Finding the point of intersection between a line and a QPainterPath - qt

Question

I'm trying to determine the point where a hitscan projectile's path (basically a line, but I've represented it as a QPainterPath in my example) intersects with an item in my scene. I am not sure if there is a way to find this point using the functions provided by QPainterPath, QLineF, etc. The code below illustrates what I'm trying to do:
#include <QtWidgets>
bool hit(const QPainterPath &projectilePath, QGraphicsScene *scene, QPointF &hitPos)
{
const QList<QGraphicsItem *> itemsInPath = scene->items(projectilePath, Qt::IntersectsItemBoundingRect);
if (!itemsInPath.isEmpty()) {
const QPointF projectileStartPos = projectilePath.elementAt(0);
float shortestDistance = std::numeric_limits<float>::max();
QGraphicsItem *closest = 0;
foreach (QGraphicsItem *item, itemsInPath) {
QPointF distanceAsPoint = item->pos() - projectileStartPos;
float distance = abs(distanceAsPoint.x() + distanceAsPoint.y());
if (distance < shortestDistance) {
shortestDistance = distance;
closest = item;
}
}
QPainterPath targetShape = closest->mapToScene(closest->shape());
// hitPos = /* the point at which projectilePath hits targetShape */
hitPos = closest->pos(); // incorrect; always gives top left
qDebug() << projectilePath.intersects(targetShape); // true
qDebug() << projectilePath.intersected(targetShape); // QPainterPath: Element count=0
// To show that they do actually intersect..
QPen p1(Qt::green);
p1.setWidth(2);
QPen p2(Qt::blue);
p2.setWidth(2);
scene->addPath(projectilePath, p1);
scene->addPath(targetShape, p2);
return true;
}
return false;
}
int main(int argc, char *argv[])
{
QApplication app(argc, argv);
QGraphicsView view;
view.setViewportUpdateMode(QGraphicsView::FullViewportUpdate);
QGraphicsScene *scene = new QGraphicsScene;
view.setScene(scene);
view.setHorizontalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
view.setVerticalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
QGraphicsItem *target = scene->addRect(0, 0, 25, 25);
target->setTransformOriginPoint(QPointF(12.5, 12.5));
target->setRotation(35);
target->setPos(100, 100);
QPainterPath projectilePath;
projectilePath.moveTo(200, 200);
projectilePath.lineTo(0, 0);
projectilePath.lineTo(200, 200);
QPointF hitPos;
if (hit(projectilePath, scene, hitPos)) {
scene->addEllipse(hitPos.x() - 2, hitPos.y() - 2, 4, 4, QPen(Qt::red));
}
scene->addPath(projectilePath, QPen(Qt::DashLine));
scene->addText("start")->setPos(180, 150);
scene->addText("end")->setPos(20, 0);
view.show();
return app.exec();
}
projectilePath.intersects(targetShape) returns true, but projectilePath.intersected(targetShape) returns an empty path.
Is there a way to achieve this?

