edge.reg.triCM {pcds}

The vertices of the CM-edge region in a triangle that contains the point

Description

Returns the edge whose region contains point, p, in the triangle tri=T(A,B,C) with edge regions based on center of mass CM=(A+B+C)/3.

This function is related to rel.edge.triCM, but unlike rel.edge.triCM the related edges are given as vertices ABC for re=3, as BCA for re=1 and as CAB for re=2 where edges are labeled as 3 for edge AB, 1 for edge BC, and 2 for edge AC. The vertices are given one vertex in each row in the output, e.g., ABC is printed as rbind(A,B,C), where row 1 has the entries of vertex A, row 2 has the entries of vertex B, and row 3 has the entries of vertex C.

If the point, p, is not inside tri, then the function yields NA as output.

Edge region for BCA is the triangle T(B,C,CM), edge region CAB is T(A,C,CM), and edge region ABC is T(A,B,CM).

See also (Ceyhan (2005, 2010)).

Usage

edge.reg.triCM(p, tri)

Arguments

p

A 2D point for which CM-edge region it resides in is to be determined in the triangle tri.

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

Value

The CM-edge region that contains point, p in the triangle tri. The related edges are given as vertices ABC for re=3, as BCA for re=1 and as CAB for re=2 where edges are labeled as 3 for edge AB, 1 for edge BC, and 2 for edge AC.

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.

See Also

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

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);

P<-c(.4,.2)  #try also P<-as.numeric(runif.tri(1,Tr)$g)
edge.reg.triCM(P,Tr)

P<-c(1.8,.5)
edge.reg.triCM(P,Tr)

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

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

plot(Tr,pch=".",xlab="",ylab="",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
L<-Tr; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE)
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)

txt<-rbind(Tr,CM,p1,p2,p3)
xc<-txt[,1]+c(-.02,.02,.02,-.05,0,0,0)
yc<-txt[,2]+c(.02,.02,.02,.02,0,0,0)
txt.str<-c("A","B","C","CM","re=T(A,B,CM)","re=T(B,C,CM)","re=T(A,C,CM)")
text(xc,yc,txt.str)