pcds (version 0.1.4)

redges.triCM: The indices of the $CM$-edge regions in a triangle that contains the points in a give data set

Description

Returns the indices of the edges whose regions contain the points in data set Dt in a triangle tri$=(A,B,C)$ and edge regions are based on the center of mass $CM$ of tri. (see the plots in the example for illustrations).

The vertices of the triangle tri are labeled as $1=A$, $2=B$, and $3=C$ also according to the row number the vertex is recorded in tri and the corresponding edges are $1=BC$, $2=AC$, and $3=AB$.

If a point in Dt is not inside tri, then the function yields NA as output for that entry. The corresponding edge region is the polygon with the vertex, $CM$, and vertices other than the non-adjacent vertex, i.e., edge region 1 is the triangle $T(B,CM,C)$, edge region 2 is $T(A,CM,C)$ and edge region 3 is $T(A,B,CM)$.

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

Usage

redges.triCM(Dt, tri)

Value

A list with the elements

re

Indices (i.e., a vector of indices) of the edges whose region contains points in Dt in the triangle tri

tri

The vertices of the triangle, where row number corresponds to the vertex index in rv.

desc

Description of the edge labels as "Edge labels are AB=1, BC=2, and AC=3".

Arguments

Dt

A set of 2D points representing the set of data points for which indices of the edge regions containing them are to be determined.

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

Author

Elvan Ceyhan

References

See Also

redges.tri.cent, rverts.tri.cent and rverts.tri.nd

Examples

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

P<-c(.4,.2)
redges.triCM(P,Tr)

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

P<-c(10.5,1.6)
redges.triCM(P,Tr)

n<-10  #try also n<-20
set.seed(1)
dat<-runif.tri(n,Tr)$g

re<-redges.triCM(dat,Tr)
re
CM<-(A+B+C)/3
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

Xlim<-range(Tr[,1],dat[,1])
Ylim<-range(Tr[,2],dat[,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)
points(dat,pch=".",col=1)
L<-Tr; R<-matrix(rep(CM,3),ncol=2,byrow=TRUE)
segments(L[,1], L[,2], R[,1], R[,2], lty=2)

xc<-Tr[,1]+c(-.02,.03,.02)
yc<-Tr[,2]+c(.02,.02,.04)
txt.str<-c("A","B","C")
text(xc,yc,txt.str)

txt<-rbind(CM,Ds)
xc<-txt[,1]+c(.05,.06,-.05,-.02)
yc<-txt[,2]+c(.03,.03,.05,-.08)
txt.str<-c("CM","re=2","re=3","re=1")
text(xc,yc,txt.str)
text(dat,labels=factor(re$re))

redges.triCM(dat,Tr)

dat.fr<-data.frame(a=dat)
redges.triCM(dat.fr,Tr)

dat.fr<-data.frame(a=Tr)
redges.triCM(dat,dat.fr)