qdistancefield.cpp

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// Copyright (C) 2016 The Qt Company Ltd.
// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
 
#include "qdistancefield_p.h"
#include <qmath.h>
#include <QtCore/qalloc.h>
#include <QtGui/qimagereader.h>
#include <private/qdatabuffer_p.h>
#include <private/qimage_p.h>
#include <private/qpathsimplifier_p.h>
 
QT_BEGIN_NAMESPACE
 
using namespace Qt::StringLiterals;
 
Q_STATIC_LOGGING_CATEGORY(lcDistanceField, "qt.distanceField");
 
namespace
{
    enum FillHDir
    {
        LeftToRight,
        RightToLeft
    };
 
    enum FillVDir
    {
        TopDown,
        BottomUp
    };
 
    enum FillClip
    {
        NoClip,
        Clip
    };
}
 
template <FillClip clip, FillHDir dir>
inline void fillLine(qint32 *, int, int, int, qint32, qint32)
{
}
 
template <>
inline void fillLine<Clip, LeftToRight>(qint32 *line, int width, int lx, int rx, qint32 d, qint32 dd)
{
    int fromX = qMax(0, lx >> 8);
    int toX = qMin(width, rx >> 8);
    int x = toX - fromX;
    if (x <= 0)
        return;
    qint32 val = d + (((fromX << 8) + 0xff - lx) * dd >> 8);
    line += fromX;
    do {
        *line = abs(val) < abs(*line) ? val : *line;
        val += dd;
        ++line;
    } while (--x);
}
 
template <>
inline void fillLine<Clip, RightToLeft>(qint32 *line, int width, int lx, int rx, qint32 d, qint32 dd)
{
    int fromX = qMax(0, lx >> 8);
    int toX = qMin(width, rx >> 8);
    int x = toX - fromX;
    if (x <= 0)
        return;
    qint32 val = d + (((toX << 8) + 0xff - rx) * dd >> 8);
    line += toX;
    do {
        val -= dd;
        --line;
        *line = abs(val) < abs(*line) ? val : *line;
    } while (--x);
}
 
template <>
inline void fillLine<NoClip, LeftToRight>(qint32 *line, int, int lx, int rx, qint32 d, qint32 dd)
{
    int fromX = lx >> 8;
    int toX = rx >> 8;
    int x = toX - fromX;
    if (x <= 0)
        return;
    qint32 val = d + ((~lx & 0xff) * dd >> 8);
    line += fromX;
    do {
        *line = abs(val) < abs(*line) ? val : *line;
        val += dd;
        ++line;
    } while (--x);
}
 
template <>
inline void fillLine<NoClip, RightToLeft>(qint32 *line, int, int lx, int rx, qint32 d, qint32 dd)
{
    int fromX = lx >> 8;
    int toX = rx >> 8;
    int x = toX - fromX;
    if (x <= 0)
        return;
    qint32 val = d + ((~rx & 0xff) * dd >> 8);
    line += toX;
    do {
        val -= dd;
        --line;
        *line = abs(val) < abs(*line) ? val : *line;
    } while (--x);
}
 
template <FillClip clip, FillVDir vDir, FillHDir hDir>
inline void fillLines(qint32 *bits, int width, int height, int upperY, int lowerY,
                      int &lx, int ldx, int &rx, int rdx, qint32 &d, qint32 ddy, qint32 ddx)
{
    Q_UNUSED(height);
    Q_ASSERT(upperY < lowerY);
    int y = lowerY - upperY;
    if (vDir == TopDown) {
        qint32 *line = bits + upperY * width;
        do {
            fillLine<clip, hDir>(line, width, lx, rx, d, ddx);
            lx += ldx;
            d += ddy;
            rx += rdx;
            line += width;
        } while (--y);
    } else {
        qint32 *line = bits + lowerY * width;
        do {
            lx -= ldx;
            d -= ddy;
            rx -= rdx;
            line -= width;
            fillLine<clip, hDir>(line, width, lx, rx, d, ddx);
        } while (--y);
    }
}
 
template <FillClip clip>
void drawTriangle(qint32 *bits, int width, int height, const QPoint *center,
                  const QPoint *v1, const QPoint *v2, qint32 value)
{
    const int y1 = clip == Clip ? qBound(0, v1->y() >> 8, height) : v1->y() >> 8;
    const int y2 = clip == Clip ? qBound(0, v2->y() >> 8, height) : v2->y() >> 8;
    const int yC = clip == Clip ? qBound(0, center->y() >> 8, height) : center->y() >> 8;
 
    const int v1Frac = clip == Clip ? (y1 << 8) + 0xff - v1->y() : ~v1->y() & 0xff;
    const int v2Frac = clip == Clip ? (y2 << 8) + 0xff - v2->y() : ~v2->y() & 0xff;
    const int centerFrac = clip == Clip ? (yC << 8) + 0xff - center->y() : ~center->y() & 0xff;
 
    int dx1 = 0, x1 = 0, dx2 = 0, x2 = 0;
    qint32 dd1, d1, dd2, d2;
    if (v1->y() != center->y()) {
        dx1 = ((v1->x() - center->x()) << 8) / (v1->y() - center->y());
        x1 = center->x() + centerFrac * (v1->x() - center->x()) / (v1->y() - center->y());
    }
    if (v2->y() != center->y()) {
        dx2 = ((v2->x() - center->x()) << 8) / (v2->y() - center->y());
        x2 = center->x() + centerFrac * (v2->x() - center->x()) / (v2->y() - center->y());
    }
 
