请参见以下网站中的Matlab几何工具箱: http://people.sc.fsu.edu/~jburkardt/m_src/geometry/geometry.html

按Ctrl +f，输入“segment”，查找线段相关函数。函数“segment_point_dist_2d.”和segment_point_dist_3d。M "是你需要的。

几何代码有C版本、c++版本、FORTRAN77版本、FORTRAN90版本和MATLAB版本。

%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))));

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;
    }
}

我制作了一个交互式Desmos图来演示如何实现这一点:

https://www.desmos.com/calculator/kswrm8ddum

红点是A点，绿点是B点，C点是蓝色点。 您可以拖动图形中的点来查看值的变化。 左边的值“s”是线段的参数(即s = 0表示点A, s = 1表示点B)。 值“d”是第三点到经过A和B的直线的距离。

编辑:

有趣的小见解:坐标(s, d)是坐标系中第三点C的坐标，AB是单位x轴，单位y轴垂直于AB。

I'm assuming you want to find the shortest distance between the point and a line segment; to do this, you need to find the line (lineA) which is perpendicular to your line segment (lineB) which goes through your point, determine the intersection between that line (lineA) and your line which goes through your line segment (lineB); if that point is between the two points of your line segment, then the distance is the distance between your point and the point you just found which is the intersection of lineA and lineB; if the point is not between the two points of your line segment, you need to get the distance between your point and the closer of two ends of the line segment; this can be done easily by taking the square distance (to avoid a square root) between the point and the two points of the line segment; whichever is closer, take the square root of that one.

在数学

它使用线段的参数描述，并将点投影到线段定义的直线中。当参数在线段内从0到1时，如果投影在这个范围之外，我们计算到相应端点的距离，而不是法线到线段的直线。

Clear["Global`*"];
 distance[{start_, end_}, pt_] := 
   Module[{param},
   param = ((pt - start).(end - start))/Norm[end - start]^2; (*parameter. the "."
                                                       here means vector product*)

   Which[
    param < 0, EuclideanDistance[start, pt],                 (*If outside bounds*)
    param > 1, EuclideanDistance[end, pt],
    True, EuclideanDistance[pt, start + param (end - start)] (*Normal distance*)
    ]
   ];  

策划的结果:

Plot3D[distance[{{0, 0}, {1, 0}}, {xp, yp}], {xp, -1, 2}, {yp, -1, 2}]

画出比截断距离更近的点:

等高线图: