pcds (version 0.1.6)

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

Description

Returns the incidence matrix for the AS-PCD whose vertices are the given 2D numerical data set, Xp.

AS proximity regions are defined with respect to the triangle tri\(=T(v=1,v=2,v=3)\) and vertex regions 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. Loops are allowed, so the diagonal entries are all equal to 1.

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

Usage

IncMatAStri(Xp, tri, M = "CC")

Value

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

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.

Author

Elvan Ceyhan

References

See Also

IncMatAS, IncMatPEtri, and IncMatCStri

Examples

if (FALSE) {
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<-IncMatAStri(Xp,Tr,M)
IM

dom.greedy(IM)
dom.exact(IM)
}