qtdeclarative/src/quick/scenegraph/util/qquadpath.cpp

991 lines
34 KiB
C++

// Copyright (C) 2023 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 "qquadpath_p.h"
#include <private/qsgcurveprocessor_p.h>
#include <QtGui/private/qbezier_p.h>
#include <QtMath>
#include <QtCore/QLoggingCategory>
#include <QtCore/QVarLengthArray>
QT_BEGIN_NAMESPACE
static qreal qt_scoreQuadratic(const QBezier &b, QPointF qcp)
{
static bool init = false;
const int numSteps = 21;
Q_STATIC_ASSERT(numSteps % 2 == 1); // numTries must be odd
static qreal t2s[numSteps];
static qreal tmts[numSteps];
if (!init) {
// Precompute bezier factors
qreal t = 0.20;
const qreal step = (1 - (2 * t)) / (numSteps - 1);
for (int i = 0; i < numSteps; i++) {
t2s[i] = t * t;
tmts[i] = 2 * t * (1 - t);
t += step;
}
init = true;
}
const QPointF midPoint = b.midPoint();
auto distForIndex = [&](int i) -> qreal {
QPointF qp = (t2s[numSteps - 1 - i] * b.pt1()) + (tmts[i] * qcp) + (t2s[i] * b.pt4());
QPointF d = midPoint - qp;
return QPointF::dotProduct(d, d);
};
const int halfSteps = (numSteps - 1) / 2;
bool foundIt = false;
const qreal centerDist = distForIndex(halfSteps);
qreal minDist = centerDist;
// Search for the minimum in right half
for (int i = 0; i < halfSteps; i++) {
qreal tDist = distForIndex(halfSteps + 1 + i);
if (tDist < minDist) {
minDist = tDist;
} else {
foundIt = (i > 0);
break;
}
}
if (!foundIt) {
// Search in left half
minDist = centerDist;
for (int i = 0; i < halfSteps; i++) {
qreal tDist = distForIndex(halfSteps - 1 - i);
if (tDist < minDist) {
minDist = tDist;
} else {
foundIt = (i > 0);
break;
}
}
}
return foundIt ? minDist : centerDist;
}
static QPointF qt_quadraticForCubic(const QBezier &b)
{
const QLineF st = b.startTangent();
const QLineF et = b.endTangent();
const QPointF midPoint = b.midPoint();
bool valid = true;
QPointF quadControlPoint;
if (st.intersects(et, &quadControlPoint) == QLineF::NoIntersection) {
valid = false;
} else {
// Check if intersection is on wrong side
const QPointF bl = b.pt4() - b.pt1();
const QPointF ml = midPoint - b.pt1();
const QPointF ql = quadControlPoint - b.pt1();
qreal cx1 = (ml.x() * bl.y()) - (ml.y() * bl.x());
qreal cx2 = (ql.x() * bl.y()) - (ql.y() * bl.x());
valid = (std::signbit(cx1) == std::signbit(cx2));
}
return valid ? quadControlPoint : midPoint;
}
static int qt_getInflectionPoints(const QBezier &orig, qreal *tpoints)
{
auto isValidRoot = [](qreal r) {
return qIsFinite(r) && (r > 0) && (!qFuzzyIsNull(float(r))) && (r < 1)
&& (!qFuzzyIsNull(float(r - 1)));
};
// normalize so pt1.x,pt1.y,pt4.y == 0
QTransform xf;
const QLineF l(orig.pt1(), orig.pt4());
xf.rotate(l.angle());
xf.translate(-orig.pt1().x(), -orig.pt1().y());
const QBezier n = orig.mapBy(xf);
const qreal x2 = n.pt2().x();
const qreal x3 = n.pt3().x();
const qreal x4 = n.pt4().x();
const qreal y2 = n.pt2().y();
const qreal y3 = n.pt3().y();
const qreal p = x3 * y2;
const qreal q = x4 * y2;
const qreal r = x2 * y3;
const qreal s = x4 * y3;
const qreal a = 18 * ((-3 * p) + (2 * q) + (3 * r) - s);
if (qFuzzyIsNull(float(a))) {
if (std::signbit(y2) != std::signbit(y3) && qFuzzyCompare(float(x4 - x3), float(x2))) {
tpoints[0] = 0.5; // approx
return 1;
} else if (!a) {
return 0;
}
}
const qreal b = 18 * (((3 * p) - q) - (3 * r));