    const qint32 div = (v2->x() - center->x()) * (v1->y() - center->y())
                     - (v2->y() - center->y()) * (v1->x() - center->x());
    const qint32 dd = div ? qint32((qint64(value * (v1->y() - v2->y())) << 8) / div) : 0;
 
    if (y2 < yC) {
        if (y1 < yC) {
            // Center at the bottom.
            if (y2 < y1) {
                // y2 < y1 < yC
                // Long right edge.
                d1 = centerFrac * value / (v1->y() - center->y());
                dd1 = ((value << 8) / (v1->y() - center->y()));
                fillLines<clip, BottomUp, LeftToRight>(bits, width, height, y1, yC, x1, dx1,
                                                       x2, dx2, d1, dd1, dd);
                dx1 = ((v1->x() - v2->x()) << 8) / (v1->y() - v2->y());
                x1 = v1->x() + v1Frac * (v1->x() - v2->x()) / (v1->y() - v2->y());
                fillLines<clip, BottomUp, LeftToRight>(bits, width, height, y2, y1, x1, dx1,
                                                       x2, dx2, value, 0, dd);
            } else {
                // y1 <= y2 < yC
                // Long left edge.
                d2 = centerFrac * value / (v2->y() - center->y());
                dd2 = ((value << 8) / (v2->y() - center->y()));
                fillLines<clip, BottomUp, RightToLeft>(bits, width, height, y2, yC, x1, dx1,
                                                       x2, dx2, d2, dd2, dd);
                if (y1 != y2) {
                    dx2 = ((v1->x() - v2->x()) << 8) / (v1->y() - v2->y());
                    x2 = v2->x() + v2Frac * (v1->x() - v2->x()) / (v1->y() - v2->y());
                    fillLines<clip, BottomUp, RightToLeft>(bits, width, height, y1, y2, x1, dx1,
                                                           x2, dx2, value, 0, dd);
                }
            }
        } else {
            // y2 < yC <= y1
            // Center to the right.
            int dx = ((v1->x() - v2->x()) << 8) / (v1->y() - v2->y());
            int xUp, xDn;
            xUp = xDn = v2->x() + (clip == Clip ? (yC << 8) + 0xff - v2->y()
                                                : (center->y() | 0xff) - v2->y())
                        * (v1->x() - v2->x()) / (v1->y() - v2->y());
            fillLines<clip, BottomUp, LeftToRight>(bits, width, height, y2, yC, xUp, dx,
                                                   x2, dx2, value, 0, dd);
            if (yC != y1)
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, yC, y1, xDn, dx,
                                                      x1, dx1, value, 0, dd);
        }
    } else {
        if (y1 < yC) {
            // y1 < yC <= y2
            // Center to the left.
            int dx = ((v1->x() - v2->x()) << 8) / (v1->y() - v2->y());
            int xUp, xDn;
            xUp = xDn = v1->x() + (clip == Clip ? (yC << 8) + 0xff - v1->y()
                                                : (center->y() | 0xff) - v1->y())
                        * (v1->x() - v2->x()) / (v1->y() - v2->y());
            fillLines<clip, BottomUp, RightToLeft>(bits, width, height, y1, yC, x1, dx1,
                                                   xUp, dx, value, 0, dd);
            if (yC != y2)
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, yC, y2, x2, dx2,
                                                      xDn, dx, value, 0, dd);
        } else {
            // Center at the top.
            if (y2 < y1) {
                // yC <= y2 < y1
                // Long right edge.
                if (yC != y2) {
                    d2 = centerFrac * value / (v2->y() - center->y());
                    dd2 = ((value << 8) / (v2->y() - center->y()));
                    fillLines<clip, TopDown, LeftToRight>(bits, width, height, yC, y2, x2, dx2,
                                                          x1, dx1, d2, dd2, dd);
                }
                dx2 = ((v1->x() - v2->x()) << 8) / (v1->y() - v2->y());
                x2 = v2->x() + v2Frac * (v1->x() - v2->x()) / (v1->y() - v2->y());
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, y2, y1, x2, dx2,
                                                      x1, dx1, value, 0, dd);
            } else {
                // Long left edge.
                // yC <= y1 <= y2
                if (yC != y1) {
                    d1 = centerFrac * value / (v1->y() - center->y());
                    dd1 = ((value << 8) / (v1->y() - center->y()));
                    fillLines<clip, TopDown, RightToLeft>(bits, width, height, yC, y1, x2, dx2,
                                                          x1, dx1, d1, dd1, dd);
                }
                if (y1 != y2) {
                    dx1 = ((v1->x() - v2->x()) << 8) / (v1->y() - v2->y());
                    x1 = v1->x() + v1Frac * (v1->x() - v2->x()) / (v1->y() - v2->y());
                    fillLines<clip, TopDown, RightToLeft>(bits, width, height, y1, y2, x2, dx2,
                                                          x1, dx1, value, 0, dd);
                }
            }
        }
    }
}
 
template <FillClip clip>
void drawRectangle(qint32 *bits, int width, int height,
                   const QPoint *int1, const QPoint *center1, const QPoint *ext1,
                   const QPoint *int2, const QPoint *center2, const QPoint *ext2,
                   qint32 extValue)
{
    if (center1->y() > center2->y()) {
        qSwap(center1, center2);
        qSwap(int1, ext2);
        qSwap(ext1, int2);
        extValue = -extValue;
    }
 
