funsAB2MTe {pcds}

The lines joining the three vertices of the standard equilateral triangle to a center, M, of it

Description

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

Usage

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.

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.

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.

See Also

lineA2CMinTe and lineB2CMinTe

Examples

#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)