const qreal c = 18 * (r - p);
const qreal rad = (b * b) - (4 * a * c);
if (rad < 0)
return 0;
const qreal sqr = qSqrt(rad);
const qreal root1 = (-b + sqr) / (2 * a);
const qreal root2 = (-b - sqr) / (2 * a);
int res = 0;
if (isValidRoot(root1))
tpoints[res++] = root1;
if (root2 != root1 && isValidRoot(root2))
tpoints[res++] = root2;
if (res == 2 && tpoints[0] > tpoints[1])
qSwap(tpoints[0], tpoints[1]);
return res;
}
static void qt_addToQuadratics(const QBezier &b, QPolygonF *p, int maxSplits, qreal maxDiff)
{
QPointF qcp = qt_quadraticForCubic(b);
if (maxSplits <= 0 || qt_scoreQuadratic(b, qcp) < maxDiff) {
p->append(qcp);
p->append(b.pt4());
} else {
QBezier rhs = b;
QBezier lhs;
rhs.parameterSplitLeft(0.5, &lhs);
qt_addToQuadratics(lhs, p, maxSplits - 1, maxDiff);
qt_addToQuadratics(rhs, p, maxSplits - 1, maxDiff);
}
}
static void qt_toQuadratics(const QBezier &b, QPolygonF *out, qreal errorLimit = 0.01)
{
out->resize(0);
out->append(b.pt1());
{
// Shortcut if the cubic is really a quadratic
const qreal f = 3.0 / 2.0;
const QPointF c1 = b.pt1() + f * (b.pt2() - b.pt1());
const QPointF c2 = b.pt4() + f * (b.pt3() - b.pt4());
if (c1 == c2) {
out->append(c1);
out->append(b.pt4());
return;
}
}
const QRectF cpr = b.bounds();
const QPointF dim = cpr.bottomRight() - cpr.topLeft();
qreal maxDiff = QPointF::dotProduct(dim, dim) * errorLimit * errorLimit; // maxdistance^2
qreal infPoints[2];
int numInfPoints = qt_getInflectionPoints(b, infPoints);
const int maxSubSplits = numInfPoints > 0 ? 2 : 3;
qreal t0 = 0;
// number of main segments == #inflectionpoints + 1
for (int i = 0; i < numInfPoints + 1; i++) {
qreal t1 = (i < numInfPoints) ? infPoints[i] : 1;
QBezier segment = b.bezierOnInterval(t0, t1);
qt_addToQuadratics(segment, out, maxSubSplits, maxDiff);
t0 = t1;
}
}
QVector2D QQuadPath::Element::pointAtFraction(float t) const
{
if (isLine()) {
return sp + t * (ep - sp);
} else {
const float r = 1 - t;
return (r * r * sp) + (2 * t * r * cp) + (t * t * ep);
}
}
QQuadPath::Element QQuadPath::Element::segmentFromTo(float t0, float t1) const
{
if (t0 <= 0 && t1 >= 1)
return *this;
Element part;
part.sp = pointAtFraction(t0);
part.ep = pointAtFraction(t1);
if (isLine()) {
part.cp = 0.5f * (part.sp + part.ep);
part.m_isLine = true;
} else {
// Split curve right at t0, yields { t0, rcp, endPoint } quad segment
const QVector2D rcp = (1 - t0) * controlPoint() + t0 * endPoint();
// Split that left at t1, yields { t0, lcp, t1 } quad segment
float segmentT = (t1 - t0) / (1 - t0);
part.cp = (1 - segmentT) * part.sp + segmentT * rcp;
}
return part;
}
QQuadPath::Element QQuadPath::Element::reversed() const {
Element swappedElement;
swappedElement.ep = sp;
swappedElement.cp = cp;
swappedElement.sp = ep;
swappedElement.m_isLine = m_isLine;
return swappedElement;
}
float QQuadPath::Element::extent() const
{
// TBD: cache this value if we start using it a lot
QVector2D min(qMin(sp.x(), ep.x()), qMin(sp.y(), ep.y()));
QVector2D max(qMax(sp.x(), ep.x()), qMax(sp.y(), ep.y()));
if (!isLine()) {
min = QVector2D(qMin(min.x(), cp.x()), qMin(min.y(), cp.y()));
max = QVector2D(qMax(max.x(), cp.x()), qMax(max.y(), cp.y()));
}
return (max - min).length();
}
// Returns the number of intersections between element and a horizontal line at y.
