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;

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})

用t-sql编码

点为(@px， @py)，线段从(@ax， @ay)到(@bx， @by)

create function fn_sqr (@NumberToSquare decimal(18,10)) 
returns decimal(18,10)
as 
begin
    declare @Result decimal(18,10)
    set @Result = @NumberToSquare * @NumberToSquare
    return @Result
end
go

create function fn_Distance(@ax decimal (18,10) , @ay decimal (18,10), @bx decimal(18,10),  @by decimal(18,10)) 
returns decimal(18,10)
as
begin
    declare @Result decimal(18,10)
    set @Result = (select dbo.fn_sqr(@ax - @bx) + dbo.fn_sqr(@ay - @by) )
    return @Result
end
go

create function fn_DistanceToSegmentSquared(@px decimal(18,10), @py decimal(18,10), @ax decimal(18,10), @ay decimal(18,10), @bx decimal(18,10), @by decimal(18,10)) 
returns decimal(18,10)
as 
begin
    declare @l2 decimal(18,10)
    set @l2 = (select dbo.fn_Distance(@ax, @ay, @bx, @by))
    if @l2 = 0
        return dbo.fn_Distance(@px, @py, @ax, @ay)
    declare @t decimal(18,10)
    set @t = ((@px - @ax) * (@bx - @ax) + (@py - @ay) * (@by - @ay)) / @l2
    if (@t < 0) 
        return dbo.fn_Distance(@px, @py, @ax, @ay);
    if (@t > 1) 
        return dbo.fn_Distance(@px, @py, @bx, @by);
    return dbo.fn_Distance(@px, @py,  @ax + @t * (@bx - @ax),  @ay + @t * (@by - @ay))
end
go

create function fn_DistanceToSegment(@px decimal(18,10), @py decimal(18,10), @ax decimal(18,10), @ay decimal(18,10), @bx decimal(18,10), @by decimal(18,10)) 
returns decimal(18,10)
as 
begin
    return sqrt(dbo.fn_DistanceToSegmentSquared(@px, @py , @ax , @ay , @bx , @by ))
end
go

--example execution for distance from a point at (6,1) to line segment that runs from (4,2) to (2,1)
select dbo.fn_DistanceToSegment(6, 1, 4, 2, 2, 1) 
--result = 2.2360679775

--example execution for distance from a point at (-3,-2) to line segment that runs from (0,-2) to (-2,1)
select dbo.fn_DistanceToSegment(-3, -2, 0, -2, -2, 1) 
--result = 2.4961508830

--example execution for distance from a point at (0,-2) to line segment that runs from (0,-2) to (-2,1)
select dbo.fn_DistanceToSegment(0,-2, 0, -2, -2, 1) 
--result = 0.0000000000

JavaScript中一个基于这个公式的更简洁的解决方案:

distToSegment: function (point, linePointA, linePointB){

    var x0 = point.X;
    var y0 = point.Y;

    var x1 = linePointA.X;
    var y1 = linePointA.Y;

    var x2 = linePointB.X;
    var y2 = linePointB.Y;

    var Dx = (x2 - x1);
    var Dy = (y2 - y1);

    var numerator = Math.abs(Dy*x0 - Dx*y0 - x1*y2 + x2*y1);
    var denominator = Math.sqrt(Dx*Dx + Dy*Dy);
    if (denominator == 0) {
        return this.dist2(point, linePointA);
    }

    return numerator/denominator;

}

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:

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;
    }
}