描述
在Qt中,要计算一个点到一条线段的垂线段的长度(即点到线段上最近点的距离,且这个点是垂直于线段的),你不能直接使用
QVector2D::distanceToLine
,因为这个方法计算的是点到直线的垂直距离,而不是到线段的垂直距离。线段有起点和终点,而直线是无限延伸的。为了计算点到线段的垂线段长度,你需要考虑几种情况:
- 如果点的投影在线段上,则垂线段长度就是点到投影点的距离。
- 如果点的投影在线段的起点或终点之外,则垂线段长度是点到线段起点或终点的距离中的较小值(这个没搞清楚。好在我当前的需求,不会出现投影在线段之外的情况)。
下面是一个使用
QVector2D
和简单的几何计算来实现这一功能的示例代码:
实验代码
函数:
qreal Widget::pointToSegmentDistance(const QVector2D &point, const QVector2D &segmentStart, const QVector2D &segmentEnd) {
QVector2D segmentDirection = segmentEnd - segmentStart;
QVector2D vecFromStartToPoint = point - segmentStart;
// 计算投影系数
qreal t = QVector2D::dotProduct(vecFromStartToPoint, segmentDirection) / QVector2D::dotProduct(segmentDirection, segmentDirection);
qDebug() << t;
// 如果投影系数小于0,则最近点是线段起点
if (t < 0.0) {
return QVector2D(point - segmentStart).length();
}
// 如果投影系数大于1,则最近点是线段终点
if (t > 1.0) {
return QVector2D(point - segmentEnd).length();
}
// 投影在线段上,计算垂线段长度
QVector2D projection = segmentStart + t * segmentDirection;
return QVector2D(point - projection).length();
}
在paintEvent函数中实现划线,并调用 pointToSegmentDistance计算垂线段距离
void Widget::paintEvent(QPaintEvent *event)
{
qreal distance;
QPainter painter(this);
QPen pen(Qt::blue,3);
painter.setPen(pen);
QPointF point(100,100);
pen.setColor(Qt::blue);
painter.setPen(pen);
painter.drawPoint(point);
pen.setColor(Qt::red);
painter.setPen(pen);
painter.drawText(QPointF(100,100),"point");
QVector2D point_2d(point);
QLineF line(50,50,50,150);
pen.setColor(Qt::blue);
painter.setPen(pen);
painter.drawLine(line);
pen.setColor(Qt::red);
painter.setPen(pen);
painter.drawText(line.center(),"line_1");
QVector2D line_start_2d(line.p1());
QVector2D line_end_2d(line.p2());
distance = pointToSegmentDistance(point_2d,line_start_2d,line_end_2d);
qDebug() << " to line 1 distance : " << distance;
QLineF line2(50,50,150,50);
pen.setColor(Qt::blue);
painter.setPen(pen);
painter.drawLine(line2);
pen.setColor(Qt::red);
painter.setPen(pen);
painter.drawText(line2.center(),"line_2");
QVector2D line2_start_2d(line2.p1());
QVector2D line2_end_2d(line2.p2());
distance = pointToSegmentDistance(point_2d,line2_start_2d,line2_end_2d);
qDebug() << " to line 2 distance : " << distance;
QLineF line3(150,50,150,150);
pen.setColor(Qt::blue);
painter.setPen(pen);
painter.drawLine(line3);
pen.setColor(Qt::red);
painter.setPen(pen);
painter.drawText(line3.center(),"line_3");
QVector2D line3_start_2d(line3.p1());
QVector2D line3_end_2d(line3.p2());
distance = pointToSegmentDistance(point_2d,line3_start_2d,line3_end_2d);
qDebug() << " to line 3 distance : " << distance;
QLineF line4(150,200,150,300);
pen.setColor(Qt::blue);
painter.setPen(pen);
painter.drawLine(line4);
pen.setColor(Qt::red);
painter.setPen(pen);
painter.drawText(line4.center(),"line_4");
QVector2D line4_start_2d(line4.p1());
QVector2D line4_end_2d(line4.p2());
distance = pointToSegmentDistance(point_2d,line4_start_2d,line4_end_2d);
qDebug() << " to line 4 distance : " << distance;
QLineF line5(300,200,300,150);
pen.setColor(Qt::blue);
painter.setPen(pen);
painter.drawLine(line5);
pen.setColor(Qt::red);
painter.setPen(pen);
painter.drawText(line5.center(),"line_5");
QVector2D line5_start_2d(line5.p1());
QVector2D line5_end_2d(line5.p2());
distance = pointToSegmentDistance(point_2d,line5_start_2d,line5_end_2d);
qDebug() << " to line 5 distance : " << distance;
}
测试结果:
qDebug输出的结果: