我需要一个基本函数来查找点与线段之间最短的距离。您可以使用任何编程语言编写解决方案,我可以将其转换为我正在使用的语言(Javascript)。
编辑:我的线段由两个端点定义。因此,我的线段AB
由两个点A(x1,y1)
和B(x2,y2)
定义。我正在尝试查找该线段与点C(x3,y3)
之间的距离。我的几何技能有些生疏,所以我看到的示例很令人困惑,对此我感到抱歉。
我需要一个基本函数来查找点与线段之间最短的距离。您可以使用任何编程语言编写解决方案,我可以将其转换为我正在使用的语言(Javascript)。
编辑:我的线段由两个端点定义。因此,我的线段AB
由两个点A(x1,y1)
和B(x2,y2)
定义。我正在尝试查找该线段与点C(x3,y3)
之间的距离。我的几何技能有些生疏,所以我看到的示例很令人困惑,对此我感到抱歉。
你可以尝试使用 PHP 库 geo-math-php
composer require rkondratuk/geo-math-php:^1
例子:
<?php
use PhpGeoMath\Model\GeoSegment;
use PhpGeoMath\Model\Polar3dPoint;
$polarPoint1 = new Polar3dPoint(
40.758742779050706, -73.97855507715238, Polar3dPoint::EARTH_RADIUS_IN_METERS
);
$polarPoint2 = new Polar3dPoint(
40.74843388072615, -73.98566565776102, Polar3dPoint::EARTH_RADIUS_IN_METERS
);
$polarPoint3 = new Polar3dPoint(
40.74919365249446, -73.98133456388013, Polar3dPoint::EARTH_RADIUS_IN_METERS
);
$arcSegment = new GeoSegment($polarPoint1, $polarPoint2);
$nearestPolarPoint = $arcSegment->calcNearestPoint($polarPoint3);
// Shortest distance from point-3 to segment(point-1, point-2)
$geoDistance = $nearestPolarPoint->calcGeoDistanceToPoint($polarPoint3);
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;
针对3D线段和点的Eigen C++版本
// 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();
}
Swift 实现 http://paulbourke.net/geometry/pointlineplane/source.c
static func magnitude(p1: CGPoint, p2: CGPoint) -> CGFloat {
let vector = CGPoint(x: p2.x - p1.x, y: p2.y - p1.y)
return sqrt(pow(vector.x, 2) + pow(vector.y, 2))
}
/// http://paulbourke.net/geometry/pointlineplane/
/// http://paulbourke.net/geometry/pointlineplane/source.c
static func pointDistanceToLine(point: CGPoint, lineStart: CGPoint, lineEnd: CGPoint) -> CGFloat? {
let lineMag = magnitude(p1: lineEnd, p2: lineStart)
let u = (((point.x - lineStart.x) * (lineEnd.x - lineStart.x)) +
((point.y - lineStart.y) * (lineEnd.y - lineStart.y))) /
(lineMag * lineMag)
if u < 0 || u > 1 {
// closest point does not fall within the line segment
return nil
}
let intersectionX = lineStart.x + u * (lineEnd.x - lineStart.x)
let intersectionY = lineStart.y + u * (lineEnd.y - lineStart.y)
return magnitude(p1: point, p2: CGPoint(x: intersectionX, y: intersectionY))
}
#distance beetween segment ab and point c in 2D space
getDistance_ort_2 <- function(a, b, c){
#go to complex numbers
A<-c(a[1]+1i*a[2],b[1]+1i*b[2])
q=c[1]+1i*c[2]
#function to get coefficients of line (ab)
getAlphaBeta <- function(A)
{ a<-Re(A[2])-Re(A[1])
b<-Im(A[2])-Im(A[1])
ab<-as.numeric()
ab[1] <- -Re(A[1])*b/a+Im(A[1])
ab[2] <-b/a
if(Im(A[1])==Im(A[2])) ab<- c(Im(A[1]),0)
if(Re(A[1])==Re(A[2])) ab <- NA
return(ab)
}
#function to get coefficients of line ortogonal to line (ab) which goes through point q
getAlphaBeta_ort<-function(A,q)
{ ab <- getAlphaBeta(A)
coef<-c(Re(q)/ab[2]+Im(q),-1/ab[2])
if(Re(A[1])==Re(A[2])) coef<-c(Im(q),0)
return(coef)
}
#function to get coordinates of interception point
#between line (ab) and its ortogonal which goes through point q
getIntersection_ort <- function(A, q){
A.ab <- getAlphaBeta(A)
q.ab <- getAlphaBeta_ort(A,q)
if (!is.na(A.ab[1])&A.ab[2]==0) {
x<-Re(q)
y<-Im(A[1])}
if (is.na(A.ab[1])) {
x<-Re(A[1])
y<-Im(q)
}
if (!is.na(A.ab[1])&A.ab[2]!=0) {
x <- (q.ab[1] - A.ab[1])/(A.ab[2] - q.ab[2])
y <- q.ab[1] + q.ab[2]*x}
xy <- x + 1i*y
return(xy)
}
intersect<-getIntersection_ort(A,q)
if ((Mod(A[1]-intersect)+Mod(A[2]-intersect))>Mod(A[1]-A[2])) {dist<-min(Mod(A[1]-q),Mod(A[2]-q))
} else dist<-Mod(q-intersect)
return(dist)
}
我需要一个基于grumdrig的被接受答案的Godot(GDscript)实现,所以我写了一个。
func minimum_distance(v: Vector2, w: Vector2, p: Vector2):
# Return minimum distance between line segment vw and point p
var l2: float = (v - w).length_squared() # i.e. |w-v|^2 - avoid a sqrt
if l2 == 0.0:
return p.distance_to(v) # v == w case
# 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
# We clamp t from [0,1] to handle points outside the segment vw.
var t: float = max(0, min(1, (p - v).dot(w - v) / l2))
var projection: Vector2 = v + t * (w - v) # Projection falls on the segment
return p.distance_to(projection)
LineString
类。 - TC1