GLSL版:

// line (a -> b ) point p[enter image description here][1]
float distanceToLine(vec2 a, vec2 b, vec2 p) {
    float aside = dot((p - a),(b - a));
    if(aside< 0.0) return length(p-a);
    float bside = dot((p - b),(a - b));
    if(bside< 0.0) return length(p-b);
    vec2 pointOnLine = (bside*a + aside*b)/pow(length(a-b),2.0);
    return length(p - pointOnLine);
}

%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))));

只是遇到了这个，我想我应该添加一个Lua实现。它假设点以表{x=xVal, y=yVal}给出，直线或线段由包含两个点的表给出(见下面的例子):

function distance( P1, P2 )
    return math.sqrt((P1.x-P2.x)^2 + (P1.y-P2.y)^2)
end

-- Returns false if the point lies beyond the reaches of the segment
function distPointToSegment( line, P )
    if line[1].x == line[2].x and line[1].y == line[2].y then
        print("Error: Not a line!")
        return false
    end

    local d = distance( line[1], line[2] )

    local t = ((P.x - line[1].x)*(line[2].x - line[1].x) + (P.y - line[1].y)*(line[2].y - line[1].y))/(d^2)

    local projection = {}
    projection.x = line[1].x + t*(line[2].x-line[1].x)
    projection.y = line[1].y + t*(line[2].y-line[1].y)

    if t >= 0 and t <= 1 then   -- within line segment?
        return distance( projection, {x=P.x, y=P.y} )
    else
        return false
    end
end

-- Returns value even if point is further down the line (outside segment)
function distPointToLine( line, P )
    if line[1].x == line[2].x and line[1].y == line[2].y then
        print("Error: Not a line!")
        return false
    end

    local d = distance( line[1], line[2] )

    local t = ((P.x - line[1].x)*(line[2].x - line[1].x) + (P.y - line[1].y)*(line[2].y - line[1].y))/(d^2)

    local projection = {}
    projection.x = line[1].x + t*(line[2].x-line[1].x)
    projection.y = line[1].y + t*(line[2].y-line[1].y)

    return distance( projection, {x=P.x, y=P.y} )
end

使用示例:

local P1 = {x = 0, y = 0}
local P2 = {x = 10, y = 10}
local line = { P1, P2 }
local P3 = {x = 7, y = 15}
print(distPointToLine( line, P3 ))  -- prints 5.6568542494924
print(distPointToSegment( line, P3 )) -- prints false

特征c++版本的3D线段和点

// Return minimum distance between line segment: head--->tail and point
double MinimumDistance(Eigen::Vector3d head, Eigen::Vector3d tail,Eigen::Vector3d point)
{
    double l2 = std::pow((head - tail).norm(),2);
    if(l2 ==0.0) return (head - point).norm();// head == tail case

    // Consider the line extending the segment, parameterized as head + t (tail - point).
    // We find projection of point onto the line.
    // It falls where t = [(point-head) . (tail-head)] / |tail-head|^2
    // We clamp t from [0,1] to handle points outside the segment head--->tail.

    double t = max(0,min(1,(point-head).dot(tail-head)/l2));
    Eigen::Vector3d projection = head + t*(tail-head);

    return (point - projection).norm();
}

基于Joshua Javascript的AutoHotkeys版本:

plDist(x, y, x1, y1, x2, y2) {
    A:= x - x1
    B:= y - y1
    C:= x2 - x1
    D:= y2 - y1

    dot:= A*C + B*D
    sqLen:= C*C + D*D
    param:= dot / sqLen

    if (param < 0 || ((x1 = x2) && (y1 = y2))) {
        xx:= x1
        yy:= y1
    } else if (param > 1) {
        xx:= x2
        yy:= y2
    } else {
        xx:= x1 + param*C
        yy:= y1 + param*D
    }

    dx:= x - xx
    dy:= y - yy

    return sqrt(dx*dx + dy*dy)
}

这里是与c++答案相同的东西，但移植到pascal。点参数的顺序已经改变，以适应我的代码，但还是一样的东西。

function Dot(const p1, p2: PointF): double;
begin
  Result := p1.x * p2.x + p1.y * p2.y;
end;
function SubPoint(const p1, p2: PointF): PointF;
begin
  result.x := p1.x - p2.x;
  result.y := p1.y - p2.y;
end;

function ShortestDistance2(const p,v,w : PointF) : double;
var
  l2,t : double;
  projection,tt: PointF;
begin
  // Return minimum distance between line segment vw and point p
  //l2 := length_squared(v, w);  // i.e. |w-v|^2 -  avoid a sqrt
  l2 := Distance(v,w);
  l2 := MPower(l2,2);
  if (l2 = 0.0) then begin
    result:= Distance(p, v);   // v == w case
    exit;
  end;
  // Consider the line extending the segment, parameterized as v + t (w - v).
  // We find projection of point p onto the line.
  // It falls where t = [(p-v) . (w-v)] / |w-v|^2
  t := Dot(SubPoint(p,v),SubPoint(w,v)) / l2;
  if (t < 0.0) then begin
    result := Distance(p, v);       // Beyond the 'v' end of the segment
    exit;
  end
  else if (t > 1.0) then begin
    result := Distance(p, w);  // Beyond the 'w' end of the segment
    exit;
  end;
  //projection := v + t * (w - v);  // Projection falls on the segment
  tt.x := v.x + t * (w.x - v.x);
  tt.y := v.y + t * (w.y - v.y);
  result := Distance(p, tt);
end;