - gain, loc))
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# The part after the crossing point may use one or two tents,
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# depending on whether upper is before axisMax or not, in one
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# case we need to keep it down to eternity.
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# Case 3a1, similar to case 1neg; just one tent needed, as in
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# the drawing above.
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if upper >= axisMax:
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loc = (crossing, axisMax, axisMax)
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scalar = outGain
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out.append((scalar - gain, loc))
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# Case 3a2: Similar to case 2neg; two tents needed, to keep
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# down to eternity.
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#
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# | peak |
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# 1...................|.o................|...
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# |/ \_ |
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# gain................+....+_............|...
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# /| | \xxxxxxxxxxy|
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# / | | \_xxxxxyyyy|
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# / | | \xxyyyyyy|
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# 0---|-----------o | | o-------|--1
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# axisMin lower | | upper |
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# | | |
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# axisDef | axisMax
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# |
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# crossing
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else:
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# A tent's peak cannot fall on axis default. Nudge it.
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if upper == axisDef:
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upper += EPSILON
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# Downslope.
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loc1 = (crossing, upper, axisMax)
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scalar1 = 0
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# Eternity justify.
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loc2 = (upper, axisMax, axisMax)
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scalar2 = 0
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out.append((scalar1 - gain, loc1))
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out.append((scalar2 - gain, loc2))
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else:
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# Special-case if peak is at axisMax.
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if axisMax == peak:
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upper = peak
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# Case 3:
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# We keep delta as is and only scale the axis upper to achieve
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# the desired new tent if feasible.
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#
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# peak
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# 1.....................o....................
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# / \_|
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# ..................../....+_.........outGain
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# / | \
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# gain..............+......|..+_.............
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# /| | | \
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# 0---|-----------o | | | o----------1
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# axisMin lower| | | upper
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# | | newUpper
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# axisDef axisMax
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#
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newUpper = peak + (1 - gain) * (upper - peak)
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assert axisMax <= newUpper # Because outGain > gain
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# Disabled because ots doesn't like us:
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# https://github.com/fonttools/fonttools/issues/3350
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if False and newUpper <= axisDef + (axisMax - axisDef) * 2:
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upper = newUpper
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if not negative and axisDef + (axisMax - axisDef) * MAX_F2DOT14 < upper:
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# we clamp +2.0 to the max F2Dot14 (~1.99994) for convenience
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upper = axisDef + (axisMax - axisDef) * MAX_F2DOT14
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assert peak < upper
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loc = (max(axisDef, lower), peak, upper)
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scalar = 1
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out.append((scalar - gain, loc))
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# Case 4: New limit doesn't fit; we need to chop into two tents,
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# because the shape of a triangle with part of one side cut off
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# cannot be represented as a triangle itself.
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#
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# | peak |
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# 1.........|......o.|....................
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# ..........|...../x\|.............outGain
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# | |xxy|\_
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# | /xxxy| \_
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# | |xxxxy| \_
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# | /xxxxy| \_
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# 0---|-----|-oxxxxxx| o----------1
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# axisMin | lower | upper
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# | |
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# axisDef axisMax
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#
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else:
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loc1 = (max(axisDef, lower), peak, axisMax)
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scalar1 = 1
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loc2 = (peak, axisMax, axisMax)
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scalar2 = outGain
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out.append((scalar1 - gain, loc1))
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# Don't add a dirac delta!
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if peak < axisMax:
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out.append((scalar2 - gain, loc2))
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# Now, the negative side
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# Case 1neg: Lower extends beyond axisMin: we chop. Simple.
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#
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# | |peak
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# 1..................|...|.o.................
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# | |/ \
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# gain...............|...+...\...............
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# |x_/| \
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# |/ | \
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# _/| | \
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# 0---------------o | | o----------1
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# lower | | upper
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# | |
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# axisMin axisDef
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#
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if lower <= axisMin:
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loc = (axisMin, axisMin, axisDef)
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scalar = supportScalar({"tag": axisMin}, {"tag": tent})
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out.append((scalar - gain, loc))
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# Case 2neg: Lower is betwen axisMin and axisDef: we add two
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# tents to keep it down all the way to eternity.
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#
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# | |peak
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# 1...|...............|.o.................
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# | |/ \
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# gain|...............+...\...............
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# |yxxxxxxxxxxxxx/| \
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# |yyyyyyxxxxxxx/ | \
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# |yyyyyyyyyyyx/ | \
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# 0---|-----------o | o----------1
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# axisMin lower | upper
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# |
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# axisDef
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#
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else:
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# A tent's peak cannot fall on axis default. Nudge it.
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if lower == axisDef:
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lower -= EPSILON
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# Downslope.
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loc1 = (axisMin, lower, axisDef)
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scalar1 = 0
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# Eternity justify.
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loc2 = (axisMin, axisMin, lower)
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scalar2 = 0
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out.append((scalar1 - gain, loc1))
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out.append((scalar2 - gain, loc2))
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return out
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@lru_cache(128)
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def rebaseTent(tent, axisLimit):
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"""Given a tuple (lower,peak,upper) "tent" and new axis limits
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(axisMin,axisDefault,axisMax), solves how to represent the tent
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under the new axis configuration. All values are in normalized
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-1,0,+1 coordinate system. Tent values can be outside this range.
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Return value is a list of tuples. Each tuple is of the form
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(scalar,tent), where scalar is a multipler to multiply any
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delta-sets by, and tent is a new tent for that output delta-set.
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If tent value is None, that is a special deltaset that should
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be always-enabled (called "gain")."""
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axisMin, axisDef, axisMax, _distanceNegative, _distancePositive = axisLimit
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assert -1 <= axisMin <= axisDef <= axisMax <= +1
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lower, peak, upper = tent
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assert -2 <= lower <= peak <= upper <= +2
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assert peak != 0
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sols = _solve(tent, axisLimit)
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n = lambda v: axisLimit.renormalizeValue(v)
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sols = [
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(scalar, (n(v[0]), n(v[1]), n(v[2])) if v is not None else None)
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for scalar, v in sols
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if scalar
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]
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return sols
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