Collider.cpp

// SPDX-License-Identifier: MIT OR MPL-2.0 OR LGPL-2.1-or-later OR GPL-2.0-or-later
// Copyright 2010, SIL International, All rights reserved.

#include <algorithm>
#include <limits>
#include <cmath>
#include <string>
#include <functional>
#include "inc/Collider.h"
#include "inc/Segment.h"
#include "inc/Slot.h"
#include "inc/GlyphCache.h"
#include "inc/Sparse.h"

#define ISQRT2 0.707106781f

// Possible rounding error for subbox boundaries: 0.016 = 1/64 = 1/256 * 4
// (values in font range from 0..256)
// #define SUBBOX_RND_ERR 0.016

using namespace graphite2;

////    SHIFT-COLLIDER    ////

// Initialize the Collider to hold the basic movement limits for the
// target slot, the one we are focusing on fixing.
bool ShiftCollider::initSlot(Segment *seg, Slot *aSlot, const Rect &limit, float margin, float marginWeight,
    const Position &currShift, const Position &currOffset, int dir, GR_MAYBE_UNUSED json * const dbgout)
{
    int i;
    float mx, mn;
    float a, shift;
    const GlyphCache &gc = seg->getFace()->glyphs();
    unsigned short gid = aSlot->gid();
    if (!gc.check(gid))
        return false;
    const BBox &bb = gc.getBoundingBBox(gid);
    const SlantBox &sb = gc.getBoundingSlantBox(gid);
    //float sx = aSlot->origin().x + currShift.x;
    //float sy = aSlot->origin().y + currShift.y;
    if (currOffset.x != 0.f || currOffset.y != 0.f)
        _limit = Rect(limit.bl - currOffset, limit.tr - currOffset);
    else
        _limit = limit;
    // For a ShiftCollider, these indices indicate which vector we are moving by:
    // each _ranges represents absolute space with respect to the origin of the slot. Thus take into account true origins but subtract the vmin for the slot
    for (i = 0; i < 4; ++i)
    {
        switch (i) {
            case 0 :	// x direction
                mn = _limit.bl.x + currOffset.x;
                mx = _limit.tr.x + currOffset.x;
                _len[i] = bb.xa - bb.xi;
                a = currOffset.y + currShift.y;
                _ranges[i].initialise<XY>(mn, mx, margin, marginWeight, a);
                break;
            case 1 :	// y direction
                mn = _limit.bl.y + currOffset.y;
                mx = _limit.tr.y + currOffset.y;
                _len[i] = bb.ya - bb.yi;
                a = currOffset.x + currShift.x;
                _ranges[i].initialise<XY>(mn, mx, margin, marginWeight, a);
                break;
            case 2 :	// sum (negatively sloped diagonal boundaries)
                // pick closest x,y limit boundaries in s direction
                shift = currOffset.x + currOffset.y + currShift.x + currShift.y;
                mn = -2 * min(currShift.x - _limit.bl.x, currShift.y - _limit.bl.y) + shift;
                mx = 2 * min(_limit.tr.x - currShift.x, _limit.tr.y - currShift.y) + shift;
                _len[i] = sb.sa - sb.si;
                a = currOffset.x - currOffset.y + currShift.x - currShift.y;
                _ranges[i].initialise<SD>(mn, mx, margin / ISQRT2, marginWeight, a);
                break;
            case 3 :	// diff (positively sloped diagonal boundaries)
                // pick closest x,y limit boundaries in d direction
                shift = currOffset.x - currOffset.y + currShift.x - currShift.y;
                mn = -2 * min(currShift.x - _limit.bl.x, _limit.tr.y - currShift.y) + shift;
                mx = 2 * min(_limit.tr.x - currShift.x, currShift.y - _limit.bl.y) + shift;
                _len[i] = sb.da - sb.di;
                a = currOffset.x + currOffset.y + currShift.x + currShift.y;
                _ranges[i].initialise<SD>(mn, mx, margin / ISQRT2, marginWeight, a);
                break;
        }
    }

	_target = aSlot;
    if ((dir & 1) == 0)
    {
        // For LTR, switch and negate x limits.
        _limit.bl.x = -1 * limit.tr.x;
        //_limit.tr.x = -1 * limit.bl.x;
    }
    _currOffset = currOffset;
    _currShift = currShift;
    _origin = aSlot->origin() - currOffset;     // the original anchor position of the glyph

	_margin = margin;
	_marginWt = marginWeight;

    SlotCollision *c = seg->collisionInfo(aSlot);
    _seqClass = c->seqClass();
	_seqProxClass = c->seqProxClass();
    _seqOrder = c->seqOrder();
    return true;
}

template <class O>
float sdm(float vi, float va, float mx, float my, O op)
{
    float res = 2 * mx - vi;
    if (op(res, vi + 2 * my))
    {
        res = va + 2 * my;
        if (op(res, 2 * mx - va))
            res = mx + my;
    }
    return res;
}