    Q_ASSERT(ext1->x() - center1->x() == center1->x() - int1->x());
    Q_ASSERT(ext1->y() - center1->y() == center1->y() - int1->y());
    Q_ASSERT(ext2->x() - center2->x() == center2->x() - int2->x());
    Q_ASSERT(ext2->y() - center2->y() == center2->y() - int2->y());
 
    const int yc1 = clip == Clip ? qBound(0, center1->y() >> 8, height) : center1->y() >> 8;
    const int yc2 = clip == Clip ? qBound(0, center2->y() >> 8, height) : center2->y() >> 8;
    const int yi1 = clip == Clip ? qBound(0, int1->y() >> 8, height) : int1->y() >> 8;
    const int yi2 = clip == Clip ? qBound(0, int2->y() >> 8, height) : int2->y() >> 8;
    const int ye1 = clip == Clip ? qBound(0, ext1->y() >> 8, height) : ext1->y() >> 8;
    const int ye2 = clip == Clip ? qBound(0, ext2->y() >> 8, height) : ext2->y() >> 8;
 
    const int center1Frac = clip == Clip ? (yc1 << 8) + 0xff - center1->y() : ~center1->y() & 0xff;
    const int center2Frac = clip == Clip ? (yc2 << 8) + 0xff - center2->y() : ~center2->y() & 0xff;
    const int int1Frac = clip == Clip ? (yi1 << 8) + 0xff - int1->y() : ~int1->y() & 0xff;
    const int ext1Frac = clip == Clip ? (ye1 << 8) + 0xff - ext1->y() : ~ext1->y() & 0xff;
 
    int dxC = 0, dxE = 0; // cap slope, edge slope
    qint32 ddC = 0;
    if (ext1->y() != int1->y()) {
        dxC = ((ext1->x() - int1->x()) << 8) / (ext1->y() - int1->y());
        ddC = (extValue << 9) / (ext1->y() - int1->y());
    }
    if (ext1->y() != ext2->y())
        dxE = ((ext1->x() - ext2->x()) << 8) / (ext1->y() - ext2->y());
 
    const qint32 div = (ext1->x() - int1->x()) * (ext2->y() - int1->y())
                     - (ext1->y() - int1->y()) * (ext2->x() - int1->x());
    const qint32 dd = div ? qint32((qint64(extValue * (ext2->y() - ext1->y())) << 9) / div) : 0;
 
    int xe1, xe2, xc1, xc2;
    qint32 d;
 
    qint32 intValue = -extValue;
 
    if (center2->x() < center1->x()) {
        // Leaning to the right. '/'
        if (int1->y() < ext2->y()) {
            // Mostly vertical.
            Q_ASSERT(ext1->y() != ext2->y());
            xe1 = ext1->x() + ext1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
            xe2 = int1->x() + int1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
            if (ye1 != yi1) {
                xc2 = center1->x() + center1Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
                xc2 += (ye1 - yc1) * dxC;
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, ye1, yi1, xe1, dxE,
                                                      xc2, dxC, extValue, 0, dd);
            }
            if (yi1 != ye2)
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, yi1, ye2, xe1, dxE,
                                                      xe2, dxE, extValue, 0, dd);
            if (ye2 != yi2) {
                xc1 = center2->x() + center2Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
                xc1 += (ye2 - yc2) * dxC;
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, ye2, yi2, xc1, dxC,
                                                      xe2, dxE, intValue, 0, dd);
            }
        } else {
            // Mostly horizontal.
            Q_ASSERT(ext1->y() != int1->y());
            xc1 = center2->x() + center2Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
            xc2 = center1->x() + center1Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
            xc1 += (ye2 - yc2) * dxC;
            xc2 += (ye1 - yc1) * dxC;
            if (ye1 != ye2) {
                xe1 = ext1->x() + ext1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, ye1, ye2, xe1, dxE,
                                                      xc2, dxC, extValue, 0, dd);
            }
            if (ye2 != yi1) {
                d = (clip == Clip ? (ye2 << 8) + 0xff - center2->y()
                                  : (ext2->y() | 0xff) - center2->y())
                    * 2 * extValue / (ext1->y() - int1->y());
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, ye2, yi1, xc1, dxC,
                                                      xc2, dxC, d, ddC, dd);
            }
            if (yi1 != yi2) {
                xe2 = int1->x() + int1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, yi1, yi2, xc1, dxC,
                                                      xe2, dxE, intValue, 0, dd);
            }
        }
    } else {
        // Leaning to the left. '\'
        if (ext1->y() < int2->y()) {
            // Mostly vertical.
            Q_ASSERT(ext1->y() != ext2->y());
            xe1 = ext1->x() + ext1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
            xe2 = int1->x() + int1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
            if (yi1 != ye1) {
                xc1 = center1->x() + center1Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
                xc1 += (yi1 - yc1) * dxC;
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, yi1, ye1, xc1, dxC,
                                                      xe2, dxE, intValue, 0, dd);
            }
            if (ye1 != yi2)
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, ye1, yi2, xe1, dxE,
                                                      xe2, dxE, intValue, 0, dd);
            if (yi2 != ye2) {
                xc2 = center2->x() + center2Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
                xc2 += (yi2 - yc2) * dxC;
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, yi2, ye2, xe1, dxE,
                                                      xc2, dxC, extValue, 0, dd);
            }
        } else {
            // Mostly horizontal.
            Q_ASSERT(ext1->y() != int1->y());
            xc1 = center1->x() + center1Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
            xc2 = center2->x() + center2Frac * (ext1->x() - int1->x()) / (ext1->y() - int1->y());
            xc1 += (yi1 - yc1) * dxC;
            xc2 += (yi2 - yc2) * dxC;
            if (yi1 != yi2) {
                xe2 = int1->x() + int1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, yi1, yi2, xc1, dxC,
                                                      xe2, dxE, intValue, 0, dd);
            }
            if (yi2 != ye1) {
                d = (clip == Clip ? (yi2 << 8) + 0xff - center2->y()
                                  : (int2->y() | 0xff) - center2->y())
                    * 2 * extValue / (ext1->y() - int1->y());
                fillLines<clip, TopDown, RightToLeft>(bits, width, height, yi2, ye1, xc1, dxC,
                                                      xc2, dxC, d, ddC, dd);
            }
            if (ye1 != ye2) {
                xe1 = ext1->x() + ext1Frac * (ext1->x() - ext2->x()) / (ext1->y() - ext2->y());
                fillLines<clip, TopDown, LeftToRight>(bits, width, height, ye1, ye2, xe1, dxE,
                                                      xc2, dxC, extValue, 0, dd);
            }
        }
    }
}
 
