funsAB2CMTe: The lines joining two vertices to the center of mass in standard equilateral triangle

Description

Two functions, lA_CM.Te and lB_CM.Te of class "TriLines". Returns the equation, slope, intercept, and \(y\)-coordinates of the lines joining \(A\) and \(CM\) and also \(B\) and \(CM\).

lA_CM.Te is the line joining \(A\) to the center of mass, \(CM\), and

lB_CM.Te is the line joining \(B\) to the center of mass, \(CM\), in the standard equilateral triangle \(T_e=(A,B,C)\) with \(A=(0,0)\), \(B=(1,0)\), \(C=(1/2,\sqrt{3}/2)\); \(x\)-coordinates are provided in vector x.

Usage

lA_CM.Te(x)
lB_CM.Te(x)

Value

A list with the elements

txt1: Longer description of the line.
txt2: Shorter description of the line (to be inserted over the line in the plot).
mtitle: The "main" title for the plot of the line.
cent: The center chosen inside the standard equilateral triangle.
cent.name: The name of the center inside the standard equilateral triangle. It is "CM" for these two functions.
tri: The triangle (it is the standard equilateral triangle for this function).
x: The input vector, can be a scalar or a vector of scalars, which constitute the \(x\)-coordinates of the point(s) of interest on the line.
y: The output vector, will be a scalar if x is a scalar or a vector of scalars if x is a vector of scalar, constitutes the \(y\)-coordinates of the point(s) of interest on the line.
slope: Slope of the line.
intercept: Intercept of the line.
equation: Equation of the line.

Arguments

x: A single scalar or a vector of scalars which is the argument of the functions lA_CM.Te and lB_CM.Te.

Author

Elvan Ceyhan

Examples

Run this code

#Examples for lA_CM.Te
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C)
xfence<-abs(A[1]-B[1])*.25 #how far to go at the lower and upper ends in the x-coordinate
x<-seq(min(A[1],B[1])-xfence,max(A[1],B[1])+xfence,by=.1)  #try also by=.01

lnACM<-lA_CM.Te(x)
lnACM
summary(lnACM)
plot(lnACM)

CM<-(A+B+C)/3;
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

Xlim<-range(Te[,1])
Ylim<-range(Te[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Te,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Te)
L<-Te; R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)

txt<-rbind(Te,CM,D1,D2,D3,c(.25,lA_CM.Te(.25)$y),c(.75,lB_CM.Te(.75)$y))
xc<-txt[,1]+c(-.02,.02,.02,.05,.05,-.03,.0,0,0)
yc<-txt[,2]+c(.02,.02,.02,.02,0,.02,-.04,0,0)
txt.str<-c("A","B","C","CM","D1","D2","D3","lA_CM.Te(x)","lB_CM.Te(x)")
text(xc,yc,txt.str)

lA_CM.Te(.25)$y

#Examples for lB_CM.Te
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C)
xfence<-abs(A[1]-B[1])*.25 #how far to go at the lower and upper ends in the x-coordinate
x<-seq(min(A[1],B[1])-xfence,max(A[1],B[1])+xfence,by=.1)  #try also by=.01

lnBCM<-lB_CM.Te(x)
lnBCM
summary(lnBCM)
plot(lnBCM,xlab="x",ylab="y")

lB_CM.Te(.25)$y