// The t values of max 2 intersection(s) are stored in the fractions array
int QQuadPath::Element::intersectionsAtY(float y, float *fractions, bool swapXY) const
{
Q_ASSERT(!isLine());
auto getY = [=](QVector2D p) -> float { return swapXY ? -p.x() : p.y(); };
const float y0 = getY(startPoint()) - y;
const float y1 = getY(controlPoint()) - y;
const float y2 = getY(endPoint()) - y;
int numRoots = 0;
const float a = y0 - (2 * y1) + y2;
if (a) {
const float b = (y1 * y1) - (y0 * y2);
if (b >= 0) {
const float sqr = qSqrt(b);
const float root1 = -(-y0 + y1 + sqr) / a;
if (qIsFinite(root1) && root1 >= 0 && root1 <= 1)
fractions[numRoots++] = root1;
const float root2 = (y0 - y1 + sqr) / a;
if (qIsFinite(root2) && root2 != root1 && root2 >= 0 && root2 <= 1)
fractions[numRoots++] = root2;
}
} else if (y1 != y2) {
const float root1 = (y2 - (2 * y1)) / (2 * (y2 - y1));
if (qIsFinite(root1) && root1 >= 0 && root1 <= 1)
fractions[numRoots++] = root1;
}
return numRoots;
}
static float crossProduct(const QVector2D &sp, const QVector2D &p, const QVector2D &ep)
{
QVector2D v1 = ep - sp;
QVector2D v2 = p - sp;
return (v2.x() * v1.y()) - (v2.y() * v1.x());
}
bool QQuadPath::isPointOnLeft(const QVector2D &p, const QVector2D &sp, const QVector2D &ep)
{
// Use cross product to compare directions of base vector and vector from start to p
return crossProduct(sp, p, ep) >= 0.0f;
}
bool QQuadPath::isPointOnLine(const QVector2D &p, const QVector2D &sp, const QVector2D &ep)
{
return qFuzzyIsNull(crossProduct(sp, p, ep));
}
// Assumes sp != ep
bool QQuadPath::isPointNearLine(const QVector2D &p, const QVector2D &sp, const QVector2D &ep)
{
// epsilon is max length of p-to-baseline relative to length of baseline. So 0.01 means that
// the distance from p to the baseline must be less than 1% of the length of the baseline.
constexpr float epsilon = 0.01f;
QVector2D bv = ep - sp;
float bl2 = QVector2D::dotProduct(bv, bv);
float t = QVector2D::dotProduct(p - sp, bv) / bl2;
QVector2D pv = p - (sp + t * bv);
return (QVector2D::dotProduct(pv, pv) / bl2) < (epsilon * epsilon);
}
QVector2D QQuadPath::closestPointOnLine(const QVector2D &p, const QVector2D &sp, const QVector2D &ep)
{
QVector2D line = ep - sp;
float t = QVector2D::dotProduct(p - sp, line) / QVector2D::dotProduct(line, line);
return sp + qBound(0.0f, t, 1.0f) * line;
}
// NOTE: it is assumed that subpaths are closed
bool QQuadPath::contains(const QVector2D &point) const
{
return contains(point, 0, elementCount() - 1);
}
bool QQuadPath::contains(const QVector2D &point, int fromIndex, int toIndex) const
{
// if (!controlPointRect().contains(pt) : good opt when we add cpr caching
// return false;
int winding_number = 0;
for (int ei = fromIndex; ei <= toIndex; ei++) {
const Element &e = m_elements.at(ei);
int dir = 1;
float y1 = e.startPoint().y();
float y2 = e.endPoint().y();
if (y2 < y1) {
qSwap(y1, y2);
dir = -1;
}
if (e.m_isLine) {
if (point.y() < y1 || point.y() >= y2 || y1 == y2)
continue;
const float t = (point.y() - e.startPoint().y()) / (e.endPoint().y() - e.startPoint().y());
const float x = e.startPoint().x() + t * (e.endPoint().x() - e.startPoint().x());
if (x <= point.x())
winding_number += dir;
} else {
y1 = qMin(y1, e.controlPoint().y());
y2 = qMax(y2, e.controlPoint().y());
if (point.y() < y1 || point.y() >= y2)
continue;
float ts[2];
const int numRoots = e.intersectionsAtY(point.y(), ts);
// Count if there is exactly one intersection to the left
bool oneHit = false;
float tForHit = -1;
for (int i = 0; i < numRoots; i++) {
if (e.pointAtFraction(ts[i]).x() <= point.x()) {
oneHit = !oneHit;
tForHit = ts[i];
}
}
if (oneHit) {
dir = e.tangentAtFraction(tForHit).y() < 0 ? -1 : 1;
winding_number += dir;
}
}
};
return (fillRule() == Qt::WindingFill ? (winding_number != 0) : ((winding_number % 2) != 0));
}
// similar as contains. But we treat the element with the index elementIdx in a special way
// that should be numerically more stable. The result is a contains for a point on the left
// and for the right side of the element.