static void drawPolygons(qint32 *bits, int width, int height, const QPoint *vertices,
                         const quint32 *indices, int indexCount, qint32 value)
{
    Q_ASSERT(indexCount != 0);
    typedef QVarLengthArray<quint16, 16> ScanLine;
    QVarLengthArray<ScanLine, 128> scans(height);
    int first = 0;
    for (int i = 1; i < indexCount; ++i) {
        quint32 idx1 = indices[i - 1];
        quint32 idx2 = indices[i];
        Q_ASSERT(idx1 != quint32(-1));
        if (idx2 == quint32(-1)) {
            idx2 = indices[first];
            Q_ASSERT(idx2 != quint32(-1));
            first = ++i;
        }
        const QPoint *v1 = &vertices[idx1];
        const QPoint *v2 = &vertices[idx2];
        if (v2->y() < v1->y())
            qSwap(v1, v2);
        int fromY = qMax(0, v1->y() >> 8);
        int toY = qMin(height, v2->y() >> 8);
        if (fromY >= toY)
            continue;
        int dx = ((v2->x() - v1->x()) << 8) / (v2->y() - v1->y());
        int x = v1->x() + ((fromY << 8) + 0xff - v1->y()) * (v2->x() - v1->x()) / (v2->y() - v1->y());
        for (int y = fromY; y < toY; ++y) {
            quint32 c = quint32(x >> 8);
            if (c < quint32(width))
                scans[y].append(quint16(c));
            x += dx;
        }
    }
    for (int i = 0; i < height; ++i) {
        quint16 *scanline = scans[i].data();
        int size = scans[i].size();
        for (int j = 1; j < size; ++j) {
            int k = j;
            quint16 value = scanline[k];
            for (; k != 0 && value < scanline[k - 1]; --k)
                scanline[k] = scanline[k - 1];
            scanline[k] = value;
        }
        qint32 *line = bits + i * width;
        int j = 0;
        for (; j + 1 < size; j += 2) {
            for (quint16 x = scanline[j]; x < scanline[j + 1]; ++x)
                line[x] = value;
        }
        if (j < size) {
            for (int x = scanline[j]; x < width; ++x)
                line[x] = value;
        }
    }
}
 
static void makeDistanceField(QDistanceFieldData *data, const QPainterPath &path, int dfScale, int offs)
{
    if (!data || !data->data)
        return;
 
    if (path.isEmpty()) {
        memset(data->data, 0, data->nbytes);
        return;
    }
 
    int imgWidth = data->width;
    int imgHeight = data->height;
 
    QTransform transform;
    transform.translate(offs, offs);
    transform.scale(qreal(1) / dfScale, qreal(1) / dfScale);
 
    QDataBuffer<quint32> pathIndices(0);
    QDataBuffer<QPoint> pathVertices(0);
    qSimplifyPath(path, pathVertices, pathIndices, transform);
    if (pathVertices.isEmpty()) {
        qCWarning(lcDistanceField) << "Unexpected glyph path structure, bailing out";
        memset(data->data, 0, data->nbytes);
        return;
    }
 
    const qint32 interiorColor = -0x7f80; // 8:8 signed format, -127.5
    const qint32 exteriorColor = 0x7f80; // 8:8 signed format, 127.5
 
    QScopedArrayPointer<qint32> bits(new qint32[imgWidth * imgHeight]);
    for (int i = 0; i < imgWidth * imgHeight; ++i)
        bits[i] = exteriorColor;
 
    const qreal angleStep = qDegreesToRadians(qreal(15));
    const QPoint rotation(qRound(qCos(angleStep) * 0x4000),
                          qRound(qSin(angleStep) * 0x4000)); // 2:14 signed
 
    const quint32 *indices = pathIndices.data();
    QVarLengthArray<QPoint> normals;
    QVarLengthArray<QPoint> vertices;
 
