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。
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
这里它使用Swift
/* Distance from a point (p1) to line l1 l2 */
func distanceFromPoint(p: CGPoint, toLineSegment l1: CGPoint, and l2: CGPoint) -> CGFloat {
let A = p.x - l1.x
let B = p.y - l1.y
let C = l2.x - l1.x
let D = l2.y - l1.y
let dot = A * C + B * D
let len_sq = C * C + D * D
let param = dot / len_sq
var xx, yy: CGFloat
if param < 0 || (l1.x == l2.x && l1.y == l2.y) {
xx = l1.x
yy = l1.y
} else if param > 1 {
xx = l2.x
yy = l2.y
} else {
xx = l1.x + param * C
yy = l1.y + param * D
}
let dx = p.x - xx
let dy = p.y - yy
return sqrt(dx * dx + dy * dy)
}
其他回答
在f#中,点c到a和b之间的线段的距离为:
let pointToLineSegmentDistance (a: Vector, b: Vector) (c: Vector) =
let d = b - a
let s = d.Length
let lambda = (c - a) * d / s
let p = (lambda |> max 0.0 |> min s) * d / s
(a + p - c).Length
向量d沿着线段从a指向b。d/s与c-a的点积给出了无限直线与点c之间最接近点的参数。使用min和max函数将该参数钳制到范围0..s,使该点位于a和b之间。最后,a+p-c的长度是c到线段上最近点的距离。
使用示例:
pointToLineSegmentDistance (Vector(0.0, 0.0), Vector(1.0, 0.0)) (Vector(-1.0, 1.0))
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))
在我自己的问题线程如何计算在C, c# / .NET 2.0或Java的所有情况下一个点和线段之间的最短2D距离?当我找到一个c#的答案时,我被要求把它放在这里:所以它是从http://www.topcoder.com/tc?d1=tutorials&d2=geometry1&module=Static修改的:
//Compute the dot product AB . BC
private double DotProduct(double[] pointA, double[] pointB, double[] pointC)
{
double[] AB = new double[2];
double[] BC = new double[2];
AB[0] = pointB[0] - pointA[0];
AB[1] = pointB[1] - pointA[1];
BC[0] = pointC[0] - pointB[0];
BC[1] = pointC[1] - pointB[1];
double dot = AB[0] * BC[0] + AB[1] * BC[1];
return dot;
}
//Compute the cross product AB x AC
private double CrossProduct(double[] pointA, double[] pointB, double[] pointC)
{
double[] AB = new double[2];
double[] AC = new double[2];
AB[0] = pointB[0] - pointA[0];
AB[1] = pointB[1] - pointA[1];
AC[0] = pointC[0] - pointA[0];
AC[1] = pointC[1] - pointA[1];
double cross = AB[0] * AC[1] - AB[1] * AC[0];
return cross;
}
//Compute the distance from A to B
double Distance(double[] pointA, double[] pointB)
{
double d1 = pointA[0] - pointB[0];
double d2 = pointA[1] - pointB[1];
return Math.Sqrt(d1 * d1 + d2 * d2);
}
//Compute the distance from AB to C
//if isSegment is true, AB is a segment, not a line.
double LineToPointDistance2D(double[] pointA, double[] pointB, double[] pointC,
bool isSegment)
{
double dist = CrossProduct(pointA, pointB, pointC) / Distance(pointA, pointB);
if (isSegment)
{
double dot1 = DotProduct(pointA, pointB, pointC);
if (dot1 > 0)
return Distance(pointB, pointC);
double dot2 = DotProduct(pointB, pointA, pointC);
if (dot2 > 0)
return Distance(pointA, pointC);
}
return Math.Abs(dist);
}
我不是要回答问题,而是要问问题,所以我希望我不会因为某些原因而得到数百万张反对票,而是批评。我只是想(并被鼓励)分享其他人的想法,因为这个帖子中的解决方案要么是用一些奇异的语言(Fortran, Mathematica),要么被某人标记为错误。对我来说唯一有用的(由Grumdrig编写)是用c++编写的,没有人标记它有错误。但是它缺少被调用的方法(dot等)。
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;
}
C#
改编自@Grumdrig
public static double MinimumDistanceToLineSegment(this Point p,
Line line)
{
var v = line.StartPoint;
var w = line.EndPoint;
double lengthSquared = DistanceSquared(v, w);
if (lengthSquared == 0.0)
return Distance(p, v);
double t = Math.Max(0, Math.Min(1, DotProduct(p - v, w - v) / lengthSquared));
var projection = v + t * (w - v);
return Distance(p, projection);
}
public static double Distance(Point a, Point b)
{
return Math.Sqrt(DistanceSquared(a, b));
}
public static double DistanceSquared(Point a, Point b)
{
var d = a - b;
return DotProduct(d, d);
}
public static double DotProduct(Point a, Point b)
{
return (a.X * b.X) + (a.Y * b.Y);
}