pcds package - RDocumentation

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This is an R package that contains the functions for construction and visualization of proximity catch digraphs (PCDs) for one, two and three dimensional data. The PCD families considered are Arc-Slice (AS) PCDs, Proportional-Edge (PE) PCDs and Central Similarity (CS) PCDs. The package also contains functions for testing spatial patterns of segregation and association against complete spatial randomness (CSR) and Uniformness in one and two dimensional cases. Also included are the functions for generating points from these spatial patterns.

Install from GitHub : devtools::install_github("elvanceyhan/pcds")

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Install

install.packages('pcds')

Monthly Downloads

256

Version

0.1.8

License

GPL-2

Maintainer

Elvan Ceyhan

Last Published

December 19th, 2023

Functions in pcds (0.1.8)

The indicator for the presence of an arc from a point to another for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

CSarc.dens.test1D

A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data

The distance between two vectors, matrices, or data frames

IarcASbasic.tri

The indicator for the presence of an arc from a point to another for Arc Slice Proximity Catch Digraphs (AS-PCDs) - standard basic triangle case

CSarc.dens.test.int

A test of uniformity of 1D data in a given interval based on Central Similarity Proximity Catch Digraph (CS-PCD)

Arc density of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Arc density of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

IarcCS.Te.onesixth

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one-sixth of the standard equilateral triangle case

CSarc.dens.test

A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data

IarcASset2pnt.tri

The indicator for the presence of an arc from a point in set S to the point p for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

IarcCSset2pnt.std.tri

The indicator for the presence of an arc from a point in set S to the point p for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case

IarcCSset2pnt.tri

The indicator for the presence of an arc from a point in set S to the point p for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

IarcCSt1.std.tri

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with \(t=1\)

IarcCSbasic.tri

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard basic triangle case

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end-interval case

The indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs)

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

IarcCSedge.reg.std.tri

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end-interval case

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one interval case

IarcPEset2pnt.tri

The indicator for the presence of an arc from a point in set S to the point p for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

An alternative to the function IarcCStri which yields the indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs)

The indicator for the presence of an arc from one 3D point to another 3D point for Proportional Edge Proximity Catch Digraphs (PE-PCDs)

Idom.num1ASbasic.tri

The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - standard basic triangle case

Idom.num1CS.Te.onesixth

The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one-sixth of the standard equilateral triangle case

IarcPEset2pnt.std.tri

The indicator for the presence of an arc from a point in set S to the point p or Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

Idom.num1CSstd.tri

The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Idom.num.up.bnd

Indicator for an upper bound for the domination number by the exact algorithm

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

Idom.num1CSt1std.tri

The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with \(t=1\)

IarcPEstd.tetra

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case

The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) for an interval

Idom.num2PEtetra

The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case

The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

Idom.num2ASbasic.tri

The indicator for two points being a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - standard basic triangle case

The indicator for two points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

Idom.num2PEbasic.tri

The indicator for two points being a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard basic triangle case

Idom.num1PEstd.tetra

The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case

IarcPEbasic.tri

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard basic triangle case

Idom.num1PEbasic.tri

The indicator for a point being a dominating point or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard basic triangle case

Idom.num1PEtetra

The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case

Idom.num2CS.Te.onesixth

The indicator for two points constituting a dominating set for Central Similarity Proximity Catch Digraphs (CS-PCDs) - first one-sixth of the standard equilateral triangle case

Idom.num3PEtetra

The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case

The indicator for two points constituting a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) for an interval

Idom.num3PEstd.tetra

The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case

Idom.numCSup.bnd.tri

Indicator for an upper bound for the domination number of Central Similarity Proximity Catch Digraph (CS-PCD) by the exact algorithm - one triangle case

Idom.num2PEstd.tetra

The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case

The indicator for the set of points S being a dominating set or not for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case

Idom.setPEstd.tri

The indicator for the set of points S being a dominating set or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

The vertices of the Arc Slice (AS) Proximity Region in the standard basic triangle

The vertices of the Proportional Edge (PE) Proximity Region in a tetrahedron

The vertices of the Proportional Edge (PE) Proximity Region in the standard regular tetrahedron

Idom.setCSstd.tri

The indicator for the set of points S being a dominating set or not for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

