harfbuzz/src/hb-subset-instancer-solver.cc

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/*
* Copyright © 2023 Behdad Esfahbod
*
* This is part of HarfBuzz, a text shaping library.
*
* Permission is hereby granted, without written agreement and without
* license or royalty fees, to use, copy, modify, and distribute this
* software and its documentation for any purpose, provided that the
* above copyright notice and the following two paragraphs appear in
* all copies of this software.
*
* IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
* DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
* ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
* IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
* DAMAGE.
*
* THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
* BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
* ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
* PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
*/
#include "hb.hh"
/* This file is a straight port of the following:
*
* https://github.com/fonttools/fonttools/blob/f73220816264fc383b8a75f2146e8d69e455d398/Lib/fontTools/varLib/instancer/solver.py
*
* Where that file returns None for a triple, we return Triple{}.
* This should be safe.
*/
constexpr static float EPSILON = 1.f / (1 << 14);
constexpr static float MAX_F2DOT14 = float (0x7FFF) / (1 << 14);
struct Triple {
Triple () :
minimum (0.f), middle (0.f), maximum (0.f) {}
Triple (float minimum_, float middle_, float maximum_) :
minimum (minimum_), middle (middle_), maximum (maximum_) {}
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bool operator == (const Triple &o) const
{
return minimum == o.minimum &&
middle == o.middle &&
maximum == o.maximum;
}
float minimum;
float middle;
float maximum;
};
static inline Triple _reverse_negate(const Triple &v)
{ return {-v.maximum, -v.middle, -v.minimum}; }
static inline float supportScalar (float coord, const Triple &tent)
{
/* Copied from VarRegionAxis::evaluate() */
float start = tent.minimum, peak = tent.middle, end = tent.maximum;
if (unlikely (start > peak || peak > end))
return 1.;
if (unlikely (start < 0 && end > 0 && peak != 0))
return 1.;
if (peak == 0 || coord == peak)
return 1.;
if (coord <= start || end <= coord)
return 0.;
/* Interpolate */
if (coord < peak)
return (coord - start) / (peak - start);
else
return (end - coord) / (end - peak);
}
using result_item_t = hb_pair_t<float, Triple>;
using result_t = hb_vector_t<result_item_t>;
static inline result_t
_solve (Triple tent, Triple axisLimit, bool negative = false)
{
float axisMin = axisLimit.minimum;
float axisDef = axisLimit.middle;
float axisMax = axisLimit.maximum;
float lower = tent.minimum;
float peak = tent.middle;
float upper = tent.maximum;
// Mirror the problem such that axisDef <= peak
if (axisDef > peak)
{
result_t vec = _solve (_reverse_negate (tent),
_reverse_negate (axisLimit),
!negative);
for (auto &p : vec)
p = hb_pair (p.first, _reverse_negate (p.second));
return vec;
}
// axisDef <= peak
/* 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 && axisMax < peak)
return result_t{}; // No overlap
/* 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 scale deltas
* by the scalar value for the restricted axis at the new limit, and solve
* recursively.
*
* |peak
* 1...............................|.o..........
* |/ \
* / \
* /| \
* / | \
* 0--------------------------- o | o----1
* lower | upper
* |
* axisMax
*
* Convert to:
*
* 1............................................
* |
* o peak
* /|
* /x|
* 0--------------------------- o o upper ----1
* lower |
* |
* axisMax
*/
if (axisMax < peak)
{
float mult = supportScalar (axisMax, tent);
tent = Triple{lower, axisMax, axisMax};
result_t vec = _solve (tent, axisLimit);
for (auto &p : vec)
p = hb_pair (p.first * mult, p.second);
return vec;
}
// lower <= axisDef <= peak <= axisMax
float gain = supportScalar (axisDef, tent);
result_t out {hb_pair (gain, Triple{})};
// First, the positive side
// outGain is the scalar of axisMax at the tent.
float outGain = supportScalar (axisMax, tent);
/* 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.
float crossing = peak + ((1 - gain) * (upper - peak) / (1 - outGain));
Triple loc{peak, peak, crossing};
float scalar = 1.f;
// The part before the crossing point.
out.push (hb_pair (scalar - gain, loc));
/* The part after the crossing point may use one or two tents,
* 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, as in
* the drawing above.
*/
if (upper >= axisMax)
{
Triple loc {crossing, axisMax, axisMax};
float scalar = supportScalar (axisMax, tent);
out.push (hb_pair (scalar - gain, loc));
}
/* 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
{
// A tent's peak cannot fall on axis default. Nudge it.
if (upper == axisDef)
upper += EPSILON;
// Downslope.
Triple loc1 {crossing, upper, axisMax};
float scalar1 = 0.f;
// Eternity justify.
Triple loc2 {upper, axisMax, axisMax};
float scalar2 = 1.f; // supportScalar({"tag": axisMax}, {"tag": tent})
out.push (hb_pair (scalar1 - gain, loc1));
out.push (hb_pair (scalar2 - gain, loc2));
}
}
/* 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.