Answer 1

As the answer to Intersection point of QPainterPath and line (find QPainterPath y by x) points out, QPainterPath::intersected() only accounts for paths which have fill areas. The rectangular path trick which is also mentioned there can be implemented like this:
#include <QtWidgets>
/*!
Returns the closest element (position) in \a sourcePath to \a target,
using \l{QPoint::manhattanLength()} to determine the distances.
*/
QPointF closestPointTo(const QPointF &target, const QPainterPath &sourcePath)
{
Q_ASSERT(!sourcePath.isEmpty());
QPointF shortestDistance = sourcePath.elementAt(0) - target;
qreal shortestLength = shortestDistance.manhattanLength();
for (int i = 1; i < sourcePath.elementCount(); ++i) {
const QPointF distance(sourcePath.elementAt(i) - target);
const qreal length = distance.manhattanLength();
if (length < shortestLength) {
shortestDistance = sourcePath.elementAt(i);
shortestLength = length;
}
}
return shortestDistance;
}
/*!
Returns \c true if \a projectilePath intersects with any items in \a scene,
setting \a hitPos to the position of the intersection.
*/
bool hit(const QPainterPath &projectilePath, QGraphicsScene *scene, QPointF &hitPos)
{
const QList<QGraphicsItem *> itemsInPath = scene->items(projectilePath, Qt::IntersectsItemBoundingRect);
if (!itemsInPath.isEmpty()) {
const QPointF projectileStartPos = projectilePath.elementAt(0);
float shortestDistance = std::numeric_limits<float>::max();
QGraphicsItem *closest = 0;
foreach (QGraphicsItem *item, itemsInPath) {
QPointF distanceAsPoint = item->pos() - projectileStartPos;
float distance = abs(distanceAsPoint.x() + distanceAsPoint.y());
if (distance < shortestDistance) {
shortestDistance = distance;
closest = item;
}
}
QPainterPath targetShape = closest->mapToScene(closest->shape());
// QLineF has normalVector(), which is useful for extending our path to a rectangle.
// The path needs to be a rectangle, as QPainterPath::intersected() only accounts
// for intersections between fill areas, which projectilePath doesn't have.
QLineF pathAsLine(projectileStartPos, projectilePath.elementAt(1));
// Extend the first point in the path out by 1 pixel.
QLineF startEdge = pathAsLine.normalVector();
startEdge.setLength(1);
// Swap the points in the line so the normal vector is at the other end of the line.
pathAsLine.setPoints(pathAsLine.p2(), pathAsLine.p1());
QLineF endEdge = pathAsLine.normalVector();
// The end point is currently pointing the wrong way; move it to face the same
// direction as startEdge.
endEdge.setLength(-1);
// Now we can create a rectangle from our edges.
QPainterPath rectPath(startEdge.p1());
rectPath.lineTo(startEdge.p2());
rectPath.lineTo(endEdge.p2());
rectPath.lineTo(endEdge.p1());
rectPath.lineTo(startEdge.p1());
// Visualize the rectangle that we created.
scene->addPath(rectPath, QPen(QBrush(Qt::blue), 2));
// Visualize the intersection of the rectangle with the item.
scene->addPath(targetShape.intersected(rectPath), QPen(QBrush(Qt::cyan), 2));
// The hit position will be the element (point) of the rectangle that is the
// closest to where the projectile was fired from.
hitPos = closestPointTo(projectileStartPos, targetShape.intersected(rectPath));
return true;
}
return false;
}
int main(int argc, char *argv[])
{
QApplication app(argc, argv);
QGraphicsView view;
QGraphicsScene *scene = new QGraphicsScene;
view.setScene(scene);
view.setHorizontalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
view.setVerticalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
QGraphicsItem *target = scene->addRect(0, 0, 25, 25);
target->setTransformOriginPoint(QPointF(12.5, 12.5));
target->setRotation(35);
target->setPos(100, 100);
QPainterPath projectilePath;
projectilePath.moveTo(200, 200);
projectilePath.lineTo(0, 0);
projectilePath.lineTo(200, 200);
QPointF hitPos;
if (hit(projectilePath, scene, hitPos)) {
scene->addEllipse(hitPos.x() - 2, hitPos.y() - 2, 4, 4, QPen(Qt::red));
}
scene->addPath(projectilePath, QPen(Qt::DashLine));
scene->addText("start")->setPos(180, 150);
scene->addText("end")->setPos(20, 0);
view.show();
return app.exec();
}
This has pretty good precision (± 1 pixel, since QLineF::length() is an integer), but there might be a neater way to achieve the same thing.

Answer 2

Just for the record (and if someone else steps here). The above answer is excellent. There's just a little bug in the closestPoint function that may happens if the first point is already the closest one. It should return elementAt(0) instead of elementAt(0) - target.
Here is the fixed function:
QPointF closestPointTo(const QPointF &target, const QPainterPath &sourcePath)
{
Q_ASSERT(!sourcePath.isEmpty());
QPointF shortestDistance;
qreal shortestLength = std::numeric_limits<int>::max();
for (int i = 0; i < sourcePath.elementCount(); ++i) {
const QPointF distance(sourcePath.elementAt(i) - target);
const qreal length = distance.manhattanLength();
if (length < shortestLength) {
shortestDistance = sourcePath.elementAt(i);
shortestLength = length;
}
}
return shortestDistance;
}