pcds (version 0.1.8)

rel.vert.triCC: The index of the \(CC\)-vertex region in a triangle that contains a point

Description

Returns the index of the vertex whose region contains point p in a triangle tri\(=(A,B,C)\) and vertex regions are based on the circumcenter \(CC\) 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. If the point, p, is not inside tri, then the function yields NA as output. The corresponding vertex region is the polygon whose interior points are closest to that vertex. If tri is equilateral triangle, then \(CC\) and \(CM\) (center of mass) coincide.

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

Usage

rel.vert.triCC(p, tri)

Value

A list with two elements

rv

Index of the \(CC\)-vertex region that contains point, p in the triangle tri

tri

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

Arguments

p

A 2D point for which \(CC\)-vertex 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.

Author

Elvan Ceyhan

References

See Also

rel.vert.tri, rel.vert.triCM, rel.vert.basic.triCM, rel.vert.basic.triCC, rel.vert.basic.tri, and rel.vert.std.triCM

Examples

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

P<-c(1.3,1.2)
rel.vert.triCC(P,Tr)

CC<-circumcenter.tri(Tr)  #the circumcenter
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)

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

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

txt<-rbind(Tr,CC,Ds)
xc<-txt[,1]+c(-.07,.08,.06,.12,-.1,-.1,-.09)
yc<-txt[,2]+c(.02,-.02,.03,.0,.02,.06,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)

RV1<-(A+.5*(D3-A)+A+.5*(D2-A))/2
RV2<-(B+.5*(D3-B)+B+.5*(D1-B))/2
RV3<-(C+.5*(D2-C)+C+.5*(D1-C))/2

txt<-rbind(RV1,RV2,RV3)
xc<-txt[,1]
yc<-txt[,2]
txt.str<-c("rv=1","rv=2","rv=3")
text(xc,yc,txt.str)

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

Rv<-vector()
for (i in 1:n)
  Rv<-c(Rv,rel.vert.triCC(Xp[i,],Tr)$rv)
Rv

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

plot(Tr,asp=1,xlab="",ylab="",
main="Illustration of CC-Vertex Regions\n in a Triangle",
pch=".",axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(Xp,pch=".")
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)
text(Xp,labels=factor(Rv))

txt<-rbind(Tr,CC,Ds)
xc<-txt[,1]+c(-.07,.08,.06,.12,-.1,-.1,-.09)
yc<-txt[,2]+c(.02,-.02,.03,.0,.02,.06,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)
# }