我需要一个基本函数来求点到线段的最短距离。你可以随意用任何你想要的语言来编写解决方案;我可以把它翻译成什么我正在使用(Javascript)。

编辑:线段由两个端点定义。线段AB由两点A (x1,y1)和B (x2,y2)定义。我要求的是这条线段到点C (x3,y3)的距离。我的几何技能生疏了,所以我看到的例子让我很困惑,我很遗憾地承认。


当前回答

快速实现http://paulbourke.net/geometry/pointlineplane/source.c

    static func magnitude(p1: CGPoint, p2: CGPoint) -> CGFloat {
        let vector = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
        return sqrt(pow(vector.x, 2) + pow(vector.y, 2))
    }

    /// http://paulbourke.net/geometry/pointlineplane/
    /// http://paulbourke.net/geometry/pointlineplane/source.c
    static func pointDistanceToLine(point: CGPoint, lineStart: CGPoint, lineEnd: CGPoint) -> CGFloat? {

        let lineMag = magnitude(p1: lineEnd, p2: lineStart)
        let u = (((point.x - lineStart.x) * (lineEnd.x - lineStart.x)) +
                ((point.y - lineStart.y) * (lineEnd.y - lineStart.y))) /
                (lineMag * lineMag)

        if u < 0 || u > 1 {
            // closest point does not fall within the line segment
            return nil
        }

        let intersectionX = lineStart.x + u * (lineEnd.x - lineStart.x)
        let intersectionY = lineStart.y + u * (lineEnd.y - lineStart.y)

        return magnitude(p1: point, p2: CGPoint(x: intersectionX, y: intersectionY))
    }

其他回答

上面的函数在垂直线上不起作用。这是一个工作正常的函数! 与点p1 p2相交。CheckPoint为p;

public float DistanceOfPointToLine2(PointF p1, PointF p2, PointF p)
{
  //          (y1-y2)x + (x2-x1)y + (x1y2-x2y1)
  //d(P,L) = --------------------------------
  //         sqrt( (x2-x1)pow2 + (y2-y1)pow2 )

  double ch = (p1.Y - p2.Y) * p.X + (p2.X - p1.X) * p.Y + (p1.X * p2.Y - p2.X * p1.Y);
  double del = Math.Sqrt(Math.Pow(p2.X - p1.X, 2) + Math.Pow(p2.Y - p1.Y, 2));
  double d = ch / del;
  return (float)d;
}

这是我最后写的代码。这段代码假设一个点以{x:5, y:7}的形式定义。注意,这不是绝对最有效的方法,但它是我能想到的最简单、最容易理解的代码。

// a, b, and c in the code below are all points

function distance(a, b)
{
    var dx = a.x - b.x;
    var dy = a.y - b.y;
    return Math.sqrt(dx*dx + dy*dy);
}

function Segment(a, b)
{
    var ab = {
        x: b.x - a.x,
        y: b.y - a.y
    };
    var length = distance(a, b);

    function cross(c) {
        return ab.x * (c.y-a.y) - ab.y * (c.x-a.x);
    };

    this.distanceFrom = function(c) {
        return Math.min(distance(a,c),
                        distance(b,c),
                        Math.abs(cross(c) / length));
    };
}

这里没有看到Java实现,所以我将Javascript函数从接受的答案转换为Java代码:

static double sqr(double x) {
    return x * x;
}
static double dist2(DoublePoint v, DoublePoint w) {
    return sqr(v.x - w.x) + sqr(v.y - w.y);
}
static double distToSegmentSquared(DoublePoint p, DoublePoint v, DoublePoint w) {
    double l2 = dist2(v, w);
    if (l2 == 0) return dist2(p, v);
    double t = ((p.x - v.x) * (w.x - v.x) + (p.y - v.y) * (w.y - v.y)) / l2;
    if (t < 0) return dist2(p, v);
    if (t > 1) return dist2(p, w);
    return dist2(p, new DoublePoint(
            v.x + t * (w.x - v.x),
            v.y + t * (w.y - v.y)
    ));
}
static double distToSegment(DoublePoint p, DoublePoint v, DoublePoint w) {
    return Math.sqrt(distToSegmentSquared(p, v, w));
}
static class DoublePoint {
    public double x;
    public double y;

    public DoublePoint(double x, double y) {
        this.x = x;
        this.y = y;
    }
}

对于感兴趣的人,这里是Joshua的Javascript代码到Objective-C的简单转换:

- (double)distanceToPoint:(CGPoint)p fromLineSegmentBetween:(CGPoint)l1 and:(CGPoint)l2
{
    double A = p.x - l1.x;
    double B = p.y - l1.y;
    double C = l2.x - l1.x;
    double D = l2.y - l1.y;

    double dot = A * C + B * D;
    double len_sq = C * C + D * D;
    double param = dot / len_sq;

    double xx, yy;

    if (param < 0 || (l1.x == l2.x && l1.y == l2.y)) {
        xx = l1.x;
        yy = l1.y;
    }
    else if (param > 1) {
        xx = l2.x;
        yy = l2.y;
    }
    else {
        xx = l1.x + param * C;
        yy = l1.y + param * D;
    }

    double dx = p.x - xx;
    double dy = p.y - yy;

    return sqrtf(dx * dx + dy * dy);
}

我需要这个解决方案与MKMapPoint一起工作,所以我将分享它,以防其他人需要它。只是一些小的改变,这将返回米为单位的距离:

- (double)distanceToPoint:(MKMapPoint)p fromLineSegmentBetween:(MKMapPoint)l1 and:(MKMapPoint)l2
{
    double A = p.x - l1.x;
    double B = p.y - l1.y;
    double C = l2.x - l1.x;
    double D = l2.y - l1.y;

    double dot = A * C + B * D;
    double len_sq = C * C + D * D;
    double param = dot / len_sq;

    double xx, yy;

    if (param < 0 || (l1.x == l2.x && l1.y == l2.y)) {
        xx = l1.x;
        yy = l1.y;
    }
    else if (param > 1) {
        xx = l2.x;
        yy = l2.y;
    }
    else {
        xx = l1.x + param * C;
        yy = l1.y + param * D;
    }

    return MKMetersBetweenMapPoints(p, MKMapPointMake(xx, yy));
}

和这个答案一样,只是用的是Visual Basic。使其可作为Microsoft Excel和VBA/宏中的用户定义函数使用。

函数返回点(x,y)到由(x1,y1)和(x2,y2)定义的线段的最近距离。

Function DistanceToSegment(x As Double, y As Double, x1 As Double, y1 As Double, x2 As Double, y2 As Double)

  Dim A As Double
  A = x - x1
  Dim B As Double
  B = y - y1
  Dim C  As Double
  C = x2 - x1
  Dim D As Double
  D = y2 - y1

  Dim dot As Double
  dot = A * C + B * D
  Dim len_sq As Double
  len_sq = C * C + D * D
  Dim param As Double
  param = -1

  If (len_sq <> 0) Then
      param = dot / len_sq
  End If

  Dim xx As Double
  Dim yy As Double

  If (param < 0) Then
    xx = x1
    yy = y1
  ElseIf (param > 1) Then
    xx = x2
    yy = y2
  Else
    xx = x1 + param * C
    yy = y1 + param * D
  End If

  Dim dx As Double
  dx = x - xx
  Dim dy As Double
  dy = y - yy

  DistanceToSegment = Math.Sqr(dx * dx + dy * dy)

End Function