// Mark an area with a cost that can vary along the x or y axis. The region is expressed in terms of the centre of the target glyph in each axis
void ShiftCollider::addBox_slope(bool isx, const Rect &box, const BBox &bb, const SlantBox &sb, const Position &org, float weight, float m, bool minright, int axis)
{
    float a, c;
    switch (axis) {
        case 0 :
             if (box.bl.y < org.y + bb.ya && box.tr.y > org.y + bb.yi && box.width() > 0)
            {
                a = org.y + 0.5f * (bb.yi + bb.ya);
                c = 0.5f * (bb.xi + bb.xa);
                if (isx)
                    _ranges[axis].weighted<XY>(box.bl.x - c, box.tr.x - c, weight, a, m,
                                                (minright ? box.tr.x : box.bl.x) - c, a, 0, false);
                else
                    _ranges[axis].weighted<XY>(box.bl.x - c, box.tr.x - c, weight, a, 0, 0, org.y,
                                                m * (a * a + sqr((minright ? box.tr.y : box.bl.y) - 0.5f * (bb.yi + bb.ya))), false);
            }
            break;
        case 1 :
            if (box.bl.x < org.x + bb.xa && box.tr.x > org.x + bb.xi && box.height() > 0)
            {
                a = org.x + 0.5f * (bb.xi + bb.xa);
                c = 0.5f * (bb.yi + bb.ya);
                if (isx)
                    _ranges[axis].weighted<XY>(box.bl.y - c, box.tr.y - c, weight, a, 0, 0, org.x,
                                                m * (a * a + sqr((minright ? box.tr.x : box.bl.x) - 0.5f * (bb.xi + bb.xa))), false);
                else
                    _ranges[axis].weighted<XY>(box.bl.y - c, box.tr.y - c, weight, a, m,
                                                (minright ? box.tr.y : box.bl.y) - c, a, 0, false);
            }
            break;
        case 2 :
            if (box.bl.x - box.tr.y < org.x - org.y + sb.da && box.tr.x - box.bl.y > org.x - org.y + sb.di)
            {
                float d = org.x - org.y + 0.5f * (sb.di + sb.da);
                c = 0.5f * (sb.si + sb.sa);
                float smax = min(2 * box.tr.x - d, 2 * box.tr.y + d);
                float smin = max(2 * box.bl.x - d, 2 * box.bl.y + d);
                if (smin > smax) return;
                float si;
                a = d;
                if (isx)
                    si = 2 * (minright ? box.tr.x : box.bl.x) - a;
                else
                    si = 2 * (minright ? box.tr.y : box.bl.y) + a;
                _ranges[axis].weighted<SD>(smin - c, smax - c, weight / 2, a, m / 2, si, 0, 0, isx);
            }
            break;
        case 3 :
            if (box.bl.x + box.bl.y < org.x + org.y + sb.sa && box.tr.x + box.tr.y > org.x + org.y + sb.si)
            {
                float s = org.x + org.y + 0.5f * (sb.si + sb.sa);
                c = 0.5f * (sb.di + sb.da);
                float dmax = min(2 * box.tr.x - s, s - 2 * box.bl.y);
                float dmin = max(2 * box.bl.x - s, s - 2 * box.tr.y);
                if (dmin > dmax) return;
                float di;
                a = s;
                if (isx)
                    di = 2 * (minright ? box.tr.x : box.bl.x) - a;
                else
                    di = 2 * (minright ? box.tr.y : box.bl.y) + a;
                _ranges[axis].weighted<SD>(dmin - c, dmax - c, weight / 2, a, m / 2, di, 0, 0, !isx);
            }
            break;
        default :
            break;
    }
    return;
}

// Mark an area with an absolute cost, making it completely inaccessible.
inline void ShiftCollider::removeBox(const Rect &box, const BBox &bb, const SlantBox &sb, const Position &org, int axis)
{
    float c;
    switch (axis) {
        case 0 :
            if (box.bl.y < org.y + bb.ya && box.tr.y > org.y + bb.yi && box.width() > 0)
            {
                c = 0.5f * (bb.xi + bb.xa);
                _ranges[axis].exclude(box.bl.x - c, box.tr.x - c);
            }
            break;
        case 1 :
            if (box.bl.x < org.x + bb.xa && box.tr.x > org.x + bb.xi && box.height() > 0)
            {
                c = 0.5f * (bb.yi + bb.ya);
                _ranges[axis].exclude(box.bl.y - c, box.tr.y - c);
            }
            break;
        case 2 :
            if (box.bl.x - box.tr.y < org.x - org.y + sb.da && box.tr.x - box.bl.y > org.x - org.y + sb.di
                && box.width() > 0 && box.height() > 0)
            {
                float di = org.x - org.y + sb.di;
                float da = org.x - org.y + sb.da;
                float smax = sdm(di, da, box.tr.x, box.tr.y, std::greater<float>());
                float smin = sdm(da, di, box.bl.x, box.bl.y, std::less<float>());
                c = 0.5f * (sb.si + sb.sa);
                _ranges[axis].exclude(smin - c, smax - c);
            }
            break;
        case 3 :
            if (box.bl.x + box.bl.y < org.x + org.y + sb.sa && box.tr.x + box.tr.y > org.x + org.y + sb.si
                && box.width() > 0 && box.height() > 0)
            {
                float si = org.x + org.y + sb.si;
                float sa = org.x + org.y + sb.sa;
                float dmax = sdm(si, sa, box.tr.x, -box.bl.y, std::greater<float>());
                float dmin = sdm(sa, si, box.bl.x, -box.tr.y, std::less<float>());
                c = 0.5f * (sb.di + sb.da);
                _ranges[axis].exclude(dmin - c, dmax - c);
            }
            break;
        default :
            break;
    }
    return;
}

// Adjust the movement limits for the target to avoid having it collide
// with the given neighbor slot. Also determine if there is in fact a collision
// between the target and the given slot.
bool ShiftCollider::mergeSlot(Segment *seg, Slot *slot, const SlotCollision *cslot, const Position &currShift,
		bool isAfter,  // slot is logically after _target
		bool sameCluster, bool &hasCol, bool isExclusion,
        GR_MAYBE_UNUSED json * const dbgout )
{
    bool isCol = false;
    const float sx = slot->origin().x - _origin.x + currShift.x;
    const float sy = slot->origin().y - _origin.y + currShift.y;
    const float sd = sx - sy;
    const float ss = sx + sy;
    float vmin, vmax;
    float omin, omax, otmin, otmax;
    float cmin, cmax;   // target limits
    float torg;
    const GlyphCache &gc = seg->getFace()->glyphs();
    const unsigned short gid = slot->gid();
    if (!gc.check(gid))
        return false;
    const BBox &bb = gc.getBoundingBBox(gid);

    // SlotCollision * cslot = seg->collisionInfo(slot);
    int orderFlags = 0;
    bool sameClass = _seqProxClass == 0 && cslot->seqClass() == _seqClass;
    if (sameCluster && _seqClass
        && (sameClass || (_seqProxClass != 0 && cslot->seqClass() == _seqProxClass)))
		// Force the target glyph to be in the specified direction from the slot we're testing.
        orderFlags = _seqOrder;

    // short circuit if only interested in direct collision and we are out of range
    if (orderFlags || (sx + bb.xa + _margin >= _limit.bl.x && sx + bb.xi - _margin <= _limit.tr.x)
                    || (sy + bb.ya + _margin >= _limit.bl.y && sy + bb.yi - _margin <= _limit.tr.y))

    {
        const float tx = _currOffset.x + _currShift.x;
        const float ty = _currOffset.y + _currShift.y;
        const float td = tx - ty;
        const float ts = tx + ty;
        const SlantBox &sb = gc.getBoundingSlantBox(gid);
        const unsigned short tgid = _target->gid();
        const BBox &tbb = gc.getBoundingBBox(tgid);
        const SlantBox &tsb = gc.getBoundingSlantBox(tgid);
        float seq_above_wt = cslot->seqAboveWt();
        float seq_below_wt = cslot->seqBelowWt();
        float seq_valign_wt = cslot->seqValignWt();
        float lmargin;
        // if isAfter, invert orderFlags for diagonal orders.
        if (isAfter)
        {
            // invert appropriate bits
            orderFlags ^= (sameClass ? 0x3F : 0x3);
            // consider 2 bits at a time, non overlapping. If both bits set, clear them
            orderFlags = orderFlags ^ ((((orderFlags >> 1) & orderFlags) & 0x15) * 3);
        }

#if !defined GRAPHITE2_NTRACING
        if (dbgout)
            dbgout->setenv(0, slot);
#endif

        // Process main bounding octabox.
        for (int i = 0; i < 4; ++i)
        {
            switch (i) {
                case 0 :	// x direction
                    vmin = max(max(bb.xi - tbb.xa + sx, sb.di - tsb.da + ty + sd), sb.si - tsb.sa - ty + ss);
                    vmax = min(min(bb.xa - tbb.xi + sx, sb.da - tsb.di + ty + sd), sb.sa - tsb.si - ty + ss);
                    otmin = tbb.yi + ty;
                    otmax = tbb.ya + ty;
                    omin = bb.yi + sy;
                    omax = bb.ya + sy;
                    torg = _currOffset.x;
                    cmin = _limit.bl.x + torg;
                    cmax = _limit.tr.x - tbb.xi + tbb.xa + torg;
                    lmargin = _margin;
                    break;
                case 1 :	// y direction
                    vmin = max(max(bb.yi - tbb.ya + sy, tsb.di - sb.da + tx - sd), sb.si - tsb.sa - tx + ss);
                    vmax = min(min(bb.ya - tbb.yi + sy, tsb.da - sb.di + tx - sd), sb.sa - tsb.si - tx + ss);
                    otmin = tbb.xi + tx;
                    otmax = tbb.xa + tx;
                    omin = bb.xi + sx;
                    omax = bb.xa + sx;
                    torg = _currOffset.y;
                    cmin = _limit.bl.y + torg;
                    cmax = _limit.tr.y - tbb.yi + tbb.ya + torg;
                    lmargin = _margin;
                    break;
                case 2 :    // sum - moving along the positively-sloped vector, so the boundaries are the
                            // negatively-sloped boundaries.
                    vmin = max(max(sb.si - tsb.sa + ss, 2 * (bb.yi - tbb.ya + sy) + td), 2 * (bb.xi - tbb.xa + sx) - td);
                    vmax = min(min(sb.sa - tsb.si + ss, 2 * (bb.ya - tbb.yi + sy) + td), 2 * (bb.xa - tbb.xi + sx) - td);
                    otmin = tsb.di + td;
                    otmax = tsb.da + td;
                    omin = sb.di + sd;
                    omax = sb.da + sd;
                    torg = _currOffset.x + _currOffset.y;
                    cmin = _limit.bl.x + _limit.bl.y + torg;
                    cmax = _limit.tr.x + _limit.tr.y - tsb.si + tsb.sa + torg;
                    lmargin = _margin / ISQRT2;
                    break;
                case 3 :    // diff - moving along the negatively-sloped vector, so the boundaries are the
                            // positively-sloped boundaries.
                    vmin = max(max(sb.di - tsb.da + sd, 2 * (bb.xi - tbb.xa + sx) - ts), -2 * (bb.ya - tbb.yi + sy) + ts);
                    vmax = min(min(sb.da - tsb.di + sd, 2 * (bb.xa - tbb.xi + sx) - ts), -2 * (bb.yi - tbb.ya + sy) + ts);
                    otmin = tsb.si + ts;
                    otmax = tsb.sa + ts;
                    omin = sb.si + ss;
                    omax = sb.sa + ss;
                    torg = _currOffset.x - _currOffset.y;
                    cmin = _limit.bl.x - _limit.tr.y + torg;
                    cmax = _limit.tr.x - _limit.bl.y - tsb.di + tsb.da + torg;
                    lmargin = _margin / ISQRT2;
                    break;
                default :
                    continue;
            }

#if !defined GRAPHITE2_NTRACING
            if (dbgout)
                dbgout->setenv(1, reinterpret_cast<void *>(-1));
#define DBGTAG(x) if (dbgout) dbgout->setenv(1, reinterpret_cast<void *>(-x));
#else
#define DBGTAG(x)
#endif

            if (orderFlags)
            {
                Position org(tx, ty);
                float xminf = _limit.bl.x + _currOffset.x + tbb.xi;
                float xpinf = _limit.tr.x + _currOffset.x + tbb.xa;
                float ypinf = _limit.tr.y + _currOffset.y + tbb.ya;
                float yminf = _limit.bl.y + _currOffset.y + tbb.yi;
                switch (orderFlags) {
                    case SlotCollision::SEQ_ORDER_RIGHTUP :
                    {
                        float r1Xedge = cslot->seqAboveXoff() + 0.5f * (bb.xi + bb.xa) + sx;
                        float r3Xedge = cslot->seqBelowXlim() + bb.xa + sx + 0.5f * (tbb.xa - tbb.xi);
                        float r2Yedge = 0.5f * (bb.yi + bb.ya) + sy;

