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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-subset-instancer-solver.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);
+
+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);
+}
+
+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;
+ * 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)
+ {
+ // Note that this is the branch taken if both gain and outGain are 0.
+
+ // Crossing point on the axis.
+ float crossing = peak + (1 - gain) * (upper - peak);
+
+ Triple loc{hb_max (lower, axisDef), 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 = outGain;
+
+ 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 = 0.f;
+
+ out.push (hb_pair (scalar1 - gain, loc1));
+ out.push (hb_pair (scalar2 - gain, loc2));
+ }
+ }
+
+ else
+ {
+ // Special-case if peak is at axisMax.
+ if (axisMax == peak)
+ upper = peak;
+
+ /* Case 3:
+ * we keep deltas as is and only scale the axis upper to achieve
+ * the desired new tent if feasible.
+ *
+ * peak
+ * 1.....................o....................
+ * / \_|
+ * ..................../....+_.........outGain
+ * / | \
+ * gain..............+......|..+_.............
+ * /| | | \
+ * 0---|-----------o | | | o----------1
+ * axisMin lower| | | upper
+ * | | newUpper
+ * axisDef axisMax
+ */
+ float newUpper = peak + (1 - gain) * (upper - peak);
+ assert (axisMax <= newUpper); // Because outGain > gain
+ if (newUpper <= axisDef + (axisMax - axisDef) * 2)
+ {
+ upper = newUpper;
+ 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);
+ }
+
+ Triple loc {hb_max (axisDef, lower), peak, upper};
+ float scalar = 1.f;
+
+ out.push (hb_pair (scalar - gain, loc));
+ }
+
+ /* 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\|.............outGain
+ * | |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 = outGain;
+
+ 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;
+}
+
+static inline TripleDistances _reverse_triple_distances (const TripleDistances &v)
+{ return TripleDistances (v.positive, v.negative); }
+
+float renormalizeValue (float v, const Triple &triple,
+ const TripleDistances &triple_distances, bool extrapolate)
+{
+ 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)
+ return 0.f;
+
+ if (def < 0.f)
+ return -renormalizeValue (-v, _reverse_negate (triple),
+ _reverse_triple_distances (triple_distances), extrapolate);
+
+ /* default >= 0 and v != default */
+ if (v > def)
+ return (v - def) / (upper - def);
+
+ /* v < def */
+ if (lower >= 0.f)
+ return (v - def) / (def - lower);
+
+ /* lower < 0 and v < default */
+ float total_distance = triple_distances.negative * (-lower) + triple_distances.positive * def;
+
+ float v_distance;
+ if (v >= 0.f)
+ v_distance = (def - v) * triple_distances.positive;
+ else
+ v_distance = (-v) * triple_distances.negative + triple_distances.positive * def;
+
+ return (-v_distance) /total_distance;
+}
+
+result_t
+rebase_tent (Triple tent, Triple axisLimit, TripleDistances axis_triple_distances)
+{
+ 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, &axis_triple_distances] (float v) { return renormalizeValue (v, axisLimit, axis_triple_distances); };
+
+ 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 out;
+}
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