pcds (version 0.1.8)

rel.edge.std.triCM: The index of the edge region in the standard equilateral triangle that contains a point

Description

Returns the index of the edge whose region contains point, p, in the standard equilateral triangle \(T_e=T(A=(0,0),B=(1,0),C=(1/2,\sqrt{3}/2))\) with edge regions based on center of mass \(CM=(A+B+C)/3\).

Edges are labeled as 3 for edge \(AB\), 1 for edge \(BC\), and 2 for edge \(AC\). If the point, p, is not inside tri, then the function yields NA as output. Edge region 1 is the triangle \(T(B,C,M)\), edge region 2 is \(T(A,C,M)\), and edge region 3 is \(T(A,B,M)\).

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012,ceyhan:arc-density-CS;textualpcds).

Usage

rel.edge.std.triCM(p)

Value

A list with three elements

re

Index of the \(CM\)-edge region that contains point, p in the standard equilateral triangle \(T_e\)

tri

The vertices of the standard equilateral triangle \(T_e\), where row labels are \(A\), \(B\), and \(C\) with edges are labeled as 3 for edge \(AB\), 1 for edge \(BC\), and 2 for edge \(AC\).

desc

Description of the edge labels

Arguments

p

A 2D point for which \(CM\)-edge region it resides in is to be determined in the the standard equilateral triangle \(T_e\).

Author

Elvan Ceyhan

References

See Also

rel.edge.triCM, rel.edge.tri, rel.edge.basic.triCM, rel.edge.basic.tri, and edge.reg.triCM

Examples

# \donttest{
P<-c(.4,.2)
rel.edge.std.triCM(P)

A<-c(0,0); B<-c(1,0); C<-c(0.5,sqrt(3)/2);
Te<-rbind(A,B,C)
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
CM<-(A+B+C)/3

n<-20  #try also n<-40
Xp<-runif.std.tri(n)$gen.points

re<-vector()
for (i in 1:n)
  re<-c(re,rel.edge.std.triCM(Xp[i,])$re)
re

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

plot(Te,asp=1,xlab="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01))
points(Xp,pch=".")
polygon(Te)
L<-Te; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE)
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)
text(Xp,labels=factor(re))

txt<-rbind(Te,CM)
xc<-txt[,1]+c(-.03,.03,.03,-.06)
yc<-txt[,2]+c(.02,.02,.02,.03)
txt.str<-c("A","B","C","CM")
text(xc,yc,txt.str)

p1<-(A+B+CM)/3
p2<-(B+C+CM)/3
p3<-(A+C+CM)/3

plot(Te,xlab="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.01,.01),ylim=Ylim+yd*c(-.01,.01))
polygon(Te)
L<-Te; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE)
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)

txt<-rbind(Te,CM,p1,p2,p3)
xc<-txt[,1]+c(-.03,.03,.03,-.06,0,0,0)
yc<-txt[,2]+c(.02,.02,.02,.03,0,0,0)
txt.str<-c("A","B","C","CM","re=3","re=1","re=2")
text(xc,yc,txt.str)
# }