                        // DBGTAG(1x) means the regions are up and right
                        // region 1
                        DBGTAG(11)
                        addBox_slope(true, Rect(Position(xminf, r2Yedge), Position(r1Xedge, ypinf)),
                                        tbb, tsb, org, 0, seq_above_wt, true, i);
                        // region 2
                        DBGTAG(12)
                        removeBox(Rect(Position(xminf, yminf), Position(r3Xedge, r2Yedge)), tbb, tsb, org, i);
                        // region 3, which end is zero is irrelevant since m weight is 0
                        DBGTAG(13)
                        addBox_slope(true, Rect(Position(r3Xedge, yminf), Position(xpinf, r2Yedge - cslot->seqValignHt())),
                                        tbb, tsb, org, seq_below_wt, 0, true, i);
                        // region 4
                        DBGTAG(14)
                        addBox_slope(false, Rect(Position(sx + bb.xi, r2Yedge), Position(xpinf, r2Yedge + cslot->seqValignHt())),
                                        tbb, tsb, org, 0, seq_valign_wt, true, i);
                        // region 5
                        DBGTAG(15)
                        addBox_slope(false, Rect(Position(sx + bb.xi, r2Yedge - cslot->seqValignHt()), Position(xpinf, r2Yedge)),
                                        tbb, tsb, org, seq_below_wt, seq_valign_wt, false, i);
                        break;
                    }
                    case SlotCollision::SEQ_ORDER_LEFTDOWN :
                    {
                        float r1Xedge = 0.5f * (bb.xi + bb.xa) + cslot->seqAboveXoff() + sx;
                        float r3Xedge = bb.xi - cslot->seqBelowXlim() + sx - 0.5f * (tbb.xa - tbb.xi);
                        float r2Yedge = 0.5f * (bb.yi + bb.ya) + sy;
                        // DBGTAG(2x) means the regions are up and right
                        // region 1
                        DBGTAG(21)
                        addBox_slope(true, Rect(Position(r1Xedge, yminf), Position(xpinf, r2Yedge)),
                                        tbb, tsb, org, 0, seq_above_wt, false, i);
                        // region 2
                        DBGTAG(22)
                        removeBox(Rect(Position(r3Xedge, r2Yedge), Position(xpinf, ypinf)), tbb, tsb, org, i);
                        // region 3
                        DBGTAG(23)
                        addBox_slope(true, Rect(Position(xminf, r2Yedge - cslot->seqValignHt()), Position(r3Xedge, ypinf)),
                                        tbb, tsb, org, seq_below_wt, 0, false, i);
                        // region 4
                        DBGTAG(24)
                        addBox_slope(false, Rect(Position(xminf, r2Yedge), Position(sx + bb.xa, r2Yedge + cslot->seqValignHt())),
                                        tbb, tsb, org, 0, seq_valign_wt, true, i);
                        // region 5
                        DBGTAG(25)
                        addBox_slope(false, Rect(Position(xminf, r2Yedge - cslot->seqValignHt()),
                                        Position(sx + bb.xa, r2Yedge)), tbb, tsb, org, seq_below_wt, seq_valign_wt, false, i);
                        break;
                    }
                    case SlotCollision::SEQ_ORDER_NOABOVE : // enforce neighboring glyph being above
                        DBGTAG(31);
                        removeBox(Rect(Position(bb.xi - tbb.xa + sx, sy + bb.ya),
                                        Position(bb.xa - tbb.xi + sx, ypinf)), tbb, tsb, org, i);
                        break;
                    case SlotCollision::SEQ_ORDER_NOBELOW :	// enforce neighboring glyph being below
                        DBGTAG(32);
                        removeBox(Rect(Position(bb.xi - tbb.xa + sx, yminf),
                                        Position(bb.xa - tbb.xi + sx, sy + bb.yi)), tbb, tsb, org, i);
                        break;
                    case SlotCollision::SEQ_ORDER_NOLEFT :  // enforce neighboring glyph being to the left
                        DBGTAG(33)
                        removeBox(Rect(Position(xminf, bb.yi - tbb.ya + sy),
                                        Position(bb.xi - tbb.xa + sx, bb.ya - tbb.yi + sy)), tbb, tsb, org, i);
                        break;
                    case SlotCollision::SEQ_ORDER_NORIGHT : // enforce neighboring glyph being to the right
                        DBGTAG(34)
                        removeBox(Rect(Position(bb.xa - tbb.xi + sx, bb.yi - tbb.ya + sy),
                                        Position(xpinf, bb.ya - tbb.yi + sy)), tbb, tsb, org, i);
                        break;
                    default :
                        break;
                }
            }

            if (vmax < cmin - lmargin || vmin > cmax + lmargin || omax < otmin - lmargin || omin > otmax + lmargin)
                continue;

