pcds (version 0.1.8)

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

Description

Returns the index of the edge whose region contains point, p, in the triangle tri\(=T(A,B,C)\) with edge regions based on center \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) 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, 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.tri(p, tri, M)

Value

A list with three elements

re

Index of the M-edge region that contains point, p 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

Arguments

p

A 2D point for which M-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.

M

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.

Author

Elvan Ceyhan

References

See Also

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

Examples

# \donttest{
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)

rel.edge.tri(P,Tr,M)

n<-20  #try also n<-40
Xp<-runif.tri(n,Tr)$g

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

Xlim<-range(Tr[,1],Xp[,1])
Ylim<-range(Tr[,2],Xp[,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(Xp,pch=".")
L<-Tr; R<-rbind(M,M,M)
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)
text(Xp,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="", main="Illustration of M-edge regions in a triangle",
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,.02,.02,.02)
yc<-txt[,2]+c(.02,.02,.04,.05,.02,.02,.02)
txt.str<-c("A","B","C","M","re=3","re=1","re=2")
text(xc,yc,txt.str)
# }