# The points of intersection of a line and a circle Returns the intersection point(s) of a line and a circle. The line is determined by the two points `p1` and `p2` and the circle is centered at point `cent` and has radius `rad`. If the circle does not intersect the line, the function yields `NULL`; if the circle intersects at only one point, it yields only that point; otherwise it yields both intersection points as output. When there are two intersection points, they are listed in the order of the $x$-coordinates of `p1` and `p2`; and if the $x$-coordinates of `p1` and `p2` are equal, intersection points are listed in the order of $y$-coordinates of `p1` and `p2`. ```r intersect.line.circle(p1, p2, cent, rad) ``` ## Arguments - `p1, p2`: 2D points that determine the straight line (i.e., through which the straight line passes). - `cent`: A 2D point representing the center of the circle. - `rad`: A positive real number representing the radius of the circle. ## Returns point(s) of intersection between the circle and the line (if they do not intersect, the function yields `NULL` as the output) ## Examples ```r P1<-c(.3,.2)*100 P2<-c(.6,.3)*100 cent<-c(1.1,1.1)*100 rad<-2*100 intersect.line.circle(P1,P2,cent,rad) intersect.line.circle(P2,P1,cent,rad) intersect.line.circle(P1,P1+c(0,1),cent,rad) intersect.line.circle(P1+c(0,1),P1,cent,rad) dist.point2line(cent,P1,P2) rad2<-dist.point2line(cent,P1,P2)$d intersect.line.circle(P1,P2,cent,rad2) intersect.line.circle(P1,P2,cent,rad=.8) intersect.line.circle(P1,P2,cent,rad=.78) #plot of the line and the circle A<-c(.3,.2); B<-c(.6,.3); cent<-c(1,1); rad<-2 #check dist.point2line(cent,A,B)$dis, .3 IPs<-intersect.line.circle(A,B,cent,rad) xr<-range(A[1],B[1],cent[1]) xf<-(xr[2]-xr[1])*.1 #how far to go at the lower and upper ends in the x-coordinate x<-seq(xr[1]-rad-xf,xr[2]+rad+xf,l=20) #try also l=100 lnAB<-Line(A,B,x) y<-lnAB$y Xlim<-range(x,cent[1]) Ylim<-range(y,A[2],B[2],cent[2]-rad,cent[2]+rad) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(rbind(A,B,cent),pch=1,asp=1,xlab="x",ylab="y", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) lines(x,y,lty=1) interp::circles(cent[1],cent[2],rad) IP.txt<-c() if (!is.null(IPs)) { for (i in 1:(length(IPs)/2)) IP.txt<-c(IP.txt,paste("I",i, sep = "")) } txt<-rbind(A,B,cent,IPs) text(txt+cbind(rep(xd*.03,nrow(txt)),rep(-yd*.03,nrow(txt))),c("A","B","M",IP.txt)) ``` ## See Also `intersect2lines` ## Author(s) Elvan Ceyhan

intersect.line.circle function