QQuadPath::Element::FillSide QQuadPath::fillSideOf(int elementIdx, float elementT) const
{
constexpr float toleranceT = 1e-3f;
const QVector2D point = m_elements.at(elementIdx).pointAtFraction(elementT);
const QVector2D tangent = m_elements.at(elementIdx).tangentAtFraction(elementT);
const bool swapXY = qAbs(tangent.x()) > qAbs(tangent.y());
auto getX = [=](QVector2D p) -> float { return swapXY ? p.y() : p.x(); };
auto getY = [=](QVector2D p) -> float { return swapXY ? -p.x() : p.y(); };
int winding_number = 0;
for (int i = 0; i < elementCount(); i++) {
const Element &e = m_elements.at(i);
int dir = 1;
float y1 = getY(e.startPoint());
float y2 = getY(e.endPoint());
if (y2 < y1) {
qSwap(y1, y2);
dir = -1;
}
if (e.m_isLine) {
if (getY(point) < y1 || getY(point) >= y2 || y1 == y2)
continue;
const float t = (getY(point) - getY(e.startPoint())) / (getY(e.endPoint()) - getY(e.startPoint()));
const float x = getX(e.startPoint()) + t * (getX(e.endPoint()) - getX(e.startPoint()));
if (x <= getX(point) && (i != elementIdx || qAbs(t - elementT) > toleranceT))
winding_number += dir;
} else {
y1 = qMin(y1, getY(e.controlPoint()));
y2 = qMax(y2, getY(e.controlPoint()));
if (getY(point) < y1 || getY(point) >= y2)
continue;
float ts[2];
const int numRoots = e.intersectionsAtY(getY(point), ts, swapXY);
// Count if there is exactly one intersection to the left
bool oneHit = false;
float tForHit = -1;
for (int j = 0; j < numRoots; j++) {
const float x = getX(e.pointAtFraction(ts[j]));
if (x <= getX(point) && (i != elementIdx || qAbs(ts[j] - elementT) > toleranceT)) {
oneHit = !oneHit;
tForHit = ts[j];
}
}
if (oneHit) {
dir = getY(e.tangentAtFraction(tForHit)) < 0 ? -1 : 1;
winding_number += dir;
}
}
};
int left_winding_number = winding_number;
int right_winding_number = winding_number;
int dir = getY(tangent) < 0 ? -1 : 1;
if (dir > 0)
left_winding_number += dir;
else
right_winding_number += dir;
bool leftInside = (fillRule() == Qt::WindingFill ? (left_winding_number != 0) : ((left_winding_number % 2) != 0));
bool rightInside = (fillRule() == Qt::WindingFill ? (right_winding_number != 0) : ((right_winding_number % 2) != 0));
if (leftInside && rightInside)
return QQuadPath::Element::FillSideBoth;
else if (leftInside)
return QQuadPath::Element::FillSideLeft;
else if (rightInside)
return QQuadPath::Element::FillSideRight;
else
return QQuadPath::Element::FillSideUndetermined; //should not happen except for numerical error.
