# The lines joining the three vertices of the standard equilateral triangle to a center, `M`, of it Three functions, `lineA2MinTe`, `lineB2MinTe` and `lineC2MinTe` of class `"TriLines"`. Returns the `equation, slope, intercept`, and $y$-coordinates of the lines joining $A$ and `M`, $B$ and `M`, and also $C$ and `M`. `lineA2MinTe` is the line joining $A$ to the center, `M`, `lineB2MinTe` is the line joining $B$ to `M`, and `lineC2MinTe` is the line joining C to `M`, 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 lineA2MinTe(x, M) lineB2MinTe(x, M) lineC2MinTe(x, M) ``` ## Arguments - `x`: A single scalar or a `vector` of scalars. - `M`: A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the standard equilateral triangle. ## 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. - **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 lineA2MinTe A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C) M<-c(.65,.2) #try also M<-c(1,1,1) 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 lnAM<-lineA2MinTe(x,M) lnAM summary(lnAM) plot(lnAM) Ds<-prj.cent2edges(Te,M) #finds the projections from a point M=(m1,m2) to the edges on the #extension of the lines joining M to the vertices in the triangle Te 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<-rbind(M,M,M) segments(L[,1], L[,2], R[,1], R[,2], lty = 2) L<-Ds; R<-rbind(M,M,M) segments(L[,1], L[,2], R[,1], R[,2], lty = 3,col=2) txt<-rbind(Te,M,Ds,c(.25,lineA2MinTe(.25,M)$y),c(.4,lineB2MinTe(.4,M)$y), c(.60,lineC2MinTe(.60,M)$y)) xc<-txt[,1]+c(-.02,.02,.02,.02,.04,-.03,.0,0,0,0) yc<-txt[,2]+c(.02,.02,.02,.05,.02,.03,-.03,0,0,0) txt.str<-c("A","B","C","M","D1","D2","D3","lineA2MinTe(x)","lineB2MinTe(x)","lineC2MinTe(x)") text(xc,yc,txt.str) lineA2MinTe(.25,M) #Examples for lineB2MinTe A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C) M<-c(.65,.2) #try also M<-c(1,1,1) 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 = .5) #try also by = .1 lnBM<-lineB2MinTe(x,M) lnBM summary(lnBM) plot(lnBM) #Examples for lineC2MinTe A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2); Te<-rbind(A,B,C) M<-c(.65,.2) #try also M<-c(1,1,1) 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 = .5) #try also by = .1 lnCM<-lineC2MinTe(x,M) lnCM summary(lnCM) plot(lnCM) ``` ## See Also `lineA2CMinTe` and `lineB2CMinTe`

funsAB2MTe function