    QVarLengthArray<int> crossProducts;
    QVarLengthArray<bool> needsClipping;
 
    drawPolygons(bits.data(), imgWidth, imgHeight, pathVertices.data(),
                 indices, pathIndices.size(), interiorColor);
 
    int index = 0;
 
    while (index < pathIndices.size()) {
        normals.clear();
        vertices.clear();
        needsClipping.clear();
 
        // Find end of polygon.
        int end = index;
        while (indices[end] != quint32(-1))
            ++end;
 
        // Calculate vertex normals.
        for (int next = index, prev = end - 1; next < end; prev = next++) {
            quint32 fromVertexIndex = indices[prev];
            quint32 toVertexIndex = indices[next];
 
            const QPoint &from = pathVertices.at(fromVertexIndex);
            const QPoint &to = pathVertices.at(toVertexIndex);
 
            QPoint n(to.y() - from.y(), from.x() - to.x());
            if (n.x() == 0 && n.y() == 0)
                continue;
            int scale = qRound((offs << 16) / qSqrt(qreal(n.x()) * n.x() + qreal(n.y()) * n.y())); // 8:16
            Q_ASSERT(scale != 0);
 
            n.rx() = n.x() * scale >> 8;
            n.ry() = n.y() * scale >> 8;
            normals.append(n);
            QPoint v(to.x() + 0x7f, to.y() + 0x7f);
            vertices.append(v);
            needsClipping.append((to.x() < offs << 8) || (to.x() >= (imgWidth - offs) << 8)
                                 || (to.y() < offs << 8) || (to.y() >= (imgHeight - offs) << 8));
        }
 
        crossProducts.resize(normals.size());
        for (int next = 0, prev = normals.size() - 1; next < normals.size(); prev = next++) {
            crossProducts[prev] = normals.at(prev).x() * normals.at(next).y()
                                - normals.at(prev).y() * normals.at(next).x();
        }
 
        // Draw quads.
        for (int next = 0, prev = normals.size() - 1; next < normals.size(); prev = next++) {
            QPoint n = normals.at(next);
            QPoint intPrev = vertices.at(prev);
            QPoint extPrev = vertices.at(prev);
            QPoint intNext = vertices.at(next);
            QPoint extNext = vertices.at(next);
 
            extPrev.rx() -= n.x();
            extPrev.ry() -= n.y();
            intPrev.rx() += n.x();
            intPrev.ry() += n.y();
            extNext.rx() -= n.x();
            extNext.ry() -= n.y();
            intNext.rx() += n.x();
            intNext.ry() += n.y();
 
            if (needsClipping[prev] || needsClipping[next]) {
                drawRectangle<Clip>(bits.data(), imgWidth, imgHeight,
                                    &intPrev, &vertices.at(prev), &extPrev,
                                    &intNext, &vertices.at(next), &extNext,
                                    exteriorColor);
            } else {
                drawRectangle<NoClip>(bits.data(), imgWidth, imgHeight,
                                      &intPrev, &vertices.at(prev), &extPrev,
                                      &intNext, &vertices.at(next), &extNext,
                                      exteriorColor);
            }
 
            const int crossProduct = crossProducts.at(prev);
            if (crossProduct < 0) {
                QPoint p = extPrev;
                if (needsClipping[prev]) {
                    for (;;) {
                        QPoint rn((n.x() * rotation.x() - n.y() * rotation.y()) >> 14,
                                  (n.y() * rotation.x() + n.x() * rotation.y()) >> 14);
                        n = rn;
                        if (n.x() * normals.at(prev).y() - n.y() * normals.at(prev).x() <= 0) {
                            p.rx() = vertices.at(prev).x() - normals.at(prev).x();
                            p.ry() = vertices.at(prev).y() - normals.at(prev).y();
                            drawTriangle<Clip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                               &extPrev, &p, exteriorColor);
                            break;
                        }
 
                        p.rx() = vertices.at(prev).x() - n.x();
                        p.ry() = vertices.at(prev).y() - n.y();
                        drawTriangle<Clip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                           &extPrev, &p, exteriorColor);
                        extPrev = p;
                    }
                } else {
                    for (;;) {
                        QPoint rn((n.x() * rotation.x() - n.y() * rotation.y()) >> 14,
                                  (n.y() * rotation.x() + n.x() * rotation.y()) >> 14);
                        n = rn;
                        if (n.x() * normals.at(prev).y() - n.y() * normals.at(prev).x() <= 0) {
                            p.rx() = vertices.at(prev).x() - normals.at(prev).x();
                            p.ry() = vertices.at(prev).y() - normals.at(prev).y();
                            drawTriangle<NoClip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                                 &extPrev, &p, exteriorColor);
                            break;
                        }
 
                        p.rx() = vertices.at(prev).x() - n.x();
                        p.ry() = vertices.at(prev).y() - n.y();
                        drawTriangle<NoClip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                             &extPrev, &p, exteriorColor);
                        extPrev = p;
                    }
                }
            } else if (crossProduct > 0) {
                QPoint p = intPrev;
                if (needsClipping[prev]) {
                    for (;;) {
                        QPoint rn((n.x() * rotation.x() + n.y() * rotation.y()) >> 14,
                                  (n.y() * rotation.x() - n.x() * rotation.y()) >> 14);
                        n = rn;
                        if (n.x() * normals.at(prev).y() - n.y() * normals.at(prev).x() >= 0) {
                            p.rx() = vertices.at(prev).x() + normals.at(prev).x();
                            p.ry() = vertices.at(prev).y() + normals.at(prev).y();
                            drawTriangle<Clip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                               &p, &intPrev, interiorColor);
                            break;
                        }
 
