Line: The line 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 two distinct 2D points a and b with $x$-coordinates provided in vector x.

This function is different from the line function in the standard stats package in R in the sense that Line(a,b,x) fits the line passing through points a and b and returns various quantities (see below) for this line and x is the $x$-coordinates of the points we want to find on the Line(a,b,x) while line(a,b) fits the line robustly whose $x$-coordinates are in a and $y$-coordinates are in b.

Line(a,b,x) and line(x,Line(A,B,x)$y) would yield the same straight line (i.e., the line with the same coefficients.)

Usage

Line(a, b, x)

Value

A list with the elements

desc: A description of the line
mtitle: The "main" title for the plot of the line
points: The input points a and b through which the straight line passes (stacked row-wise, i.e., row 1 is point a and row 2 is point b).
x: The input scalar or vector which constitutes the $x$-coordinates of the point(s) of interest on the line.
y: The output scalar or vector which constitutes the $y$-coordinates of the point(s) of interest on the line. 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 points a and b
intercept: Intercept of the line passing through points a and b
equation: Equation of the line passing through points a and b

Arguments

a, b: 2D points that determine the straight line (i.e., through which the straight line passes).
x: A scalar or a vector of scalars representing the $x$-coordinates of the line.

Author

Elvan Ceyhan

Examples

Run this code

# \donttest{
A<-c(-1.22,-2.33); B<-c(2.55,3.75)

xr<-range(A,B);
xf<-(xr[2]-xr[1])*.1
#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)
lnAB
summary(lnAB)
plot(lnAB)

line(A,B)
#this takes vector A as the x points and vector B as the y points and fits the line
#for example, try
x=runif(100); y=x+(runif(100,-.05,.05))
plot(x,y)
line(x,y)

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

#plot of the line joining A and B
plot(rbind(A,B),pch=1,xlab="x",ylab="y",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
if (!is.na(y[1])) {lines(x,y,lty=1)} else {abline(v=A[1])}
text(rbind(A+pf,B+pf),c("A","B"))
int<-round(lnAB$intercep,2)  #intercept
sl<-round(lnAB$slope,2)  #slope
text(rbind((A+B)/2+pf*3),ifelse(is.na(int),paste("x=",A[1]),
ifelse(sl==0,paste("y=",int),
ifelse(sl==1,ifelse(sign(int)<0,paste("y=x",int),paste("y=x+",int)),
ifelse(sign(int)<0,paste("y=",sl,"x",int),paste("y=",sl,"x+",int))))))
# }