pcds (version 0.1.4)

Gam1AStri: The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Description

Returns I(p is a dominating point of the AS-PCD whose vertices are the 2D data set Dt), that is, returns 1 if p is a dominating point of AS-PCD, returns 0 otherwise. Point, p, is in the region of vertex rv (default is NULL); vertices are labeled as \(1,2,3\) in the order they are stacked row-wise in tri.

AS proximity regions are defined with respect to the triangle tri and vertex regions are based on the center M="CC" for circumcenter of tri; or \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of the triangle tri; default is M="CC" the circumcenter of tri.

ch.data.pnt is for checking whether point p is a data point in Dt or not (default is FALSE), so by default this function checks whether the point p would be a dominating point if it actually were in the data set.

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

Usage

Gam1AStri(p, Dt, tri, M = "CC", rv = NULL, ch.data.pnt = FALSE)

Value

I(p is a dominating point of the AS-PCD whose vertices are the 2D data set Dt), that is, returns 1 if p is a dominating point of the AS-PCD, returns 0 otherwise

Arguments

p

A 2D point that is to be tested for being a dominating point or not of the AS-PCD.

Dt

A set of 2D points which constitutes the vertices of the AS-PCD.

tri

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

M

The center of the triangle. "CC" stands for circumcenter of the triangle tri or a 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle \(T_b\); default is M="CC" i.e., the circumcenter of tri.

rv

Index of the vertex whose region contains point p, rv takes the vertex labels as \(1,2,3\) as in the row order of the vertices in tri.

ch.data.pnt

A logical argument for checking whether point p is a data point in Dt or not (default is FALSE).

Author

Elvan Ceyhan

References

See Also

Gam1ASbastri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

set.seed(1)
dat<-runif.tri(n,Tr)$g

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

Gam1AStri(dat[1,],dat,Tr,M)
Gam1AStri(dat[1,],dat[1,],Tr,M)
Gam1AStri(c(1.5,1.5),c(1.6,1),Tr,M)
Gam1AStri(c(1.6,1),c(1.5,1.5),Tr,M)

gam.vec<-vector()
for (i in 1:n)
{gam.vec<-c(gam.vec,Gam1AStri(dat[i,],dat,Tr,M))}

ind.gam1<-which(gam.vec==1)
ind.gam1

#or try
Rv<-rv.triCC(dat[1,],Tr)$rv
Gam1AStri(dat[1,],dat,Tr,M,Rv)

Gam1AStri(c(.2,.4),dat,Tr,M)
Gam1AStri(c(.2,.4),c(.2,.4),Tr,M)

dat2<-rbind(dat,c(.2,.4))
Gam1AStri(dat[1,],dat2,Tr,M)

if (dimension(M)==3) {M<-bary2cart(M,Tr)}
#need to run this when M is given in barycentric coordinates

CC<-circ.cent.tri(Tr)  #the circumcenter

if (isTRUE(all.equal(M,CC)) || identical(M,"CC"))
{cent<-CC
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)
cent.name<-"CC"
} else
{cent<-M
cent.name<-"M"
Ds<-cp2e.tri(Tr,M)
D1<-Ds[1,]; D2<-Ds[2,]; D3<-Ds[3,]
}

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

plot(A,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(dat)
L<-rbind(cent,cent,cent); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
points(rbind(dat[ind.gam1,]),pch=4,col=2)

txt<-rbind(Tr,cent,Ds)
xc<-txt[,1]
yc<-txt[,2]
txt.str<-c("A","B","C",cent.name,"D1","D2","D3")
text(xc,yc,txt.str)

Gam1AStri(c(1.5,1.1),dat,Tr,M)

dat.fr<-data.frame(a=dat)
Gam1AStri(c(1.5,1.1),dat.fr,Tr,M)

dat.fr<-data.frame(a=Tr)
Gam1AStri(c(1.5,1.1),dat,dat.fr,M)

Gam1AStri(c(1.5,1.1),dat,Tr,M)

Gam1AStri(c(1.5,1.1),dat,Tr,M,ch.data.pnt=FALSE)
#gives an error message if ch.data.pnt=TRUE since point p is not a data point in Dt