                        p.rx() = vertices.at(prev).x() + n.x();
                        p.ry() = vertices.at(prev).y() + n.y();
                        drawTriangle<Clip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                           &p, &intPrev, interiorColor);
                        intPrev = p;
                    }
                } else {
                    for (;;) {
                        QPoint rn((n.x() * rotation.x() + n.y() * rotation.y()) >> 14,
                                  (n.y() * rotation.x() - n.x() * rotation.y()) >> 14);
                        n = rn;
                        if (n.x() * normals.at(prev).y() - n.y() * normals.at(prev).x() >= 0) {
                            p.rx() = vertices.at(prev).x() + normals.at(prev).x();
                            p.ry() = vertices.at(prev).y() + normals.at(prev).y();
                            drawTriangle<NoClip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                                 &p, &intPrev, interiorColor);
                            break;
                        }
 
                        p.rx() = vertices.at(prev).x() + n.x();
                        p.ry() = vertices.at(prev).y() + n.y();
                        drawTriangle<NoClip>(bits.data(), imgWidth, imgHeight, &vertices.at(prev),
                                             &p, &intPrev, interiorColor);
                        intPrev = p;
                    }
                }
            }
        }
 
        index = end + 1;
    }
 
    const qint32 *inLine = bits.data();
    uchar *outLine = data->data;
    for (int y = 0; y < imgHeight; ++y) {
        for (int x = 0; x < imgWidth; ++x, ++inLine, ++outLine)
            *outLine = uchar((0x7f80 - *inLine) >> 8);
    }
}
 
static bool imageHasNarrowOutlines(const QImage &im)
{
    if (im.isNull() || im.width() < 1 || im.height() < 1)
        return false;
    else if (im.width() == 1 || im.height() == 1)
        return true;
 
    int minHThick = 999;
    int minVThick = 999;
 
    int thick = 0;
    bool in = false;
    int y = (im.height() + 1) / 2;
    for (int x = 0; x < im.width(); ++x) {
        int a = qAlpha(im.pixel(x, y));
        if (a > 127) {
            in = true;
            ++thick;
        } else if (in) {
            in = false;
            minHThick = qMin(minHThick, thick);
            thick = 0;
        }
    }
 
    thick = 0;
    in = false;
    int x = (im.width() + 1) / 2;
    for (int y = 0; y < im.height(); ++y) {
        int a = qAlpha(im.pixel(x, y));
        if (a > 127) {
            in = true;
            ++thick;
        } else if (in) {
            in = false;
            minVThick = qMin(minVThick, thick);
            thick = 0;
        }
    }
 
    return minHThick == 1 || minVThick == 1;
}
 
static int QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE = 54;
static int QT_DISTANCEFIELD_DEFAULT_SCALE = 16;
static int QT_DISTANCEFIELD_DEFAULT_RADIUS = 80;
static int QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT = 2000;
 
static void initialDistanceFieldFactor()
{
    static bool initialized = false;
    if (initialized)
        return;
    initialized = true;
 
    if (qEnvironmentVariableIsSet("QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE")) {
        QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE = qEnvironmentVariableIntValue("QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE");
        qCDebug(lcDistanceField) << "set the QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE:" << QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE;
    }
 
    if (qEnvironmentVariableIsSet("QT_DISTANCEFIELD_DEFAULT_SCALE")) {
        QT_DISTANCEFIELD_DEFAULT_SCALE = qEnvironmentVariableIntValue("QT_DISTANCEFIELD_DEFAULT_SCALE");
        qCDebug(lcDistanceField) << "set the QT_DISTANCEFIELD_DEFAULT_SCALE:" << QT_DISTANCEFIELD_DEFAULT_SCALE;
    }
    if (qEnvironmentVariableIsSet("QT_DISTANCEFIELD_DEFAULT_RADIUS")) {
        QT_DISTANCEFIELD_DEFAULT_RADIUS = qEnvironmentVariableIntValue("QT_DISTANCEFIELD_DEFAULT_RADIUS");
        qCDebug(lcDistanceField) << "set the QT_DISTANCEFIELD_DEFAULT_RADIUS:" << QT_DISTANCEFIELD_DEFAULT_RADIUS;
    }
    if (qEnvironmentVariableIsSet("QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT")) {
        QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT = qEnvironmentVariableIntValue("QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT");
        qCDebug(lcDistanceField) << "set the QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT:" << QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT;
    }
}
 
bool qt_fontHasNarrowOutlines(QFontEngine *fontEngine)
{
    initialDistanceFieldFactor();
    QFontEngine *fe = fontEngine->cloneWithSize(QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE);
    if (!fe)
        return false;
 
    QImage im;
 
    const glyph_t glyph = fe->glyphIndex('O');
    if (glyph != 0)
        im = fe->alphaMapForGlyph(glyph, QFixedPoint(), QTransform());
 
    Q_ASSERT(fe->ref.loadRelaxed() == 0);
    delete fe;
 
    return imageHasNarrowOutlines(im);
}
 
bool qt_fontHasNarrowOutlines(const QRawFont &f)
{
    QRawFont font = f;
    initialDistanceFieldFactor();
    font.setPixelSize(QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE);
    if (!font.isValid())
        return false;
 
