inci.matAStri {pcds}

Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Description

Returns the incidence matrix of the AS-PCD whose vertices are the given 2D numerical data set, Xp, in the triangle tri=T(v=1,v=2,v=3).

AS proximity regions are defined with respect to the triangle tri=T(v=1,v=2,v=3) and vertex regions are based on the center, M=(m_1,m_2) in Cartesian coordinates or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of the triangle tri or based on circumcenter of tri; default is M="CC", i.e., circumcenter of tri. Loops are allowed, so the diagonal entries are all equal to 1.

See also (Ceyhan (2005, 2010)).

Usage

inci.matAStri(Xp, tri, M = "CC")

Arguments

Xp

A set of 2D points which constitute the vertices of 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.

Value

Incidence matrix for the AS-PCD whose vertices are the 2D data set, Xp, and AS proximity regions are defined with respect to the triangle tri and vertex regions based on the center M.

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.

See Also

inci.matAS, inci.matPEtri, and inci.matCStri

Examples

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

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

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

IM<-inci.matAStri(Xp,Tr,M)
IM

dom.num.greedy(IM)
dom.num.exact(IM)