inci.matAStri: Incidence matrix for Arc Slice Proximity Catch Digraphs...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

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 (\insertCiteceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).

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 2D data set, Xp, and AS proximity regions are defined with respect to the triangle tri and vertex regions based on circumcenter.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

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

Examples

## Not run: 

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

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.