            // Process sub-boxes that are defined for this glyph.
            // We only need to do this if there was in fact a collision with the main octabox.
            uint8 numsub = gc.numSubBounds(gid);
            if (numsub > 0)
            {
                bool anyhits = false;
                for (int j = 0; j < numsub; ++j)
                {
                    const BBox &sbb = gc.getSubBoundingBBox(gid, j);
                    const SlantBox &ssb = gc.getSubBoundingSlantBox(gid, j);
                    switch (i) {
                        case 0 :    // x
                            vmin = max(max(sbb.xi-tbb.xa+sx, ssb.di-tsb.da+sd+ty), ssb.si-tsb.sa+ss-ty);
                            vmax = min(min(sbb.xa-tbb.xi+sx, ssb.da-tsb.di+sd+ty), ssb.sa-tsb.si+ss-ty);
                            omin = sbb.yi + sy;
                            omax = sbb.ya + sy;
                            break;
                        case 1 :    // y
                            vmin = max(max(sbb.yi-tbb.ya+sy, tsb.di-ssb.da-sd+tx), ssb.si-tsb.sa+ss-tx);
                            vmax = min(min(sbb.ya-tbb.yi+sy, tsb.da-ssb.di-sd+tx), ssb.sa-tsb.si+ss-tx);
                            omin = sbb.xi + sx;
                            omax = sbb.xa + sx;
                            break;
                        case 2 :    // sum
                            vmin = max(max(ssb.si-tsb.sa+ss, 2*(sbb.yi-tbb.ya+sy)+td), 2*(sbb.xi-tbb.xa+sx)-td);
                            vmax = min(min(ssb.sa-tsb.si+ss, 2*(sbb.ya-tbb.yi+sy)+td), 2*(sbb.xa-tbb.xi+sx)-td);
                            omin = ssb.di + sd;
                            omax = ssb.da + sd;
                            break;
                        case 3 :    // diff
                            vmin = max(max(ssb.di-tsb.da+sd, 2*(sbb.xi-tbb.xa+sx)-ts), -2*(sbb.ya-tbb.yi+sy)+ts);
                            vmax = min(min(ssb.da-tsb.di+sd, 2*(sbb.xa-tbb.xi+sx)-ts), -2*(sbb.yi-tbb.ya+sy)+ts);
                            omin = ssb.si + ss;
                            omax = ssb.sa + ss;
                            break;
                    }
                    if (vmax < cmin - lmargin || vmin > cmax + lmargin || omax < otmin - lmargin || omin > otmax + lmargin)
                        continue;

#if !defined GRAPHITE2_NTRACING
                    if (dbgout)
                        dbgout->setenv(1, reinterpret_cast<void *>(j));
#endif
                    if (omin > otmax)
                        _ranges[i].weightedAxis(i, vmin - lmargin, vmax + lmargin, 0, 0, 0, 0, 0,
                                                sqr(lmargin - omin + otmax) * _marginWt, false);
                    else if (omax < otmin)
                        _ranges[i].weightedAxis(i, vmin - lmargin, vmax + lmargin, 0, 0, 0, 0, 0,
                                                sqr(lmargin - otmin + omax) * _marginWt, false);
                    else
                        _ranges[i].exclude_with_margins(vmin, vmax, i);
                    anyhits = true;
                }
                if (anyhits)
                    isCol = true;
            }
            else // no sub-boxes
            {
#if !defined GRAPHITE2_NTRACING
                    if (dbgout)
                        dbgout->setenv(1, reinterpret_cast<void *>(-1));
#endif
                isCol = true;
                if (omin > otmax)
                    _ranges[i].weightedAxis(i, vmin - lmargin, vmax + lmargin, 0, 0, 0, 0, 0,
                                            sqr(lmargin - omin + otmax) * _marginWt, false);
                else if (omax < otmin)
                    _ranges[i].weightedAxis(i, vmin - lmargin, vmax + lmargin, 0, 0, 0, 0, 0,
                                            sqr(lmargin - otmin + omax) * _marginWt, false);
                else
                    _ranges[i].exclude_with_margins(vmin, vmax, i);

            }
        }
    }
    bool res = true;
    if (cslot->exclGlyph() > 0 && gc.check(cslot->exclGlyph()) && !isExclusion)
    {
        // Set up the bogus slot representing the exclusion glyph.
        Slot *exclSlot = seg->newSlot();
        if (!exclSlot)
            return res;
        exclSlot->setGlyph(seg, cslot->exclGlyph());
        Position exclOrigin(slot->origin() + cslot->exclOffset());
        exclSlot->origin(exclOrigin);
        SlotCollision exclInfo(seg, exclSlot);
        res &= mergeSlot(seg, exclSlot, &exclInfo, currShift, isAfter, sameCluster, isCol, true, dbgout );
        seg->freeSlot(exclSlot);
    }
    hasCol |= isCol;
    return res;

}   // end of ShiftCollider::mergeSlot


// Figure out where to move the target glyph to, and return the amount to shift by.
Position ShiftCollider::resolve(GR_MAYBE_UNUSED Segment *seg, bool &isCol, GR_MAYBE_UNUSED json * const dbgout)
{
    float tbase;
    float totalCost = (float)(std::numeric_limits<float>::max() / 2);
    Position resultPos = Position(0, 0);
#if !defined GRAPHITE2_NTRACING
	int bestAxis = -1;
    if (dbgout)
    {
		outputJsonDbgStartSlot(dbgout, seg);
        *dbgout << "vectors" << json::array;
    }
#endif
    isCol = true;
    for (int i = 0; i < 4; ++i)
    {
        float bestCost = -1;
        float bestPos;
        // Calculate the margin depending on whether we are moving diagonally or not:
        switch (i) {
            case 0 :	// x direction
                tbase = _currOffset.x;
                break;
            case 1 :	// y direction
                tbase = _currOffset.y;
                break;
            case 2 :	// sum (negatively-sloped diagonals)
                tbase = _currOffset.x + _currOffset.y;
                break;
            case 3 :	// diff (positively-sloped diagonals)
                tbase = _currOffset.x - _currOffset.y;
                break;
        }
        Position testp;
        bestPos = _ranges[i].closest(0, bestCost) - tbase;     // Get the best relative position
#if !defined GRAPHITE2_NTRACING
        if (dbgout)
            outputJsonDbgOneVector(dbgout, seg, i, tbase, bestCost, bestPos) ;
#endif
        if (bestCost >= 0.0f)
        {
            isCol = false;
            switch (i) {
                case 0 : testp = Position(bestPos, _currShift.y); break;
                case 1 : testp = Position(_currShift.x, bestPos); break;
                case 2 : testp = Position(0.5f * (_currShift.x - _currShift.y + bestPos), 0.5f * (_currShift.y - _currShift.x + bestPos)); break;
                case 3 : testp = Position(0.5f * (_currShift.x + _currShift.y + bestPos), 0.5f * (_currShift.x + _currShift.y - bestPos)); break;
            }
            if (bestCost < totalCost - 0.01f)
            {
                totalCost = bestCost;
                resultPos = testp;
#if !defined GRAPHITE2_NTRACING
                bestAxis = i;
#endif
            }
        }
    }  // end of loop over 4 directions

