pcds (version 0.1.8)

inci.matAS: Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case

Description

Returns the incidence matrix for the AS-PCD whose vertices are a given 2D numerical data set, Xp, in the convex hull of Yp which is partitioned by the Delaunay triangles based on Yp points.

AS proximity regions are defined with respect to the Delaunay triangles based on Yp points and vertex regions are based on the center M="CC" for circumcenter of each Delaunay triangle or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of each Delaunay triangle; default is M="CC" i.e., circumcenter of each triangle.

Each Delaunay triangle is first converted to an (nonscaled) basic triangle so that M will be the same type of center for each Delaunay triangle (this conversion is not necessary when M is \(CM\)).

Convex hull of Yp is partitioned by the Delaunay triangles based on Yp points (i.e., multiple triangles are the set of these Delaunay triangles whose union constitutes the convex hull of Yp points). For the incidence matrix loops are allowed, so the diagonal entries are all equal to 1.

See (ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds) for more on AS-PCDs. Also see (okabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textualpcds) for more on Delaunay triangulation and the corresponding algorithm.

Usage

inci.matAS(Xp, Yp, M = "CC")

Value

Incidence matrix for the AS-PCD whose vertices are the 2D data set, Xp, and AS proximity regions are defined in the Delaunay triangles based on Yp points.

Arguments

Xp

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

Yp

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

M

The center of the triangle. "CC" stands for circumcenter of each Delaunay triangle or 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle; default is M="CC" i.e., the circumcenter of each triangle.

Author

Elvan Ceyhan

References

See Also

inci.matAStri, inci.matPE, and inci.matCS

Examples

# \donttest{
#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-15; ny<-5;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
Xp<-cbind(runif(nx,0,1),runif(nx,0,1))
Yp<-cbind(runif(ny,0,.25),runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))

M<-"CC"  #try also M<-c(1,1,1)

IM<-inci.matAS(Xp,Yp,M)
IM
dom.num.greedy(IM)  #try also dom.num.exact(IM)  #this might take a long time for large  nx

IM<-inci.matAS(Xp,Yp[1:3,],M)

inci.matAS(Xp,rbind(Yp,Yp))
# }