1d:T7cd,# The distance from a point to a line defined by two points Returns the distance from a point `p` to the line joining points `a` and `b` in 2D space. ```r 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). ## Returns 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` ## Examples ```r 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))) ``` ## See Also `dist.point2plane`, `dist.point2set`, and `Dist` ## Author(s) Elvan Ceyhan

dist.point2line function