paraline: The line at a point `p` parallel to the line segment joining two distinct 2D points `a` and `b`

Description

An object of class "Lines". Returns the equation, slope, intercept, and \(y\)-coordinates of the line crossing the point p and parallel to the line passing through the points a and b with \(x\)-coordinates are provided in vector x.

Usage

paraline(p, a, b, x)

Value

A list with the elements

desc: Description of the line passing through point p and parallel to line segment joining a and b
mtitle: The "main" title for the plot of the line passing through point p and parallel to line segment joining a and b
points: The input points p, a, and b (stacked row-wise, i.e., point p is in row 1, point a is in row 2 and point b is in row 3). Line parallel to ab crosses p.
x: The input vector. It can be a scalar or a vector of scalars, which constitute the \(x\)-coordinates of the point(s) of interest on the line passing through point p and parallel to line segment joining a and b.
y: The output scalar or vector which constitutes the \(y\)-coordinates of the point(s) of interest on the line passing through point p and parallel to line segment joining a and b. If x is a scalar, then y will be a scalar and if x is a vector of scalars, then y will be a vector of scalars.
slope: Slope of the line, Inf is allowed, passing through point p and parallel to line segment joining a and b
intercept: Intercept of the line passing through point p and parallel to line segment joining a and b
equation: Equation of the line passing through point p and parallel to line segment joining a and b

Arguments

p: A 2D point at which the parallel line to line segment joining a and b crosses.
a, b: 2D points that determine the line segment (the line will be parallel to this line segment).
x: A scalar or a vector of scalars representing the \(x\)-coordinates of the line parallel to ab and crossing p.

Author

Elvan Ceyhan

Examples

Run this code

# \donttest{
A<-c(1.1,1.2); B<-c(2.3,3.4); p<-c(.51,2.5)

paraline(p,A,B,.45)

pts<-rbind(A,B,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

plnAB<-paraline(p,A,B,x)
plnAB
summary(plnAB)
plot(plnAB)

y<-plnAB$y
Xlim<-range(x,pts[,1])
if (!is.na(y[1])) {Ylim<-range(y,pts[,2])} else {Ylim<-range(pts[,2])}
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
pf<-c(xd,-yd)*.025

plot(A,pch=".",xlab="",ylab="",main="Line Crossing P and Parallel to AB",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
points(pts)
txt.str<-c("A","B","p")
text(pts+rbind(pf,pf,pf),txt.str)

segments(A[1],A[2],B[1],B[2],lty=2)
if (!is.na(y[1])) {lines(x,y,type="l",lty=1,xlim=Xlim,ylim=Ylim)} else {abline(v=p[1])}
tx<-(A[1]+B[1])/2;
if (!is.na(y[1])) {ty<-paraline(p,A,B,tx)$y} else {ty=p[2]}
text(tx,ty,"line parallel to AB\n and crossing p")
# }