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[instancer.solver] Add ASCII-art

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This commit is contained in:
Behdad Esfahbod 2022-08-08 12:47:46 -06:00
parent 948788adaf
commit 6b6aba6bd4
1 changed files with 124 additions and 10 deletions
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134
Lib/fontTools/varLib/instancer/solver.py
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@ -18,14 +18,47 @@ def _solve(tent, axisLimit):
in _solve(_revnegate(tent), _revnegate(axisLimit))]
# axisDef <= peak
# case 1: the whole deltaset falls outside the new limit; we can drop it
# case 1: The whole deltaset falls outside the new limit; we can drop it
#
# peak
# 1.........................................o..........
# / \
# / \
# / \
# / \
# 0---|-----------|----------|-------- o o----1
# axisMin axisDef axisMax lower upper
#
if axisMax <= lower and axisMax < peak:
return [] # No overlap
# case 2: only the peak and outermost bound fall outside the new limit;
# case 2: Only the peak and outermost bound fall outside the new limit;
# we keep the deltaset, update peak and outermost bound and and scale deltas
# by the scalar value for the restricted axis at the new limit, and solve
# recursively.
#
# |peak
# 1...............................|.o..........
# |/ \
# / \
# /| \
# / | \
# 0---|-----------|----------- o | o----1
# axisMin axisDef lower | upper
# |
# axisMax
#
# Convert to:
#
# 1............................................
# |
# o peak
# /|
# /x|
# 0---|-----------|----------- o o upper ----1
# axisMin axisDef lower |
# |
# axisMax
if axisMax < peak:
mult = supportScalar({'tag': axisMax}, {'tag': tent})
tent = (lower, axisMax, axisMax)
@ -41,8 +74,22 @@ def _solve(tent, axisLimit):
# outGain is the scalar of axisMax at the tent.
outGain = supportScalar({'tag': axisMax}, {'tag': tent})
# case 3a: gain is more than outGain. The tent down-slope crosses
# Case 3a: Gain is more than outGain. The tent down-slope crosses
# the axis into negative. We have to split it into multiples.
#
# | peak |
# 1...................|.o.....|..............
# |/x\_ |
# gain................+....+_.|..............
# /| |y\|
# ................../.|....|..+_......outGain
# / | | | \
# 0---|-----------o | | | o----------1
# axisMin lower | | | upper
# | | |
# axisDef | axisMax
# |
# crossing
if gain > outGain:
# Crossing point on the axis.
@ -58,15 +105,30 @@ def _solve(tent, axisLimit):
# depending on whether upper is before axisMax or not, in one
# case we need to keep it down to eternity.
# case 3a1, similar to case 1neg; just one tent needed.
# Case 3a1, similar to case 1neg; just one tent needed, as in
# the drawing above.
if upper >= axisMax:
loc = (crossing, axisMax, axisMax)
scalar = supportScalar({'tag': axisMax}, {'tag': tent})
out.append((scalar - gain, loc))
# case 3a2, similar to case 2neg; two tents needed, to keep
# Case 3a2: Similar to case 2neg; two tents needed, to keep
# down to eternity.
#
# | peak |
# 1...................|.o................|...
# |/ \_ |
# gain................+....+_............|...
# /| | \xxxxxxxxxxy|
# / | | \_xxxxxyyyy|
# / | | \xxyyyyyy|
# 0---|-----------o | | o-------|--1
# axisMin lower | | upper |
# | | |
# axisDef | axisMax
# |
# crossing
else:
# Downslope.
loc1 = (crossing, upper, axisMax)
@ -79,9 +141,22 @@ def _solve(tent, axisLimit):
out.append((scalar1 - gain, loc1))
out.append((scalar2 - gain, loc2))
# case 3: outermost limit still fits within F2Dot14 bounds;
# Case 3: Outermost limit still fits within F2Dot14 bounds;
# we keep deltas as is and only scale the axes bounds. Deltas beyond -1.0
# or +1.0 will never be applied as implementations must clamp to that range.
#
# | peak |
# 1.........|............o...|..................
# | /x\ |
# | /xxx\ |
# | /xxxxx\|
# | /xxxxxxx+
# | /xxxxxxxx|\
# 0---|-----|------oxxxxxxxxx|xo---------------1
# axisMin | lower | upper
# | |
# axisDef axisMax
#
elif axisDef + (axisMax - axisDef) * 2 >= upper:
if axisDef + (axisMax - axisDef) * MAX_F2DOT14 < upper:
@ -98,9 +173,22 @@ def _solve(tent, axisLimit):
if upper > axisDef:
out.append((1 - gain, loc))
# case 4: new limit doesn't fit; we need to chop into two tents,
# Case 4: New limit doesn't fit; we need to chop into two tents,
# because the shape of a triangle with part of one side cut off
# cannot be represented as a triangle itself.
#
# | peak |
# 1.........|......o.|...................
# | /x\|
# | |xxy|\_
# | /xxxy| \_
# | |xxxxy| \_
# | /xxxxy| \_
# 0---|-----|-oxxxxxx| o----------1
# axisMin | lower | upper
# | |
# axisDef axisMax
#
else:
loc1 = (max(axisDef, lower), peak, axisMax)
@ -117,15 +205,41 @@ def _solve(tent, axisLimit):
# Now, the negative side
# case 1neg: lower extends beyond axisMin: we chop. Simple.
# Case 1neg: Lower extends beyond axisMin: we chop. Simple.
#
# | |peak
# 1..................|...|.o.................
# | |/ \
# gain...............|...+...\...............
# |x_/| \
# |/ | \
# _/| | \
# 0---------------o | | o----------1
# lower | | upper
# | |
# axisMin axisDef
#
if lower <= axisMin:
loc = (axisMin, axisMin, axisDef)
scalar = supportScalar({'tag': axisMin}, {'tag': tent})
out.append((scalar - gain, loc))
# case 2neg: lower is betwen axisMin and axisDef: we add two
# deltasets to # keep it down all the way to eternity.
# Case 2neg: Lower is betwen axisMin and axisDef: we add two
# tents to keep it down all the way to eternity.
#
# | |peak
# 1...|...............|.o.................
# | |/ \
# gain|...............+...\...............
# |yxxxxxxxxxxxxx/| \
# |yyyyyyxxxxxxx/ | \
# |yyyyyyyyyyyx/ | \
# 0---|-----------o | o----------1
# axisMin lower | upper
# |
# axisDef
#
else:
# Downslope.
loc1 = (axisMin, lower, axisDef)