#if !defined GRAPHITE2_NTRACING
    if (dbgout)
        outputJsonDbgEndSlot(dbgout, resultPos, bestAxis, isCol);
#endif

    return resultPos;

}   // end of ShiftCollider::resolve


#if !defined GRAPHITE2_NTRACING

void ShiftCollider::outputJsonDbg(json * const dbgout, Segment *seg, int axis)
{
    int axisMax = axis;
    if (axis < 0) // output all axes
    {
        *dbgout << "gid" << _target->gid()
            << "limit" << _limit
            << "target" << json::object
                << "origin" << _target->origin()
                << "margin" << _margin
                << "bbox" << seg->theGlyphBBoxTemporary(_target->gid())
                << "slantbox" << seg->getFace()->glyphs().slant(_target->gid())
                << json::close; // target object
        *dbgout << "ranges" << json::array;
        axis = 0;
        axisMax = 3;
    }
    for (int iAxis = axis; iAxis <= axisMax; ++iAxis)
    {
        *dbgout << json::flat << json::array << _ranges[iAxis].position();
        for (Zones::const_iterator s = _ranges[iAxis].begin(), e = _ranges[iAxis].end(); s != e; ++s)
            *dbgout << json::flat << json::array
                        << Position(s->x, s->xm) << s->sm << s->smx << s->c
                    << json::close;
        *dbgout << json::close;
    }
    if (axis < axisMax) // looped through the _ranges array for all axes
        *dbgout << json::close; // ranges array
}

void ShiftCollider::outputJsonDbgStartSlot(json * const dbgout, Segment *seg)
{
        *dbgout << json::object // slot - not closed till the end of the caller method
                << "slot" << objectid(dslot(seg, _target))
				<< "gid" << _target->gid()
                << "limit" << _limit
                << "target" << json::object
                    << "origin" << _origin
                    << "currShift" << _currShift
                    << "currOffset" << seg->collisionInfo(_target)->offset()
                    << "bbox" << seg->theGlyphBBoxTemporary(_target->gid())
                    << "slantBox" << seg->getFace()->glyphs().slant(_target->gid())
                    << "fix" << "shift";
        *dbgout     << json::close; // target object
}

void ShiftCollider::outputJsonDbgEndSlot(GR_MAYBE_UNUSED json * const dbgout,
	 Position resultPos, int bestAxis, bool isCol)
{
    *dbgout << json::close // vectors array
    << "result" << resultPos
	//<< "scraping" << _scraping[bestAxis]
	<< "bestAxis" << bestAxis
    << "stillBad" << isCol
    << json::close; // slot object
}

void ShiftCollider::outputJsonDbgOneVector(json * const dbgout, Segment *seg, int axis,
	float tleft, float bestCost, float bestVal)
{
	const char * label;
	switch (axis)
	{
		case 0:	label = "x";			break;
		case 1:	label = "y";			break;
		case 2:	label = "sum (NE-SW)";	break;
		case 3:	label = "diff (NW-SE)";	break;
		default: label = "???";			break;
	}

	*dbgout << json::object // vector
		<< "direction" << label
		<< "targetMin" << tleft;

	outputJsonDbgRemovals(dbgout, axis, seg);

    *dbgout << "ranges";
    outputJsonDbg(dbgout, seg, axis);

    *dbgout << "bestCost" << bestCost
        << "bestVal" << bestVal + tleft
        << json::close; // vectors object
}

void ShiftCollider::outputJsonDbgRemovals(json * const dbgout, int axis, Segment *seg)
{
    *dbgout << "removals" << json::array;
    _ranges[axis].jsonDbgOut(seg);
    *dbgout << json::close; // removals array
}

#endif // !defined GRAPHITE2_NTRACING


////    KERN-COLLIDER    ////

inline
static float localmax (float al, float au, float bl, float bu, float x)
{
    if (al < bl)
    { if (au < bu) return au < x ? au : x; }
    else if (au > bu) return bl < x ? bl : x;
    return x;
}

inline
static float localmin(float al, float au, float bl, float bu, float x)
{
    if (bl > al)
    { if (bu > au) return bl > x ? bl : x; }
    else if (au > bu) return al > x ? al : x;
    return x;
}

// Return the given edge of the glyph at height y, taking any slant box into account.
static float get_edge(Segment *seg, const Slot *s, const Position &shift, float y, float width, float margin, bool isRight)
{
    const GlyphCache &gc = seg->getFace()->glyphs();
    unsigned short gid = s->gid();
    float sx = s->origin().x + shift.x;
    float sy = s->origin().y + shift.y;
    uint8 numsub = gc.numSubBounds(gid);
    float res = isRight ? (float)-1e38 : (float)1e38;

    if (numsub > 0)
    {
        for (int i = 0; i < numsub; ++i)
        {
            const BBox &sbb = gc.getSubBoundingBBox(gid, i);
            const SlantBox &ssb = gc.getSubBoundingSlantBox(gid, i);
            if (sy + sbb.yi - margin > y + width / 2 || sy + sbb.ya + margin < y - width / 2)
                continue;
            if (isRight)
            {
                float x = sx + sbb.xa + margin;
                if (x > res)
                {
                    float td = sx - sy + ssb.da + margin + y;
                    float ts = sx + sy + ssb.sa + margin - y;
                    x = localmax(td - width / 2, td + width / 2,  ts - width / 2, ts + width / 2, x);
                    if (x > res)
                        res = x;
                }
            }
            else
            {
                float x = sx + sbb.xi - margin;
                if (x < res)
                {
                    float td = sx - sy + ssb.di - margin + y;
                    float ts = sx + sy + ssb.si - margin - y;
                    x = localmin(td - width / 2, td + width / 2, ts - width / 2, ts + width / 2, x);
                    if (x < res)
                        res = x;
                }
            }
        }
    }
    else
    {
        const BBox &bb = gc.getBoundingBBox(gid);
        const SlantBox &sb = gc.getBoundingSlantBox(gid);
        if (sy + bb.yi - margin > y + width / 2 || sy + bb.ya + margin < y - width / 2)
            return res;
        float td = sx - sy + y;
        float ts = sx + sy - y;
        if (isRight)
            res = localmax(td + sb.da - width / 2, td + sb.da + width / 2, ts + sb.sa - width / 2, ts + sb.sa + width / 2, sx + bb.xa) + margin;
        else
            res = localmin(td + sb.di - width / 2, td + sb.di + width / 2, ts + sb.si - width / 2, ts + sb.si + width / 2, sx + bb.xi) - margin;
    }
    return res;
}


