# How to find if two polygons intersect

• I'm having difficulty finding out if two polygons (or two lines for that matter) intersect. Would appreciate some help.

Here's my code.

@void Grid::onPaint()
{
QPainterPath path = createPath();
QDesktopWidget *widget = QApplication::desktop();
QScreen *screen = QApplication::screens().at(widget->primaryScreen());
QPainter painter(this);
double ppi = screen->physicalDotsPerInch();
double ascender = ((m_nib * m_ascender.spacing) / grid::MMToInch) * ppi;
double chgt = ((m_nib * m_capHgt.spacing) / grid::MMToInch) * ppi;
double xhgt = ((m_nib * m_xHgt.spacing) / grid::MMToInch) * ppi;
double des = ((m_nib * m_descender.spacing) / grid::MMToInch) * ppi;
double percent = 0;
qreal slantLinePixels = ((m_nib * m_slantLine.spacing) / grid::MMToInch) * ppi + 1;
qreal pctIncrease = (slantLinePixels + 10) / path.length();

``````while (percent + pctIncrease <= 1)
{
QPointF point = path.pointAtPercent(percentageOffset(percent));
qreal angle = (m_baselineConstraints == BaselineConstraints::StaticAngle) ? 0 : path.angleAtPercent(percentageOffset(percent));

qreal realSlantAngle = angle + m_slantLine.angle;
QLineF b, xh, ch, a, d, db, bxh, xhch, cha, ach, chxh, xhb, bd;
b.setP1(point);
b.setAngle(angle);
b.setLength(slantLinePixels);
bxh.setP1(b.p1());
bxh.setLength(xhgt);
bxh.setAngle(realSlantAngle);
xhch.setP1(bxh.p2());
xhch.setLength(chgt);
xhch.setAngle(realSlantAngle);
cha.setP1(xhch.p2());
cha.setLength(ascender);
cha.setAngle(realSlantAngle);
a.setP1(cha.p2());
a.setAngle(angle);
a.setLength(slantLinePixels);
ch.setP1(xhch.p2());
ch.setLength(slantLinePixels);
ch.setAngle(angle);
ach.setP1(a.p2());
ach.setP2(ch.p2());
xh.setP1(bxh.p2());
xh.setLength(slantLinePixels);
xh.setAngle(angle);
chxh.setP1(ch.p2());
chxh.setP2(xh.p2());
xhb.setP1(xh.p2());
xhb.setP2(b.p2());
bd.setP1(b.p2());
bd.setLength(des);
bd.setAngle(xhb.angle());
d.setP1(bd.p2());
d.setLength(slantLinePixels);
d.setAngle(((angle < 180) ? angle + 180 : angle - 180));
db.setP1(d.p2());
db.setP2(b.p1());

QLineF slant1(db.p1(), a.p1());
QLineF slant2(d.p1(), a.p2());

QPainterPath path2;
QPolygonF poly;
poly << db.p1() << a.p1() << a.p2() << d.p1() << db.p1();

foreach (QPainterPath p, m_lines) {
if (p.intersects(path2))
{
percent += .01;
continue;
}
}

m_lines.append(path2);
QPen pen = painter.pen();
pen.setColor(Qt::black);
painter.setPen(pen);

painter.drawLine(b);

drawLine(slant1, m_slantLine, painter);
drawLine(slant2, m_slantLine, painter);
drawLine(a, m_ascender, painter);
drawLine(ch, m_capHgt, painter);
drawLine(xh, m_xHgt, painter);
drawLine(d, m_descender, painter);

percent += pctIncrease;
}
m_lines.clear();
``````

}

@

Obviously this is brute force. I've tried using QPolygon::intersected() with each polygon against every other polygon and QLineF::intersect() with every other line. I don't know why nothing like this works. I would like to use QPainter::translate() and QPainter::rotate(), but that's even harder (how do I keep up with the translated and rotated line coordinates?).

Everything I've tried draws the shapes with overlapping edges.

Any help appreciated.

• I set this up with putting a square or a circle in the path.

• If I could use QPainter::translate() and rotate(), I could get rid of all that setP1() and setP2() stuff and use a set of lines that I create outside of the while loop (each iteration draws the same shape, just rotated and translated).

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