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

您可以尝试PHP geo-math-php的库

composer require rkondratuk/geo-math-php:^1

例子:

<?php

use PhpGeoMath\Model\GeoSegment;
use PhpGeoMath\Model\Polar3dPoint;

$polarPoint1 = new Polar3dPoint(
    40.758742779050706, -73.97855507715238, Polar3dPoint::EARTH_RADIUS_IN_METERS
);

$polarPoint2 = new Polar3dPoint(
    40.74843388072615, -73.98566565776102, Polar3dPoint::EARTH_RADIUS_IN_METERS
);

$polarPoint3 = new Polar3dPoint(
    40.74919365249446, -73.98133456388013, Polar3dPoint::EARTH_RADIUS_IN_METERS
);

$arcSegment = new GeoSegment($polarPoint1, $polarPoint2);
$nearestPolarPoint = $arcSegment->calcNearestPoint($polarPoint3);

// Shortest distance from point-3 to segment(point-1, point-2)
$geoDistance = $nearestPolarPoint->calcGeoDistanceToPoint($polarPoint3);

其他回答

Lua解决方案

-- distance from point (px, py) to line segment (x1, y1, x2, y2)
function distPointToLine(px,py,x1,y1,x2,y2) -- point, start and end of the segment
    local dx,dy = x2-x1,y2-y1
    local length = math.sqrt(dx*dx+dy*dy)
    dx,dy = dx/length,dy/length -- normalization
    local p = dx*(px-x1)+dy*(py-y1)
    if p < 0 then
        dx,dy = px-x1,py-y1
        return math.sqrt(dx*dx+dy*dy), x1, y1 -- distance, nearest point
    elseif p > length then
        dx,dy = px-x2,py-y2
        return math.sqrt(dx*dx+dy*dy), x2, y2 -- distance, nearest point
    end
    return math.abs(dy*(px-x1)-dx*(py-y1)), x1+dx*p, y1+dy*p -- distance, nearest point
end

对于折线(有两条以上线段的线):

-- if the (poly-)line has several segments, just iterate through all of them:
function nearest_sector_in_line (x, y, line)
    local x1, y1, x2, y2, min_dist
    local ax,ay = line[1], line[2]
    for j = 3, #line-1, 2 do
        local bx,by = line[j], line[j+1]
        local dist = distPointToLine(x,y,ax,ay,bx,by)
        if not min_dist or dist < min_dist then
            min_dist = dist
            x1, y1, x2, y2 = ax,ay,bx,by
        end
        ax, ay = bx, by
    end
    return x1, y1, x2, y2
end

例子:

-- call it:
local x1, y1, x2, y2 = nearest_sector_in_line (7, 4, {0,0, 10,0, 10,10, 0,10})

这是一个自成体系的Delphi / Pascal版本的函数,基于上面约书亚的答案。使用TPoint用于VCL屏幕图形,但应该易于根据需要进行调整。

function DistancePtToSegment( pt, pt1, pt2: TPoint): double;
var
   a, b, c, d: double;
   len_sq: double;
   param: double;
   xx, yy: double;
   dx, dy: double;
begin
   a := pt.x - pt1.x;
   b := pt.y - pt1.y;
   c := pt2.x - pt1.x;
   d := pt2.y - pt1.y;

   len_sq := (c * c) + (d * d);
   param := -1;

   if (len_sq <> 0) then
   begin
      param := ((a * c) + (b * d)) / len_sq;
   end;

   if param < 0 then
   begin
      xx := pt1.x;
      yy := pt1.y;
   end
   else if param > 1 then
   begin
      xx := pt2.x;
      yy := pt2.y;
   end
   else begin
      xx := pt1.x + param * c;
      yy := pt1.y + param * d;
   end;

   dx := pt.x - xx;
   dy := pt.y - yy;
   result := sqrt( (dx * dx) + (dy * dy))
end;

公认的答案行不通 (例如,0,0和(-10,2,10,2)之间的距离应为2)。

下面是工作代码:

   def dist2line2(x,y,line):
     x1,y1,x2,y2=line
     vx = x1 - x
     vy = y1 - y
     ux = x2-x1
     uy = y2-y1
     length = ux * ux + uy * uy
     det = (-vx * ux) + (-vy * uy) #//if this is < 0 or > length then its outside the line segment
     if det < 0:
       return (x1 - x)**2 + (y1 - y)**2
     if det > length:
       return (x2 - x)**2 + (y2 - y)**2
     det = ux * vy - uy * vx
     return det**2 / length
   def dist2line(x,y,line): return math.sqrt(dist2line2(x,y,line))
%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))));

该算法基于求出指定直线与包含指定点的正交直线的交点,并计算其距离。在线段的情况下,我们必须检查交点是否在线段的点之间,如果不是这样,则最小距离是指定点与线段的一个端点之间的距离。这是一个c#实现。

Double Distance(Point a, Point b)
{
    double xdiff = a.X - b.X, ydiff = a.Y - b.Y;
    return Math.Sqrt((long)xdiff * xdiff + (long)ydiff * ydiff);
}

Boolean IsBetween(double x, double a, double b)
{
    return ((a <= b && x >= a && x <= b) || (a > b && x <= a && x >= b));
}

Double GetDistance(Point pt, Point pt1, Point pt2, out Point intersection)
{
    Double a, x, y, R;

    if (pt1.X != pt2.X) {
        a = (double)(pt2.Y - pt1.Y) / (pt2.X - pt1.X);
        x = (a * (pt.Y - pt1.Y) + a * a * pt1.X + pt.X) / (a * a + 1);
        y = a * x + pt1.Y - a * pt1.X; }
    else { x = pt1.X;  y = pt.Y; }

    if (IsBetween(x, pt1.X, pt2.X) && IsBetween(y, pt1.Y, pt2.Y)) {
        intersection = new Point((int)x, (int)y);
        R = Distance(intersection, pt); }
    else {
        double d1 = Distance(pt, pt1), d2 = Distance(pt, pt2);
        if (d1 < d2) { intersection = pt1; R = d1; }
        else { intersection = pt2; R = d2; }}

    return R;
}