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
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;
}
}
其他回答
该算法基于求出指定直线与包含指定点的正交直线的交点,并计算其距离。在线段的情况下,我们必须检查交点是否在线段的点之间,如果不是这样,则最小距离是指定点与线段的一个端点之间的距离。这是一个c#实现。
Double Distance(Point a, Point b)
{
double xdiff = a.X - b.X, ydiff = a.Y - b.Y;
return Math.Sqrt((long)xdiff * xdiff + (long)ydiff * ydiff);
}
Boolean IsBetween(double x, double a, double b)
{
return ((a <= b && x >= a && x <= b) || (a > b && x <= a && x >= b));
}
Double GetDistance(Point pt, Point pt1, Point pt2, out Point intersection)
{
Double a, x, y, R;
if (pt1.X != pt2.X) {
a = (double)(pt2.Y - pt1.Y) / (pt2.X - pt1.X);
x = (a * (pt.Y - pt1.Y) + a * a * pt1.X + pt.X) / (a * a + 1);
y = a * x + pt1.Y - a * pt1.X; }
else { x = pt1.X; y = pt.Y; }
if (IsBetween(x, pt1.X, pt2.X) && IsBetween(y, pt1.Y, pt2.Y)) {
intersection = new Point((int)x, (int)y);
R = Distance(intersection, pt); }
else {
double d1 = Distance(pt, pt1), d2 = Distance(pt, pt2);
if (d1 < d2) { intersection = pt1; R = d1; }
else { intersection = pt2; R = d2; }}
return R;
}
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
省道和颤振的解决方法:
import 'dart:math' as math;
class Utils {
static double shortestDistance(Point p1, Point p2, Point p3){
double px = p2.x - p1.x;
double py = p2.y - p1.y;
double temp = (px*px) + (py*py);
double u = ((p3.x - p1.x)*px + (p3.y - p1.y)* py) /temp;
if(u>1){
u=1;
}
else if(u<0){
u=0;
}
double x = p1.x + u*px;
double y = p1.y + u*py;
double dx = x - p3.x;
double dy = y - p3.y;
double dist = math.sqrt(dx*dx+dy*dy);
return dist;
}
}
class Point {
double x;
double y;
Point(this.x, this.y);
}
对于懒人来说,以下是我在Objective-C语言中移植@Grumdrig的解决方案:
CGFloat sqr(CGFloat x) { return x*x; }
CGFloat dist2(CGPoint v, CGPoint w) { return sqr(v.x - w.x) + sqr(v.y - w.y); }
CGFloat distanceToSegmentSquared(CGPoint p, CGPoint v, CGPoint w)
{
CGFloat l2 = dist2(v, w);
if (l2 == 0.0f) return dist2(p, v);
CGFloat t = ((p.x - v.x) * (w.x - v.x) + (p.y - v.y) * (w.y - v.y)) / l2;
if (t < 0.0f) return dist2(p, v);
if (t > 1.0f) return dist2(p, w);
return dist2(p, CGPointMake(v.x + t * (w.x - v.x), v.y + t * (w.y - v.y)));
}
CGFloat distanceToSegment(CGPoint point, CGPoint segmentPointV, CGPoint segmentPointW)
{
return sqrtf(distanceToSegmentSquared(point, segmentPointV, segmentPointW));
}
和这个答案一样,只是用的是Visual Basic。使其可作为Microsoft Excel和VBA/宏中的用户定义函数使用。
函数返回点(x,y)到由(x1,y1)和(x2,y2)定义的线段的最近距离。
Function DistanceToSegment(x As Double, y As Double, x1 As Double, y1 As Double, x2 As Double, y2 As Double)
Dim A As Double
A = x - x1
Dim B As Double
B = y - y1
Dim C As Double
C = x2 - x1
Dim D As Double
D = y2 - y1
Dim dot As Double
dot = A * C + B * D
Dim len_sq As Double
len_sq = C * C + D * D
Dim param As Double
param = -1
If (len_sq <> 0) Then
param = dot / len_sq
End If
Dim xx As Double
Dim yy As Double
If (param < 0) Then
xx = x1
yy = y1
ElseIf (param > 1) Then
xx = x2
yy = y2
Else
xx = x1 + param * C
yy = y1 + param * D
End If
Dim dx As Double
dx = x - xx
Dim dy As Double
dy = y - yy
DistanceToSegment = Math.Sqr(dx * dx + dy * dy)
End Function