*
* A second tent is needed for cases when gain is positive, though we add it
* unconditionally and it will be dropped because scalar ends up 0.
*
* TODO: See if we can just move upper closer to adjust the slope, instead of
* second tent.
*
* | peak |
* 1.........|............o...|..................
* | /x\ |
* | /xxx\ |
* | /xxxxx\|
* | /xxxxxxx+
* | /xxxxxxxx|\
* 0---|-----|------oxxxxxxxxx|xo---------------1
* axisMin | lower | upper
* | |
* axisDef axisMax
*/
else if (axisDef + (axisMax - axisDef) * 2 >= upper)
{
if (!negative && axisDef + (axisMax - axisDef) * MAX_F2DOT14 < upper)
{
// we clamp +2.0 to the max F2Dot14 (~1.99994) for convenience
upper = axisDef + (axisMax - axisDef) * MAX_F2DOT14;
assert (peak < upper);
}
// Special-case if peak is at axisMax.
if (axisMax == peak)
upper = peak;
Triple loc1 {hb_max (axisDef, lower), peak, upper};
float scalar1 = 1.f;
Triple loc2 {peak, upper, upper};
float scalar2 = 0.f;
// Don't add a dirac delta!
if (axisDef < upper)
out.push (hb_pair (scalar1 - gain, loc1));
if (peak < upper)
out.push (hb_pair (scalar2 - gain, loc2));
}
/* 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
{
Triple loc1 {hb_max (axisDef, lower), peak, axisMax};
float scalar1 = 1.f;
Triple loc2 {peak, axisMax, axisMax};
float scalar2 = supportScalar (axisMax, tent);
out.push (hb_pair (scalar1 - gain, loc1));
// Don't add a dirac delta!
if (peak < axisMax)
out.push (hb_pair (scalar2 - gain, loc2));
}
/* Now, the negative side
*
* 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)
{
Triple loc {axisMin, axisMin, axisDef};
float scalar = supportScalar (axisMin, tent);
out.push (hb_pair (scalar - gain, loc));
}
/* 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
{
// A tent's peak cannot fall on axis default. Nudge it.
if (lower == axisDef)
lower -= EPSILON;
// Downslope.
Triple loc1 {axisMin, lower, axisDef};
float scalar1 = 0.f;
// Eternity justify.
Triple loc2 {axisMin, axisMin, lower};
float scalar2 = 0.f;
out.push (hb_pair (scalar1 - gain, loc1));
out.push (hb_pair (scalar2 - gain, loc2));
}
return out;
}
/* Normalizes value based on a min/default/max triple. */
static inline float normalizeValue (float v, const Triple &triple, bool extrapolate = false)
{
/*
>>> normalizeValue(400, (100, 400, 900))
0.0
>>> normalizeValue(100, (100, 400, 900))
-1.0
>>> normalizeValue(650, (100, 400, 900))
0.5
*/
float lower = triple.minimum, def = triple.middle, upper = triple.maximum;
assert (lower <= def && def <= upper);
if (!extrapolate)
v = hb_max (hb_min (v, upper), lower);
if ((v == def) || (lower == upper))
return 0.f;
if ((v < def && lower != def) || (v > def && upper == def))
return (v - def) / (def - lower);
else
{
assert ((v > def && upper != def) ||
(v < def && lower == def));
return (v - def) / (upper - def);
}
}
/* Given a tuple (lower,peak,upper) "tent" and new axis limits
* (axisMin,axisDefault,axisMax), solves how to represent the tent
* under the new axis configuration. All values are in normalized
* -1,0,+1 coordinate system. Tent values can be outside this range.
*
* Return value: a list of tuples. Each tuple is of the form
* (scalar,tent), where scalar is a multipler to multiply any
* delta-sets by, and tent is a new tent for that output delta-set.
* If tent value is Triple{}, that is a special deltaset that should
* be always-enabled (called "gain").
*/
HB_INTERNAL result_t rebase_tent (Triple tent, Triple axisLimit);
result_t
rebase_tent (Triple tent, Triple axisLimit)
{
assert (-1.f <= axisLimit.minimum && axisLimit.minimum <= axisLimit.middle && axisLimit.middle <= axisLimit.maximum && axisLimit.maximum <= +1.f);
assert (-2.f <= tent.minimum && tent.minimum <= tent.middle && tent.middle <= tent.maximum && tent.maximum <= +2.f);
assert (tent.middle != 0.f);
result_t sols = _solve (tent, axisLimit);
auto n = [&axisLimit] (float v) { return normalizeValue (v, axisLimit, true); };
result_t out;
for (auto &p : sols)
{
if (!p.first) continue;
if (p.second == Triple{})
{
out.push (p);
continue;
}
Triple t = p.second;
out.push (hb_pair (p.first,
Triple{n (t.minimum), n (t.middle), n (t.maximum)}));
}
return sols;
}