The line crossing 3D point p in the direction of vector v (or if v is a point, in direction of \(v-r_0\))

Idom.numCSup.bnd.std.tri

The indicator for k being an upper bound for the domination number of Central Similarity Proximity Catch Digraph (CS-PCD) by the exact algorithm - standard equilateral triangle case

The line joining two distinct 2D points a and b

Idom.numASup.bnd.tri

Indicator for an upper bound for the domination number of Arc Slice Proximity Catch Digraph (AS-PCD) by the exact algorithm - one triangle case

The indicator for the set of points S being a dominating set or not for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

The vertices of the Proportional Edge (PE) Proximity Region in a standard basic triangle

The indicator for the set of points S being a dominating set or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case

The vertices of the Arc Slice (AS) Proximity Region in a general triangle

The end points of the Central Similarity (CS) Proximity Region for a point - one interval case

PEarc.dens.test

A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data

The vertices of the Proportional Edge (PE) Proximity Region in a general triangle

PEarc.dens.tetra

Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case

PEarc.dens.test.int

A test of uniformity of 1D data in a given interval based on Proportional Edge Proximity Catch Digraph (PE-PCD)

The vertices of the Central Similarity (CS) Proximity Region in a general triangle

Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

PEarc.dens.test1D

A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data

PEdom.num.binom.test1D

A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - Binomial Approximation

Pdom.num2PE1Dasy

The asymptotic probability of domination number \(= 2\) for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case

The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - multiple triangle case

PEdom.num.binom.test

A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Binomial Approximation

Xin.convex.hullY

Points from one class inside the convex hull of the points from the other class

The plane passing through three distinct 3D points a, b, and c

Asymptotic probability that domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs) equals 2 where vertices of the digraph are uniform points in a triangle

PEdom.num.nondeg

The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) with non-degeneracy centers - multiple triangle case

PEdom.num.norm.test

A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Normal Approximation

The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle intervals case

The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data

PEdom.num1Dnondeg

The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) with non-degeneracy centers - multiple interval case

The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case

The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data - multiple triangle case

The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case

The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one triangle case

The angles to draw arcs between two line segments

The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - one triangle case

The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case

PEdom.num.tetra

The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one tetrahedron case

PEdom.num.binom.test1Dint

A test of uniformity for 1D data based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - Binomial Approximation

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle intervals case

The area of a polygon in \(R^2\)

The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - one interval case

The arcs of Central Similarity Proximity Catch Digraphs (CS-PCD) for 2D data - one triangle case

The angle between two line segments

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - one triangle case

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end-interval case

cl2edges.std.tri

The closest points in a data set to edges in the standard equilateral triangle

The closest points to center in each vertex region in an interval

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - multiple triangle case

The labels of the vertices of a triangle in the basic triangle form

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case

center.nondegPE

Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs)

cl2CCvert.reg.basic.tri

The closest points to circumcenter in each \(CC\)-vertex region in a standard basic triangle

The closest points to circumcenter in each \(CC\)-vertex region in a triangle

.onAttach start message

Approximate domination number and approximate dominating set by the greedy algorithm

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - one interval case

cl2edges.vert.reg.basic.tri

The closest points among a data set in the vertex regions to the corresponding edges in a standard basic triangle

Exact domination number (i.e., domination number by the exact algorithm)

circumcenter.basic.tri

Circumcenter of a standard basic triangle form

Distance from a point to a set of finite cardinality

Parameterized centers of intervals

cl2edgesCCvert.reg

The closest points in a data set to edges in each \(CC\)-vertex region in a triangle

cl2edgesCMvert.reg

The closest points in a data set to edges in each \(CM\)-vertex region in a triangle

cl2edgesMvert.reg

The closest points among a data set in the vertex regions to the respective edges in a triangle