bool KernCollider::initSlot(Segment *seg, Slot *aSlot, const Rect &limit, float margin,
    const Position &currShift, const Position &offsetPrev, int dir,
    float ymin, float ymax, GR_MAYBE_UNUSED json * const dbgout)
{
    const GlyphCache &gc = seg->getFace()->glyphs();
    const Slot *base = aSlot;
    // const Slot *last = aSlot;
    const Slot *s;
    int numSlices;
    while (base->attachedTo())
        base = base->attachedTo();
    if (margin < 10) margin = 10;

    _limit = limit;
    _offsetPrev = offsetPrev; // kern from a previous pass

    // Calculate the height of the glyph and how many horizontal slices to use.
    if (_maxy >= 1e37f)
    {
        _sliceWidth = margin / 1.5f;
        _maxy = ymax + margin;
        _miny = ymin - margin;
        numSlices = int((_maxy - _miny + 2) / (_sliceWidth / 1.5f) + 1.f);  // +2 helps with rounding errors
        _edges.clear();
        _edges.insert(_edges.begin(), numSlices, (dir & 1) ? 1e38f : -1e38f);
        _xbound = (dir & 1) ? (float)1e38f : (float)-1e38f;
    }
    else if (_maxy != ymax || _miny != ymin)
    {
        if (_miny != ymin)
        {
            numSlices = int((ymin - margin - _miny) / _sliceWidth - 1);
            _miny += numSlices * _sliceWidth;
            if (numSlices < 0)
                _edges.insert(_edges.begin(), -numSlices, (dir & 1) ? 1e38f : -1e38f);
            else if ((unsigned)numSlices < _edges.size())    // this shouldn't fire since we always grow the range
            {
                Vector<float>::iterator e = _edges.begin();
                while (numSlices--)
                    ++e;
                _edges.erase(_edges.begin(), e);
            }
        }
        if (_maxy != ymax)
        {
            numSlices = int((ymax + margin - _miny) / _sliceWidth + 1);
            _maxy = numSlices * _sliceWidth + _miny;
            if (numSlices > (int)_edges.size())
                _edges.insert(_edges.end(), numSlices - _edges.size(), (dir & 1) ? 1e38f : -1e38f);
            else if (numSlices < (int)_edges.size())   // this shouldn't fire since we always grow the range
            {
                while ((int)_edges.size() > numSlices)
                    _edges.pop_back();
            }
        }
        goto done;
    }
    numSlices = int(_edges.size());

#if !defined GRAPHITE2_NTRACING
    // Debugging
    _seg = seg;
    _slotNear.clear();
    _slotNear.insert(_slotNear.begin(), numSlices, NULL);
    _nearEdges.clear();
    _nearEdges.insert(_nearEdges.begin(), numSlices, (dir & 1) ? -1e38f : +1e38f);
#endif

    // Determine the trailing edge of each slice (ie, left edge for a RTL glyph).
    for (s = base; s; s = s->nextInCluster(s))
    {
        SlotCollision *c = seg->collisionInfo(s);
        if (!gc.check(s->gid()))
            return false;
        const BBox &bs = gc.getBoundingBBox(s->gid());
        float x = s->origin().x + c->shift().x + ((dir & 1) ? bs.xi : bs.xa);
        // Loop over slices.
        // Note smin might not be zero if glyph s is not at the bottom of the cluster; similarly for smax.
        float toffset = c->shift().y - _miny + 1 + s->origin().y;
        int smin = max(0, int((bs.yi + toffset) / _sliceWidth));
        int smax = min(numSlices - 1, int((bs.ya + toffset) / _sliceWidth + 1));
        for (int i = smin; i <= smax; ++i)
        {
            float t;
            float y = _miny - 1 + (i + .5f) * _sliceWidth; // vertical center of slice
            if ((dir & 1) && x < _edges[i])
            {
                t = get_edge(seg, s, c->shift(), y, _sliceWidth, margin, false);
                if (t < _edges[i])
                {
                    _edges[i] = t;
                    if (t < _xbound)
                        _xbound = t;
                }
            }
            else if (!(dir & 1) && x > _edges[i])
            {
                t = get_edge(seg, s, c->shift(), y, _sliceWidth, margin, true);
                if (t > _edges[i])
                {
                    _edges[i] = t;
                    if (t > _xbound)
                        _xbound = t;
                }
            }
        }
    }
    done:
    _mingap = (float)1e37;      // less than 1e38 s.t. 1e38-_mingap is really big
    _target = aSlot;
    _margin = margin;
    _currShift = currShift;
    return true;
}   // end of KernCollider::initSlot


