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。
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
%Matlab solution by Tim from Cody
function ans=distP2S(x0,y0,x1,y1,x2,y2)
% Point is x0,y0
z=complex(x0-x1,y0-y1);
complex(x2-x1,y2-y1);
abs(z-ans*min(1,max(0,real(z/ans))));
其他回答
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;
}
}
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))
}
如果它是一条无限大的直线,而不是一条线段,最简单的方法是这样(在ruby中),其中mx + b是直线,(x1, y1)是已知的点
(y1 - mx1 - b).abs / Math.sqrt(m**2 + 1)
忍不住用python来编码:)
from math import sqrt, fabs
def pdis(a, b, c):
t = b[0]-a[0], b[1]-a[1] # Vector ab
dd = sqrt(t[0]**2+t[1]**2) # Length of ab
t = t[0]/dd, t[1]/dd # unit vector of ab
n = -t[1], t[0] # normal unit vector to ab
ac = c[0]-a[0], c[1]-a[1] # vector ac
return fabs(ac[0]*n[0]+ac[1]*n[1]) # Projection of ac to n (the minimum distance)
print pdis((1,1), (2,2), (2,0)) # Example (answer is 1.414)
fortran也是一样:)
real function pdis(a, b, c)
real, dimension(0:1), intent(in) :: a, b, c
real, dimension(0:1) :: t, n, ac
real :: dd
t = b - a ! Vector ab
dd = sqrt(t(0)**2+t(1)**2) ! Length of ab
t = t/dd ! unit vector of ab
n = (/-t(1), t(0)/) ! normal unit vector to ab
ac = c - a ! vector ac
pdis = abs(ac(0)*n(0)+ac(1)*n(1)) ! Projection of ac to n (the minimum distance)
end function pdis
program test
print *, pdis((/1.0,1.0/), (/2.0,2.0/), (/2.0,0.0/)) ! Example (answer is 1.414)
end program test
WPF版本:
public class LineSegment
{
private readonly Vector _offset;
private readonly Vector _vector;
public LineSegment(Point start, Point end)
{
_offset = (Vector)start;
_vector = (Vector)(end - _offset);
}
public double DistanceTo(Point pt)
{
var v = (Vector)pt - _offset;
// first, find a projection point on the segment in parametric form (0..1)
var p = (v * _vector) / _vector.LengthSquared;
// and limit it so it lays inside the segment
p = Math.Min(Math.Max(p, 0), 1);
// now, find the distance from that point to our point
return (_vector * p - v).Length;
}
}