}
void QQuadPath::addElement(const QVector2D &control, const QVector2D &endPoint, bool isLine)
{
if (qFuzzyCompare(m_currentPoint, endPoint))
return; // 0 length element, skip
isLine = isLine || isPointNearLine(control, m_currentPoint, endPoint); // Turn flat quad into line
if (!m_subPathToStart) {
Q_ASSERT(!m_elements.isEmpty());
m_elements.last().m_isSubpathEnd = false;
}
m_elements.resize(m_elements.size() + 1);
Element &elem = m_elements.last();
elem.sp = m_currentPoint;
elem.cp = isLine ? (0.5f * (m_currentPoint + endPoint)) : control;
elem.ep = endPoint;
elem.m_isLine = isLine;
elem.m_isSubpathStart = m_subPathToStart;
m_subPathToStart = false;
elem.m_isSubpathEnd = true;
m_currentPoint = endPoint;
}
void QQuadPath::addElement(const Element &e)
{
m_subPathToStart = false;
m_currentPoint = e.endPoint();
m_elements.append(e);
}
#if !defined(QQUADPATH_CONVEX_CHECK_ERROR_MARGIN)
# define QQUICKSHAPECURVERENDERER_CONVEX_CHECK_ERROR_MARGIN (1.0f / 32.0f)
#endif
QQuadPath::Element::FillSide QQuadPath::coordinateOrderOfElement(const QQuadPath::Element &element) const
{
QVector2D baseLine = element.endPoint() - element.startPoint();
QVector2D midPoint = element.midPoint();
// At the midpoint, the tangent of a quad is parallel to the baseline
QVector2D normal = QVector2D(-baseLine.y(), baseLine.x()).normalized();
float delta = qMin(element.extent() / 100, QQUICKSHAPECURVERENDERER_CONVEX_CHECK_ERROR_MARGIN);
QVector2D offset = (normal * delta);
bool pathContainsPointToRight = contains(midPoint + offset);
bool pathContainsPointToLeft = contains(midPoint - offset);
Element::FillSide res = Element::FillSideUndetermined;
if (pathContainsPointToRight)
res = (pathContainsPointToLeft ? Element::FillSideBoth : Element::FillSideRight);
else if (pathContainsPointToLeft)
res = Element::FillSideLeft;
return res;
}
QQuadPath QQuadPath::fromPainterPath(const QPainterPath &path, PathHints hints)
{
QQuadPath res;
res.reserve(path.elementCount());
res.setFillRule(path.fillRule());
const bool isQuadratic = hints & PathQuadratic;
QPolygonF quads;
QPointF sp;
for (int i = 0; i < path.elementCount(); ++i) {
QPainterPath::Element element = path.elementAt(i);
QPointF ep(element);
switch (element.type) {
case QPainterPath::MoveToElement:
res.moveTo(QVector2D(ep));
break;
case QPainterPath::LineToElement:
res.lineTo(QVector2D(ep));
break;
case QPainterPath::CurveToElement: {
QPointF cp1 = ep;
QPointF cp2(path.elementAt(++i));
ep = path.elementAt(++i);
if (isQuadratic) {
const qreal f = 3.0 / 2.0;
const QPointF cp = sp + f * (cp1 - sp);
res.quadTo(QVector2D(cp), QVector2D(ep));
} else {
QBezier b = QBezier::fromPoints(sp, cp1, cp2, ep);
qt_toQuadratics(b, &quads);
for (int i = 1; i < quads.size(); i += 2) {
QVector2D cp(quads[i]);
QVector2D ep(quads[i + 1]);
res.quadTo(cp, ep);
}
}
break;
}
default:
Q_UNREACHABLE();
break;
}
sp = ep;
}
res.setPathHints(hints | PathQuadratic);
return res;
}
void QQuadPath::addCurvatureData()
{
// We use the convention that the inside of a curve is on the *right* side of the
// direction of the baseline.Thus, as long as this is true: if the control point is
// on the left side of the baseline, the curve is convex and otherwise it is
// concave. The paths we get can be arbitrary order, but each subpath will have a
// consistent order. Therefore, for the first curve element in a subpath, we can
// determine if the direction already follows the convention or not, and then we
// can easily detect curvature of all subsequent elements in the subpath.
auto isSingleSided = [](Element::FillSide fillSide) {
return fillSide == Element::FillSideLeft || fillSide == Element::FillSideRight;
};
auto flagFromFillSide = [](Element::FillSide fillSide) {
if (fillSide == Element::FillSideRight || fillSide == Element::FillSideBoth)
return Element::FillOnRight;
else
return Element::CurvatureUndetermined;
};
static bool checkAnomaly = qEnvironmentVariableIntValue("QT_QUICKSHAPES_CHECK_ALL_CURVATURE") != 0;
const bool pathHasFillOnRight = testHint(PathFillOnRight);
Element::CurvatureFlags flags = Element::CurvatureUndetermined;
