# The lines joining two vertices to the center of mass in standard equilateral triangle 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`. ```r lineA2CMinTe(x) lineB2CMinTe(x) ``` ## Arguments - `x`: A single scalar or a `vector` of scalars which is the argument of the functions `lineA2CMinTe` and `lineB2CMinTe`. ## Returns 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. ## Examples ```r #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)$y #Examples for lineB2CMinTe A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C) xfence<-abs(A[1]-B[1])*.25 #how far to go at the lower and upper ends in the x-coordinate x<-seq(min(A[1],B[1])-xfence,max(A[1],B[1])+xfence,by = .1) #try also by = .01 lnBCM<-lineB2CMinTe(x) lnBCM summary(lnBCM) plot(lnBCM,xlab=" x",ylab="y") lineB2CMinTe(.25)$y ``` ## See Also `lineA2MinTe`, `lineB2MinTe`, and `lineC2MinTe` ## Author(s) Elvan Ceyhan

funsAB2CMTe function