// Determine how much the target slot needs to kern away from the given slot.
// In other words, merge information from given slot's position with what the target slot knows
// about how it can kern.
// Return false if we know there is no collision, true if we think there might be one.
bool KernCollider::mergeSlot(Segment *seg, Slot *slot, const Position &currShift, float currSpace, int dir, GR_MAYBE_UNUSED json * const dbgout)
{
    int rtl = (dir & 1) * 2 - 1;
    if (!seg->getFace()->glyphs().check(slot->gid()))
        return false;
    const Rect &bb = seg->theGlyphBBoxTemporary(slot->gid());
    const float sx = slot->origin().x + currShift.x;
    float x = (sx + (rtl > 0 ? bb.tr.x : bb.bl.x)) * rtl;
    // this isn't going to reduce _mingap so skip
    if (_hit && x < rtl * (_xbound - _mingap - currSpace))
        return false;

    const float sy = slot->origin().y + currShift.y;
    int smin = max(1, int((bb.bl.y + (1 - _miny + sy)) / _sliceWidth + 1)) - 1;
    int smax = min((int)_edges.size() - 2, int((bb.tr.y + (1 - _miny + sy)) / _sliceWidth + 1)) + 1;
    if (smin > smax)
        return false;
    bool collides = false;
    bool nooverlap = true;

    for (int i = smin; i <= smax; ++i)
    {
        float here = _edges[i] * rtl;
        if (here > (float)9e37)
            continue;
        if (!_hit || x > here - _mingap - currSpace)
        {
            float y = (float)(_miny - 1 + (i + .5f) * _sliceWidth);  // vertical center of slice
            // 2 * currSpace to account for the space that is already separating them and the space we want to add
            float m = get_edge(seg, slot, currShift, y, _sliceWidth, 0., rtl > 0) * rtl + 2 * currSpace;
            if (m < (float)-8e37)       // only true if the glyph has a gap in it
                continue;
            nooverlap = false;
            float t = here - m;
            // _mingap is positive to shrink
            if (t < _mingap || (!_hit && !collides))
            {
                _mingap = t;
                collides = true;
            }
#if !defined GRAPHITE2_NTRACING
            // Debugging - remember the closest neighboring edge for this slice.
            if (m > rtl * _nearEdges[i])
            {
                _slotNear[i] = slot;
                _nearEdges[i] = m * rtl;
            }
#endif
        }
        else
            nooverlap = false;
    }
    if (nooverlap)
        _mingap = max(_mingap, _xbound - rtl * (currSpace + _margin + x));
    if (collides && !nooverlap)
        _hit = true;
    return collides | nooverlap;   // note that true is not a necessarily reliable value

}   // end of KernCollider::mergeSlot


// Return the amount to kern by.
Position KernCollider::resolve(GR_MAYBE_UNUSED Segment *seg, GR_MAYBE_UNUSED Slot *slot,
        int dir, GR_MAYBE_UNUSED json * const dbgout)
{
    float resultNeeded = (1 - 2 * (dir & 1)) * _mingap;
    // float resultNeeded = (1 - 2 * (dir & 1)) * (_mingap - margin);
    float result = min(_limit.tr.x - _offsetPrev.x, max(resultNeeded, _limit.bl.x - _offsetPrev.x));

#if !defined GRAPHITE2_NTRACING
    if (dbgout)
    {
        *dbgout << json::object // slot
                << "slot" << objectid(dslot(seg, _target))
				<< "gid" << _target->gid()
                << "limit" << _limit
                << "miny" << _miny
                << "maxy" << _maxy
                << "slicewidth" << _sliceWidth
                << "target" << json::object
                    << "origin" << _target->origin()
                    //<< "currShift" << _currShift
                    << "offsetPrev" << _offsetPrev
                    << "bbox" << seg->theGlyphBBoxTemporary(_target->gid())
                    << "slantBox" << seg->getFace()->glyphs().slant(_target->gid())
                    << "fix" << "kern"
                    << json::close; // target object

        *dbgout << "slices" << json::array;
        for (int is = 0; is < (int)_edges.size(); is++)
        {
            *dbgout << json::flat << json::object
                << "i" << is
                << "targetEdge" << _edges[is]
                << "neighbor" << objectid(dslot(seg, _slotNear[is]))
                << "nearEdge" << _nearEdges[is]
                << json::close;
        }
        *dbgout << json::close; // slices array

        *dbgout
            << "xbound" << _xbound
            << "minGap" << _mingap
            << "needed" << resultNeeded
            << "result" << result
            << "stillBad" << (result != resultNeeded)
            << json::close; // slot object
    }
#endif

    return Position(result, 0.);

}   // end of KernCollider::resolve

void KernCollider::shift(const Position &mv, int dir)
{
    for (Vector<float>::iterator e = _edges.begin(); e != _edges.end(); ++e)
        *e += mv.x;
    _xbound += (1 - 2 * (dir & 1)) * mv.x;
}

////    SLOT-COLLISION    ////

// Initialize the collision attributes for the given slot.
SlotCollision::SlotCollision(Segment *seg, Slot *slot)
{
    initFromSlot(seg, slot);
}

void SlotCollision::initFromSlot(Segment *seg, Slot *slot)
{
    // Initialize slot attributes from glyph attributes.
	// The order here must match the order in the grcompiler code,
	// GrcSymbolTable::AssignInternalGlyphAttrIDs.
    uint16 gid = slot->gid();
    uint16 aCol = seg->silf()->aCollision(); // flags attr ID
    const GlyphFace * glyphFace = seg->getFace()->glyphs().glyphSafe(gid);
    if (!glyphFace)
        return;
    const sparse &p = glyphFace->attrs();
    _flags = p[aCol];
    _limit = Rect(Position(int16(p[aCol+1]), int16(p[aCol+2])),
                  Position(int16(p[aCol+3]), int16(p[aCol+4])));
    _margin = p[aCol+5];
    _marginWt = p[aCol+6];

    _seqClass = p[aCol+7];
	_seqProxClass = p[aCol+8];
    _seqOrder = p[aCol+9];
	_seqAboveXoff = p[aCol+10];
	_seqAboveWt = p[aCol+11];
	_seqBelowXlim = p[aCol+12];
	_seqBelowWt = p[aCol+13];
	_seqValignHt = p[aCol+14];
	_seqValignWt = p[aCol+15];

    // These attributes do not have corresponding glyph attribute:
    _exclGlyph = 0;
    _exclOffset = Position(0, 0);
}

float SlotCollision::getKern(int dir) const
{
    if ((_flags & SlotCollision::COLL_KERN) != 0)
        return float(_shift.x * ((dir & 1) ? -1 : 1));
    else
    	return 0;
}

bool SlotCollision::ignore() const
{
	return ((flags() & SlotCollision::COLL_IGNORE) || (flags() & SlotCollision::COLL_ISSPACE));
}