for (int i = 0; i < m_elements.size(); i++) {
QQuadPath::Element &element = m_elements[i];
Q_ASSERT(element.childCount() == 0);
if (element.isSubpathStart()) {
if (pathHasFillOnRight && !checkAnomaly) {
flags = Element::FillOnRight;
} else {
Element::FillSide fillSide = Element::FillSideUndetermined;
for (int j = i; !isSingleSided(fillSide) && j < m_elements.size(); j++) {
const QQuadPath::Element &subElem = m_elements.at(j);
if (j > i && subElem.isSubpathStart())
break;
fillSide = coordinateOrderOfElement(subElem);
}
flags = flagFromFillSide(fillSide);
}
} else if (checkAnomaly) {
Element::FillSide fillSide = coordinateOrderOfElement(element);
if (isSingleSided(fillSide)) {
Element::CurvatureFlags newFlags = flagFromFillSide(fillSide);
if (flags != newFlags) {
qCDebug(lcSGCurveProcessor)
<< "Curvature anomaly detected:" << element
<< "Subpath fill on right:" << (flags & Element::FillOnRight)
<< "Element fill on right:" << (newFlags & Element::FillOnRight);
flags = newFlags;
}
}
}
if (element.isLine()) {
element.m_curvatureFlags = flags;
} else {
bool controlPointOnLeft = element.isControlPointOnLeft();
bool isFillOnRight = flags & Element::FillOnRight;
bool isConvex = controlPointOnLeft == isFillOnRight;
if (isConvex)
element.m_curvatureFlags = Element::CurvatureFlags(flags | Element::Convex);
else
element.m_curvatureFlags = flags;
}
}
}
QRectF QQuadPath::controlPointRect() const
{
QRectF res;
if (elementCount()) {
QVector2D min, max;
min = max = m_elements.constFirst().sp;
// No need to recurse, as split curve's controlpoints are within the parent curve's
for (const QQuadPath::Element &e : std::as_const(m_elements)) {
min.setX(std::min({ min.x(), e.sp.x(), e.cp.x(), e.ep.x() }));
min.setY(std::min({ min.y(), e.sp.y(), e.cp.y(), e.ep.y() }));
max.setX(std::max({ max.x(), e.sp.x(), e.cp.x(), e.ep.x() }));
max.setY(std::max({ max.y(), e.sp.y(), e.cp.y(), e.ep.y() }));
}
res = QRectF(min.toPointF(), max.toPointF());
}
return res;
}
// Count leaf elements
int QQuadPath::elementCountRecursive() const
{
int count = 0;
iterateElements([&](const QQuadPath::Element &, int) { count++; });
return count;
}
QPainterPath QQuadPath::toPainterPath() const
{
// Currently only converts the main, unsplit path; no need for the split path identified
QPainterPath res;
res.reserve(elementCount());
res.setFillRule(fillRule());
for (const Element &element : m_elements) {
if (element.m_isSubpathStart)
res.moveTo(element.startPoint().toPointF());
if (element.m_isLine)
res.lineTo(element.endPoint().toPointF());
else
res.quadTo(element.controlPoint().toPointF(), element.endPoint().toPointF());
};
return res;
}
QString QQuadPath::asSvgString() const
{
QString res;
QTextStream str(&res);
for (const Element &element : m_elements) {
if (element.isSubpathStart())
str << "M " << element.startPoint().x() << " " << element.startPoint().y() << " ";
if (element.isLine())
str << "L " << element.endPoint().x() << " " << element.endPoint().y() << " ";
else
str << "Q " << element.controlPoint().x() << " " << element.controlPoint().y() << " "
<< element.endPoint().x() << " " << element.endPoint().y() << " ";
}
return res;
}
// Returns a new path since doing it inline would probably be less efficient
// (technically changing it from O(n) to O(n^2))
// Note that this function should be called before splitting any elements,
// so we can assume that the structure is a list and not a tree
QQuadPath QQuadPath::subPathsClosed(bool *didClose) const
{
Q_ASSERT(m_childElements.isEmpty());
bool closed = false;
QQuadPath res = *this;
res.m_subPathToStart = false;
res.m_elements = {};
res.m_elements.reserve(elementCount());
int subStart = -1;
int prevElement = -1;
for (int i = 0; i < elementCount(); i++) {
const auto &element = m_elements.at(i);
if (element.m_isSubpathStart) {
if (subStart >= 0 && m_elements[i - 1].ep != m_elements[subStart].sp) {
res.m_currentPoint = m_elements[i - 1].ep;
res.lineTo(m_elements[subStart].sp);
closed = true;
auto &endElement = res.m_elements.last();
endElement.m_isSubpathEnd = true;
// lineTo() can bail out if the points are too close.
