dist.point2line {pcds}

The distance from a point to a line defined by two points

Description

Returns the distance from a point p to the line joining points a and b in 2D space.

Usage

dist.point2line(p, a, b)

Arguments

p

A 2D point, distance from p to the line passing through points a and b are to be computed.

a, b

2D points that determine the straight line (i.e., through which the straight line passes).

Value

A list with two elements

dis

Distance from point p to the line passing through a and b

cl2p

The closest point on the line passing through a and b to the point p

Author(s)

Elvan Ceyhan

See Also

dist.point2plane, dist.point2set, and Dist

Examples

A<-c(1,2); B<-c(2,3); P<-c(3,1.5)

dpl<-dist.point2line(P,A,B);
dpl
C<-dpl$cl2p
pts<-rbind(A,B,C,P)

xr<-range(pts[,1])
xf<-(xr[2]-xr[1])*.25
#how far to go at the lower and upper ends in the x-coordinate
x<-seq(xr[1]-xf,xr[2]+xf,l=5)  #try also l=10, 20, or 100
lnAB<-Line(A,B,x)
y<-lnAB$y
int<-lnAB$intercept #intercept
sl<-lnAB$slope #slope

xsq<-seq(min(A[1],B[1],P[1])-xf,max(A[1],B[1],P[1])+xf,l=5)
#try also l=10, 20, or 100
pline<-(-1/sl)*(xsq-P[1])+P[2]
#line passing thru P and perpendicular to AB

Xlim<-range(pts[,1],x)
Ylim<-range(pts[,2],y)
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(rbind(P),asp=1,pch=1,xlab="x",ylab="y",
main="Illustration of the distance from P \n to the Line Crossing Points A and B",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
points(rbind(A,B),pch=1)
lines(x,y,lty=1,xlim=Xlim,ylim=Ylim)
int<-round(int,2); sl<-round(sl,2)
text(rbind((A+B)/2+xd*c(-.01,-.01)),ifelse(sl==0,paste("y=",int),
ifelse(sl==1,paste("y=x+",int),
ifelse(int==0,paste("y=",sl,"x"),paste("y=",sl,"x+",int)))))
text(rbind(A+xd*c(0,-.01),B+xd*c(.0,-.01),P+xd*c(.01,-.01)),c("A","B","P"))
lines(xsq,pline,lty=2)
segments(P[1],P[2], C[1], C[2], lty=1,col=2,lwd=2)
text(rbind(C+xd*c(-.01,-.01)),"C")
text(rbind((P+C)/2),col=2,paste("d=",round(dpl$dis,2)))