num.arcsAStri: Number of arcs of Arc Slice Proximity Catch Digraphs...

In pcds: Proximity Catch Digraphs and Their Applications

Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) and quantities related to the triangle - one triangle case

Description

An object of class "NumArcs". Returns the number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) whose vertices are the 2D data set, Xp. It also provides number of vertices (i.e., number of data points inside the triangle) and indices of the data points that reside in the triangle.

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=(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. For the number of arcs, loops are not allowed, so arcs are only possible for points inside the triangle, tri.

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

Usage

num.arcsAStri(Xp, tri, M = "CC")

Arguments

Xp	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.

Value

A list with the elements

desc	A short description of the output: number of arcs and quantities related to the triangle
num.arcs	Number of arcs of the AS-PCD
tri.num.arcs	Number of arcs of the induced subdigraph of the AS-PCD for vertices in the triangle tri
num.in.tri	Number of Xp points in the triangle, tri
ind.in.tri	The vector of indices of the Xp points that reside in the triangle
tess.points	Tessellation points, i.e., points on which the tessellation of the study region is performed, here, tessellation points are the vertices of the support triangle tri.
vertices	Vertices of the digraph, Xp.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

num.arcsAS, num.arcsPEtri, and num.arcsCStri

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

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

Narcs = num.arcsAStri(Xp,Tr,M)
Narcs
summary(Narcs)
plot(Narcs)

pcds documentation built on May 29, 2024, 9:36 a.m.