// In that case, just change the end point to be equal to the start
// (No need to test because the assignment is a no-op otherwise).
endElement.ep = m_elements[subStart].sp;
} else if (prevElement >= 0) {
res.m_elements[prevElement].m_isSubpathEnd = true;
}
subStart = i;
}
res.m_elements.append(element);
prevElement = res.m_elements.size() - 1;
}
if (subStart >= 0 && m_elements.last().ep != m_elements[subStart].sp) {
res.m_currentPoint = m_elements.last().ep;
res.lineTo(m_elements[subStart].sp);
closed = true;
}
if (!res.m_elements.isEmpty()) {
auto &endElement = res.m_elements.last();
endElement.m_isSubpathEnd = true;
endElement.ep = m_elements[subStart].sp;
}
if (didClose)
*didClose = closed;
return res;
}
QQuadPath QQuadPath::flattened() const
{
QQuadPath res;
res.reserve(elementCountRecursive());
iterateElements([&](const QQuadPath::Element &elem, int) { res.m_elements.append(elem); });
res.setPathHints(pathHints());
res.setFillRule(fillRule());
return res;
}
class ElementCutter
{
public:
ElementCutter(const QQuadPath::Element &element)
: m_element(element)
{
m_currentPoint = m_element.startPoint();
if (m_element.isLine())
m_lineLength = (m_element.endPoint() - m_element.startPoint()).length();
else
fillLUT();
}
bool consume(float length)
{
m_lastT = m_currentT;
m_lastPoint = m_currentPoint;
float nextCut = m_consumed + length;
float cutT = m_element.isLine() ? nextCut / m_lineLength : tForLength(nextCut);
if (cutT < 1) {
m_currentT = cutT;
m_currentPoint = m_element.pointAtFraction(m_currentT);
m_consumed = nextCut;
return true;
} else {
m_currentT = 1;
m_currentPoint = m_element.endPoint();
return false;
}
}
QVector2D currentCutPoint()
{
return m_currentPoint;
}
QVector2D currentControlPoint()
{
Q_ASSERT(!m_element.isLine());
// Split curve right at lastT, yields { lastPoint, rcp, endPoint } quad segment
QVector2D rcp = (1 - m_lastT) * m_element.controlPoint() + m_lastT * m_element.endPoint();
// Split that left at currentT, yields { lastPoint, lcp, currentPoint } quad segment
float segmentT = (m_currentT - m_lastT) / (1 - m_lastT);
QVector2D lcp = (1 - segmentT) * m_lastPoint + segmentT * rcp;
return lcp;
}
float lastLength()
{
float elemLength = m_element.isLine() ? m_lineLength : m_lut.last();
return elemLength - m_consumed;
}
private:
void fillLUT()
{
Q_ASSERT(!m_element.isLine());
QVector2D ap = m_element.startPoint() - 2 * m_element.controlPoint() + m_element.endPoint();
QVector2D bp = 2 * m_element.controlPoint() - 2 * m_element.startPoint();
float A = 4 * QVector2D::dotProduct(ap, ap);
float B = 4 * QVector2D::dotProduct(ap, bp);
float C = QVector2D::dotProduct(bp, bp);
float b = B / (2 * A);
float c = C / A;
float k = c - (b * b);
float l2 = b * std::sqrt(b * b + k);
float lnom = b + std::sqrt(b * b + k);
float l0 = 0.5f * std::sqrt(A);
m_lut.resize(LUTSize, 0);
for (int i = 1; i < LUTSize; i++) {
float t = float(i) / (LUTSize - 1);
float u = t + b;
float w = std::sqrt(u * u + k);
float l1 = u * w;
float lden = u + w;
float l3 = k * std::log(std::fabs(lden / lnom));
float res = l0 * (l1 - l2 + l3);
m_lut[i] = res;
}
}
float tForLength(float length)
{
Q_ASSERT(!m_element.isLine());
Q_ASSERT(!m_lut.isEmpty());
float res = 2; // I.e. invalid, outside [0, 1] range
auto it = std::upper_bound(m_lut.cbegin(), m_lut.cend(), length);
if (it != m_lut.cend()) {
float nextLength = *it--;
float prevLength = *it;
int prevIndex = std::distance(m_lut.cbegin(), it);
float fraction = (length - prevLength) / (nextLength - prevLength);
res = (prevIndex + fraction) / (LUTSize - 1);
}
return res;
}
const QQuadPath::Element &m_element;
float m_lastT = 0;
float m_currentT = 0;
QVector2D m_lastPoint;
QVector2D m_currentPoint;
float m_consumed = 0;
// For line elements:
float m_lineLength;
// For quadratic curve elements:
static constexpr int LUTSize = 21;
QVarLengthArray<float, LUTSize> m_lut;
};
QQuadPath QQuadPath::dashed(qreal lineWidth, const QList<qreal> &dashPattern, qreal dashOffset) const
