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

Description

Two functions, lineA2CMinTe and lineB2CMinTe of class "TriLines". Returns the equation, slope, intercept, and \(y\)-coordinates of the lines joining \(A\) and \(CM\) and also \(B\) and \(CM\).

lineA2CMinTe is the line joining \(A\) to the center of mass, \(CM\), and lineB2CMinTe 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

lineA2CMinTe(x)
lineB2CMinTe(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 lineA2CMinTe and lineB2CMinTe.

Author

Elvan Ceyhan

Examples

Run this code

# \donttest{
#Examples for lineA2CMinTe
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<-lineA2CMinTe(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,lineA2CMinTe(.25)$y),c(.75,lineB2CMinTe(.75)$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","lineA2CMinTe(x)","lineB2CMinTe(x)")
text(xc,yc,txt.str)

lineA2CMinTe(.25)$y
# }

# \donttest{
#Examples for lineB2CMinTe
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<-lineB2CMinTe(x)
lnBCM
summary(lnBCM)
plot(lnBCM,xlab=" x",ylab="y")

lineB2CMinTe(.25)$y
# }