    QList<quint32> glyphIndices = font.glyphIndexesForString("O"_L1);
    if (glyphIndices.isEmpty() || glyphIndices[0] == 0)
        return false;
 
    return imageHasNarrowOutlines(font.alphaMapForGlyph(glyphIndices.at(0),
                                                        QRawFont::PixelAntialiasing));
}
 
int QT_DISTANCEFIELD_BASEFONTSIZE(bool narrowOutlineFont)
{
    initialDistanceFieldFactor();
 
    if (Q_UNLIKELY(narrowOutlineFont))
        return QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE * 2;
    else
        return QT_DISTANCEFIELD_DEFAULT_BASEFONTSIZE;
}
 
int QT_DISTANCEFIELD_SCALE(bool narrowOutlineFont)
{
    initialDistanceFieldFactor();
 
    if (Q_UNLIKELY(narrowOutlineFont))
        return QT_DISTANCEFIELD_DEFAULT_SCALE / 2;
    else
        return QT_DISTANCEFIELD_DEFAULT_SCALE;
}
 
int QT_DISTANCEFIELD_RADIUS(bool narrowOutlineFont)
{
    initialDistanceFieldFactor();
 
    if (Q_UNLIKELY(narrowOutlineFont))
        return QT_DISTANCEFIELD_DEFAULT_RADIUS / 2;
    else
        return QT_DISTANCEFIELD_DEFAULT_RADIUS;
}
 
int QT_DISTANCEFIELD_HIGHGLYPHCOUNT()
{
    initialDistanceFieldFactor();
    return QT_DISTANCEFIELD_DEFAULT_HIGHGLYPHCOUNT;
}
 
QDistanceFieldData::QDistanceFieldData(const QDistanceFieldData &other)
    : QSharedData(other)
    , glyph(other.glyph)
    , width(other.width)
    , height(other.height)
    , nbytes(other.nbytes)
{
    if (nbytes && other.data)
        data = (uchar *)memcpy(malloc(nbytes), other.data, nbytes);
    else
        data = nullptr;
}
 
QDistanceFieldData::~QDistanceFieldData()
{
    QtPrivate::sizedFree(data, nbytes);
}
 
bool QDistanceFieldData::canAllocateSize(quint64 nbytes)
{
    if (nbytes > INT_MAX) { // int used for bytes internally
        qCWarning(lcDistanceField, "QDistanceFieldData: Rejecting path as size exceeds the upper "
                                   "limit of %i bytes", INT_MAX);
        return false;
    }
 
    if (const int mbLimit = QImageReader::allocationLimit()) {
        if (nbytes > quint64(mbLimit) * 1024 * 1024) {
            qCWarning(lcDistanceField, "QDistanceFieldData: Rejecting path as size exceeds the "
                                       "current allocation limit of %i megabytes", mbLimit);
            return false;
        }
    }
 
    return true;
}
 
QDistanceFieldData *QDistanceFieldData::create(const QSize &size)
{
    QDistanceFieldData *data = new QDistanceFieldData;
 
    if (size.isValid()) {
        data->width = size.width();
        data->height = size.height();
        // pixel data stored as a 1-byte alpha value
        if (canAllocateSize(quint64(data->width) * quint64(data->height))) {
            data->nbytes = data->width * data->height; // tightly packed
            data->data = (uchar *)malloc(data->nbytes);
        } else {
            data->nbytes = 0;
            data->data = nullptr;
        }
    }
 
    return data;
}
 
QDistanceFieldData *QDistanceFieldData::create(QSize size, const QPainterPath &path, bool doubleResolution)
{
    QDistanceFieldData *data = create(size);
    makeDistanceField(data,
                      path,
                      QT_DISTANCEFIELD_SCALE(doubleResolution),
                      QT_DISTANCEFIELD_RADIUS(doubleResolution) / QT_DISTANCEFIELD_SCALE(doubleResolution));
    return data;
}
 
 
QDistanceFieldData *QDistanceFieldData::create(const QPainterPath &path, bool doubleResolution)
{
    int dfMargin = QT_DISTANCEFIELD_RADIUS(doubleResolution) / QT_DISTANCEFIELD_SCALE(doubleResolution);
    int glyphWidth = qCeil(path.boundingRect().width() / QT_DISTANCEFIELD_SCALE(doubleResolution)) + dfMargin * 2;
    int glyphHeight = qCeil(path.boundingRect().height() / QT_DISTANCEFIELD_SCALE(doubleResolution)) + dfMargin * 2;
 
    return create(QSize(glyphWidth, glyphHeight), path, doubleResolution);
}
 
 
QDistanceField::QDistanceField()
    : d(new QDistanceFieldData)
{
}
 
QDistanceField::QDistanceField(int width, int height)
    : d(QDistanceFieldData::create(QSize(width, height)))
{
}
 
QDistanceField::QDistanceField(const QRawFont &font, glyph_t glyph, bool doubleResolution)
{
    setGlyph(font, glyph, doubleResolution);
}
 
QDistanceField::QDistanceField(QFontEngine *fontEngine, glyph_t glyph, bool doubleResolution)
{
    setGlyph(fontEngine, glyph, doubleResolution);
}
 
