re.tri.cent: The index of the edge region in a triangle that contains the point

Description

Returns the index of the edge whose region contains point, pt, in the triangle $t r i = T (A, B, C)$ with edge regions based on center $M = (m_{1}, m_{2})$ in Cartesian coordinates or $M = (α, β, γ)$ in barycentric coordinates in the interior of the triangle tri.

Edges are labeled as 3 for edge AB, 1 for edge BC, and 2 for edge AC. If the point, pt, 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

re.tri.cent(pt, tri, M)

Arguments

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

tri

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

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri.

Value

A list with three elements

Index of the M-edge region that contains point, pt in the triangle tri.

tri

The vertices of the triangle, 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

References

Examples

Run this code

# NOT RUN {
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);

P<-c(1.4,1.2)
M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.2)

re.tri.cent(P,Tr,M)

P<-c(.8,.2)
re.tri.cent(P,Tr,M)

P<-c(1.5,1.61)
re.tri.cent(P,Tr,M)

re.tri.cent(A,Tr,M)
re.tri.cent(B,Tr,M)
re.tri.cent(C,Tr,M)
re.tri.cent(M,Tr,M)

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

re<-vector()
for (i in 1:n)
  re<-c(re,re.tri.cent(dat[i,],Tr,M)$re)
re

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

if (dimension(M)==3) {M<-bary2cart(M,Tr)}

plot(Tr,xlab="",ylab="",axes=TRUE,pch=".",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(dat,pch=".")
L<-Tr; R<-rbind(M,M,M)
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
text(dat,labels=factor(re))

txt<-rbind(Tr,M)
xc<-txt[,1]
yc<-txt[,2]
txt.str<-c("A","B","C","M")
text(xc,yc,txt.str)

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

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

txt<-rbind(Tr,M,p1,p2,p3)
xc<-txt[,1]+c(-.02,.02,.02,.02)
yc<-txt[,2]+c(.02,.02,.04,.05)
txt.str<-c("A","B","C","M","re=3","re=1","re=2")
text(xc,yc,txt.str)

dat.fr<-data.frame(a=Tr)
re.tri.cent(P,dat.fr,M)

# }

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