Parameterized center of an interval

.onLoad getOption package settings

The vertices of the \(CM\)-edge region in a triangle that contains the point

fr2edgesCMedge.reg.std.tri

The furthest points in a data set from edges in each \(CM\)-edge region in the standard equilateral triangle

circumcenter.tetra

Circumcenter of a general tetrahedron

The function gammakCSstd.tri is for \(k\) (\(k=2,3,4,5\)) points constituting a dominating set for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

cl2faces.vert.reg.tetra

The closest points among a data set in the vertex regions to the respective faces in a tetrahedron

circumcenter.tri

Circumcenter of a general triangle

The dimension of a vector or matrix or a data frame

fr2vertsCCvert.reg

The furthest points in a data set from vertices in each \(CC\)-vertex region in a triangle

dist.point2plane

The distance from a point to a plane spanned by three 3D points

funsMuVarCSend.int

Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case

Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case

dist.point2line

The distance from a point to a line defined by two points

funsCSt1EdgeRegs

Each function is for the presence of an arc from a point in one of the edge regions to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with \(t=1\)

fr2vertsCCvert.reg.basic.tri

The furthest points from vertices in each \(CC\)-vertex region in a standard basic triangle

funsPDomNum2PE1D

The functions for probability of domination number \(= 2\) for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case

Converts of a point in Cartesian coordinates to Barycentric coordinates and vice versa

Functions provide the indices of the Delaunay triangles where the points reside

Each function is for the presence of an arc from a point in one of the edge regions to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

The lines joining two vertices to the center of mass in standard equilateral triangle

The lines joining the three vertices of the standard equilateral triangle to a center, M, of it

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - one interval case

Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - multiple triangle case

funsMuVarPEend.int

Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end-interval case

Check whether a point is inside a triangle

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

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

Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - multiple triangle case

inci.matCSstd.tri

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - multiple interval case

inci.matPEstd.tri

Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - one interval case

Two functions lineD1CCinTb and lineD2CCinTb which are of class "TriLines" --- The lines joining the midpoints of edges to the circumcenter (\(CC\)) in the standard basic triangle.

funsRankOrderTe

Returns the ranks and orders of points in decreasing distance to the edges of the triangle

kfr2vertsCCvert.reg

The k furthest points in a data set from vertices in each \(CC\)-vertex region in a triangle

kfr2vertsCCvert.reg.basic.tri

The k furthest points from vertices in each \(CC\)-vertex region in a standard basic triangle

interval.indices.set

Indices of the intervals where the 1D point(s) reside

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

Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) and related quantities of the induced subdigraphs for points in the Delaunay triangles - multiple triangle case

Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case

Check whether a point is inside a tetrahedron

Check whether a point is inside a circle

Check whether all points in a data set are inside the triangle

Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D uniform data in one triangle

inci.matPEtetra

Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and related quantities of the induced subdigraphs for points in the partition intervals - multiple interval case

num.arcsPEend.int

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end-interval case

Region index inside the Gamma-1 region

intersect.line.plane

The point of intersection of a line and a plane

Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

intersect2lines

The point of intersection of two lines defined by two pairs of points

intersect.line.circle

The points of intersection of a line and a circle

Check a point belong to a given data set

num.arcsCSend.int

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - end-interval case

num.delaunay.tri

Number of Delaunay triangles based on a 2D data set

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the interval - one interval case

Check the argument is a point of a given dimension

The plane at a point and parallel to the plane spanned by three distinct 3D points a, b, and c

Plot an Extrema object

num.arcsCSmid.int

Number of Arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - one triangle case

The line crossing the 3D point p and parallel to line joining 3D points a and b

The line at a point p parallel to the line segment joining two distinct 2D points a and b

pcds: A package for Proximity Catch Digraphs and Their Applications

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and related quantities of the induced subdigraphs for points in the Delaunay triangles - multiple triangle case

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and related quantities of the induced subdigraphs for points in the partition intervals - multiple interval case

Check whether a triangle is a standard equilateral triangle

Plot a PCDs object

Plot a Lines object

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the interval - one interval case

num.arcsCSstd.tri

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the triangle - standard equilateral triangle case

The plot of the arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data (vertices jittered along \(y\)-coordinate) - one interval case

Plot a Planes object

Plot a Patterns object

Plot a TriLines object

The plot of the arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data (vertices jittered along \(y\)-coordinate) - multiple interval case

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the triangle - one triangle case

num.arcsPEmid.int

Number of Arcs for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case

The line passing through a point and perpendicular to the line segment joining two points

The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - one triangle case

The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - multiple triangle case

The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - multiple triangle case

The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - multiple triangle case

The plot of the arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) for 1D data (vertices jittered along \(y\)-coordinate) - multiple interval case