QDistanceField::QDistanceField(QSize size, const QPainterPath &path, glyph_t glyph, bool doubleResolution)
{
    QPainterPath dfPath = path;
    dfPath.translate(-dfPath.boundingRect().topLeft());
    dfPath.setFillRule(Qt::WindingFill);
 
    d = QDistanceFieldData::create(size, dfPath, doubleResolution);
    d->glyph = glyph;
}
 
QDistanceField::QDistanceField(const QPainterPath &path, glyph_t glyph, bool doubleResolution)
{
    QPainterPath dfPath = path;
    dfPath.translate(-dfPath.boundingRect().topLeft());
    dfPath.setFillRule(Qt::WindingFill);
 
    d = QDistanceFieldData::create(dfPath, doubleResolution);
    d->glyph = glyph;
}
 
 
QDistanceField::QDistanceField(QDistanceFieldData *data)
    : d(data)
{
}
 
bool QDistanceField::isNull() const
{
    return !d->data;
}
 
glyph_t QDistanceField::glyph() const
{
    return d->glyph;
}
 
void QDistanceField::setGlyph(const QRawFont &font, glyph_t glyph, bool doubleResolution)
{
    QRawFont renderFont = font;
    renderFont.setPixelSize(QT_DISTANCEFIELD_BASEFONTSIZE(doubleResolution) * QT_DISTANCEFIELD_SCALE(doubleResolution));
 
    QPainterPath path = renderFont.pathForGlyph(glyph);
    path.translate(-path.boundingRect().topLeft());
    path.setFillRule(Qt::WindingFill);
 
    d = QDistanceFieldData::create(path, doubleResolution);
    d->glyph = glyph;
}
 
void QDistanceField::setGlyph(QFontEngine *fontEngine, glyph_t glyph, bool doubleResolution)
{
    QFixedPoint position;
    QPainterPath path;
    fontEngine->addGlyphsToPath(&glyph, &position, 1, &path, { });
    path.translate(-path.boundingRect().topLeft());
    path.setFillRule(Qt::WindingFill);
 
    d = QDistanceFieldData::create(path, doubleResolution);
    d->glyph = glyph;
}
 
int QDistanceField::width() const
{
    return d->width;
}
 
int QDistanceField::height() const
{
    return d->height;
}
 
QDistanceField QDistanceField::copy(const QRect &r) const
{
    if (isNull())
        return QDistanceField();
 
    if (r.isNull())
        return QDistanceField(new QDistanceFieldData(*d));
 
    int x = r.x();
    int y = r.y();
    int w = r.width();
    int h = r.height();
 
    int dx = 0;
    int dy = 0;
    if (w <= 0 || h <= 0)
        return QDistanceField();
 
    QDistanceField df(w, h);
    if (df.isNull())
        return df;
 
    if (x < 0 || y < 0 || x + w > d->width || y + h > d->height) {
        memset(df.d->data, 0, df.d->nbytes);
        if (x < 0) {
            dx = -x;
            x = 0;
        }
        if (y < 0) {
            dy = -y;
            y = 0;
        }
    }
 
    int pixels_to_copy = qMax(w - dx, 0);
    if (x > d->width)
        pixels_to_copy = 0;
    else if (pixels_to_copy > d->width - x)
        pixels_to_copy = d->width - x;
    int lines_to_copy = qMax(h - dy, 0);
    if (y > d->height)
        lines_to_copy = 0;
    else if (lines_to_copy > d->height - y)
        lines_to_copy = d->height - y;
 
    const uchar *src = d->data + x + y * d->width;
    uchar *dest = df.d->data + dx + dy * df.d->width;
    for (int i = 0; i < lines_to_copy; ++i) {
        memcpy(dest, src, pixels_to_copy);
        src += d->width;
        dest += df.d->width;
    }
 
    df.d->glyph = d->glyph;
 
    return df;
}
 
uchar *QDistanceField::bits()
{
    return d->data;
}
 
const uchar *QDistanceField::bits() const
{
    return d->data;
}
 
const uchar *QDistanceField::constBits() const
{
    return d->data;
}
 
uchar *QDistanceField::scanLine(int i)
{
    if (isNull())
        return nullptr;
 
    Q_ASSERT(i >= 0 && i < d->height);
    return d->data + i * d->width;
}
 
const uchar *QDistanceField::scanLine(int i) const
{
    if (isNull())
        return nullptr;
 
    Q_ASSERT(i >= 0 && i < d->height);
    return d->data + i * d->width;
}
 
const uchar *QDistanceField::constScanLine(int i) const
{
    if (isNull())
        return nullptr;
 
    Q_ASSERT(i >= 0 && i < d->height);
    return d->data + i * d->width;
}
 
QImage QDistanceField::toImage(QImage::Format format) const
{
    if (isNull())
        return QImage();
 
    QImage image(d->width, d->height, qt_depthForFormat(format) == 8 ?
                                      format : QImage::Format_ARGB32_Premultiplied);
    if (image.isNull())
        return image;
 
    if (image.depth() == 8) {
        for (int y = 0; y < d->height; ++y)
            memcpy(image.scanLine(y), scanLine(y), d->width);
    } else {
        for (int y = 0; y < d->height; ++y) {
            for (int x = 0; x < d->width; ++x) {
                uint alpha = *(d->data + x + y * d->width);
                image.setPixel(x, y, alpha << 24);
            }
        }
 
        if (image.format() != format)
            image = std::move(image).convertToFormat(format);
    }
 
    return image;
}
 
QT_END_NAMESPACE