{
QVarLengthArray<float, 16> pattern;
float patternLength = 0;
for (int i = 0; i < 2 * (dashPattern.length() / 2); i++) {
float dashLength = qMax(lineWidth * dashPattern[i], qreal(0));
pattern.append(dashLength);
patternLength += dashLength;
}
if (patternLength == 0)
return {};
int startIndex = 0;
float startOffset = std::fmod(lineWidth * dashOffset, patternLength);
if (startOffset < 0)
startOffset += patternLength;
for (float dashLength : pattern) {
if (dashLength > startOffset)
break;
startIndex = (startIndex + 1) % pattern.size(); // The % guards against accuracy issues
startOffset -= dashLength;
}
int dashIndex = startIndex;
float offset = startOffset;
QQuadPath res;
for (int i = 0; i < elementCount(); i++) {
const Element &element = elementAt(i);
if (element.isSubpathStart()) {
res.moveTo(element.startPoint());
dashIndex = startIndex;
offset = startOffset;
}
ElementCutter cutter(element);
while (true) {
bool gotAll = cutter.consume(pattern.at(dashIndex) - offset);
QVector2D nextPoint = cutter.currentCutPoint();
if (dashIndex & 1)
res.moveTo(nextPoint); // gap
else if (element.isLine())
res.lineTo(nextPoint); // dash in line
else
res.quadTo(cutter.currentControlPoint(), nextPoint); // dash in curve
if (gotAll) {
offset = 0;
dashIndex = (dashIndex + 1) % pattern.size();
} else {
offset += cutter.lastLength();
break;
}
}
}
res.setFillRule(fillRule());
res.setPathHints(pathHints());
return res;
}
void QQuadPath::splitElementAt(int index)
{
const int newChildIndex = m_childElements.size();
m_childElements.resize(newChildIndex + 2);
Element &parent = elementAt(index);
parent.m_numChildren = 2;
parent.m_firstChildIndex = newChildIndex;
Element &quad1 = m_childElements[newChildIndex];
const QVector2D mp = parent.midPoint();
quad1.sp = parent.sp;
quad1.cp = 0.5f * (parent.sp + parent.cp);
quad1.ep = mp;
quad1.m_isSubpathStart = parent.m_isSubpathStart;
quad1.m_isSubpathEnd = false;
quad1.m_curvatureFlags = parent.m_curvatureFlags;
quad1.m_isLine = parent.m_isLine; //### || isPointNearLine(quad1.cp, quad1.sp, quad1.ep);
Element &quad2 = m_childElements[newChildIndex + 1];
quad2.sp = mp;
quad2.cp = 0.5f * (parent.ep + parent.cp);
quad2.ep = parent.ep;
quad2.m_isSubpathStart = false;
quad2.m_isSubpathEnd = parent.m_isSubpathEnd;
quad2.m_curvatureFlags = parent.m_curvatureFlags;
quad2.m_isLine = parent.m_isLine; //### || isPointNearLine(quad2.cp, quad2.sp, quad2.ep);
#ifndef QT_NO_DEBUG
if (qFuzzyCompare(quad1.sp, quad1.ep) || qFuzzyCompare(quad2.sp, quad2.ep))
qCDebug(lcSGCurveProcessor) << "Splitting has resulted in ~null quad";
#endif
}
static void printElement(QDebug stream, const QQuadPath::Element &element)
{
auto printPoint = [&](QVector2D p) { stream << "(" << p.x() << ", " << p.y() << ") "; };
stream << "{ ";
printPoint(element.startPoint());
printPoint(element.controlPoint());
printPoint(element.endPoint());
stream << "} " << (element.isLine() ? "L " : "C ") << (element.isConvex() ? "X " : "O ")
<< (element.isFillOnRight() ? "R " : "L ")
<< (element.isSubpathStart() ? "S" : element.isSubpathEnd() ? "E" : "");
}
#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug stream, const QQuadPath::Element &element)
{
QDebugStateSaver saver(stream);
stream.nospace();
stream << "QuadPath::Element( ";
printElement(stream, element);
stream << " )";
return stream;
}
QDebug operator<<(QDebug stream, const QQuadPath &path)
{
QDebugStateSaver saver(stream);
stream.nospace();
stream << "QuadPath(" << path.elementCount() << " main elements, "
<< path.elementCountRecursive() << " leaf elements, "
<< (path.fillRule() == Qt::OddEvenFill ? "OddEven" : "Winding")
<< ", hints: " << path.pathHints() << Qt::endl;
int count = 0;
path.iterateElements([&](const QQuadPath::Element &e, int) {
stream << " " << count++ << (e.isSubpathStart() ? ">" : e.isSubpathEnd() ? "<" : " ");
printElement(stream, e);
stream << Qt::endl;
});
stream << ")";
return stream;
}
#endif
QT_END_NAMESPACE