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

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

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;

}

这是一个为有限线段而做的实现，而不是像这里的大多数其他函数那样的无限线(这就是为什么我做这个)。

Paul Bourke的理论实施。

Python:

def dist(x1, y1, x2, y2, x3, y3): # x3,y3 is the point
    px = x2-x1
    py = y2-y1

    norm = px*px + py*py

    u =  ((x3 - x1) * px + (y3 - y1) * py) / float(norm)

    if u > 1:
        u = 1
    elif u < 0:
        u = 0

    x = x1 + u * px
    y = y1 + u * py

    dx = x - x3
    dy = y - y3

    # Note: If the actual distance does not matter,
    # if you only want to compare what this function
    # returns to other results of this function, you
    # can just return the squared distance instead
    # (i.e. remove the sqrt) to gain a little performance

    dist = (dx*dx + dy*dy)**.5

    return dist

AS3:

public static function segmentDistToPoint(segA:Point, segB:Point, p:Point):Number
{
    var p2:Point = new Point(segB.x - segA.x, segB.y - segA.y);
    var something:Number = p2.x*p2.x + p2.y*p2.y;
    var u:Number = ((p.x - segA.x) * p2.x + (p.y - segA.y) * p2.y) / something;

    if (u > 1)
        u = 1;
    else if (u < 0)
        u = 0;

    var x:Number = segA.x + u * p2.x;
    var y:Number = segA.y + u * p2.y;

    var dx:Number = x - p.x;
    var dy:Number = y - p.y;

    var dist:Number = Math.sqrt(dx*dx + dy*dy);

    return dist;
}

Java

private double shortestDistance(float x1,float y1,float x2,float y2,float x3,float y3)
    {
        float px=x2-x1;
        float py=y2-y1;
        float temp=(px*px)+(py*py);
        float u=((x3 - x1) * px + (y3 - y1) * py) / (temp);
        if(u>1){
            u=1;
        }
        else if(u<0){
            u=0;
        }
        float x = x1 + u * px;
        float y = y1 + u * py;

        float dx = x - x3;
        float dy = y - y3;
        double dist = Math.sqrt(dx*dx + dy*dy);
        return dist;

    }

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));
    };
}

在javascript中使用几何:

var a = { x:20, y:20};//start segment    
var b = { x:40, y:30};//end segment   
var c = { x:37, y:14};//point   

// magnitude from a to c    
var ac = Math.sqrt( Math.pow( ( a.x - c.x ), 2 ) + Math.pow( ( a.y - c.y ), 2) );    
// magnitude from b to c   
var bc = Math.sqrt( Math.pow( ( b.x - c.x ), 2 ) + Math.pow( ( b.y - c.y ), 2 ) );    
// magnitude from a to b (base)     
var ab = Math.sqrt( Math.pow( ( a.x - b.x ), 2 ) + Math.pow( ( a.y - b.y ), 2 ) );    
 // perimeter of triangle     
var p = ac + bc + ab;    
 // area of the triangle    
var area = Math.sqrt( p/2 * ( p/2 - ac) * ( p/2 - bc ) * ( p/2 - ab ) );    
 // height of the triangle = distance    
var h = ( area * 2 ) / ab;    
console.log ("height: " + h);