pcds (version 0.1.4)

NumArcsAStri: Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Description

Returns the number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) whose vertices are the 2D data set, dat. The data points could be inside or outside a general triangle tri\(=T(A,B,C)=\)(rv=1,rv=2,rv=3), with vertices of tri stacked row-wise.

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" i.e., circumcenter of tri. For the number of arcs, loops are not allowed, so arcs are only possible for points inside the triangle, tri.

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

Usage

NumArcsAStri(dat, tri, M = "CC")

Value

The number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs)

Arguments

dat

A set of 2D points which constitute the vertices of the digraph (i.e., 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 tri; default is M="CC" i.e., the circumcenter of tri.

Author

Elvan Ceyhan

References

See Also

NumArcsASMT, NumArcsPEtri, and NumArcsCStri

Examples

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

n<-10  #try also n<-20
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)

NumArcsAStri(dat,Tr)  #with default M="CC"
NumArcsAStri(dat,Tr,M)

NumArcsAStri(rbind(dat,c(0,2)),Tr,M)

dat.fr<-data.frame(a=dat)
NumArcsAStri(dat.fr,Tr,M)