The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - one triangle case

The plot of the Proportional Edge (PE) Proximity Regions for a general interval (vertices jittered along \(y\)-coordinate) - one interval case

plotPEregs.tetra

The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - one tetrahedron case

The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - one triangle case

The plot of the arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) for 1D data (vertices jittered along \(y\)-coordinate) - one interval case

The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - one triangle case

The plot of the subintervals based on Yp points together with Xp points

The plot of the Proportional Edge (PE) Proximity Regions (vertices jittered along \(y\)-coordinate) - multiple interval case

The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - multiple triangle case

The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case

Plot a Uniform object

The plot of the Central Similarity (CS) Proximity Regions (vertices jittered along \(y\)-coordinate) - multiple interval case

The line crossing the 3D point p and perpendicular to the plane spanned by 3D points a, b, and c

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and related quantities of the induced subdigraphs for points in the Delaunay triangles - multiple triangle case

The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case

print.summary.Lines3D

Print a summary of a Lines3D object

print.summary.NumArcs

Print a summary of a NumArcs object

Print a Extrema object

Print a TriLines object

The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - one triangle case

The radii of points from one class with respect to points from the other class

num.arcsPEstd.tri

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - standard equilateral triangle case

The radius of a point from one class with respect to points from the other class

Print a Uniform object

print.summary.Planes

Print a summary of a Planes object

num.arcsPEtetra

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the tetrahedron - one tetrahedron case

print.summary.TriLines

Print a summary of a TriLines object

plotDelaunay.tri

The scatterplot of points from one class and plot of the Delaunay triangulation of the other class

print.summary.Patterns

Print a summary of a Patterns object

print.summary.PCDs

Print a summary of a PCDs object

Plot a Lines3D object

Plot a NumArcs object

Generation of points associated (in a Matern-like fashion) to a given set of points

Generation of points associated (in a Type I fashion) with the vertices of a triangle

rassoc.circular

Generation of points associated (in a radial or circular fashion) with a given set of points

The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - one triangle case

The plot of the Central Similarity (CS) Proximity Regions for a general interval (vertices jittered along \(y\)-coordinate) - one interval case

rassocII.std.tri

Generation of points associated (in a Type II fashion) with the edges of \(T_e\)

Print a Lines object

plotPEregs.std.tetra

The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - standard regular tetrahedron case

Print a Planes object

print.summary.Uniform

Print a summary of a Uniform object

Print a Patterns object

Print a NumArcs object

The index of the \(CM\)-edge region in a triangle that contains the point

Print a Lines3D object

Projections of a point inside a triangle to its edges

rel.edge.std.triCM

The index of the edge region in the standard equilateral triangle that contains a point

Print a PCDs object

print.summary.Extrema

Print a summary of a Extrema object

rassoc.multi.tri

Generation of points associated (in a Type I fashion) with a given set of points

print.summary.Lines

Print a summary of a Lines object

The index of the edge region in a triangle that contains the point

Generation of points associated (in a Type I fashion) with the vertices of \(T_e\)

rel.edges.triCM

The indices of the \(CM\)-edge regions in a triangle that contains the points in a give data set

rel.vert.tetraCC

The index of the \(CC\)-vertex region in a tetrahedron that contains a point

The index of the \(CM\)-vertex region in a triangle that contains a given point

rel.vert.basic.tri

The index of the vertex region in a standard basic triangle form that contains a given point

rel.vert.basic.triCC

The index of the \(CC\)-vertex region in a standard basic triangle form that contains a point

The indices of the vertex regions in a triangle that contains the points in a give data set

rel.vert.tetraCM

The index of the \(CM\)-vertex region in a tetrahedron that contains a point

Generation of points segregated (in a radial or circular fashion) from a given set of points

Generation of points segregated (in a Type I fashion) from a given set of points

rel.vert.basic.triCM

The index of the \(CM\)-vertex region in a standard basic triangle form that contains a point

The indices of the M-edge regions in a triangle that contains the points in a give data set

rel.verts.triCM

The indices of the \(CM\)-vertex regions in a triangle that contains the points in a give data set

The alternative function for the indices of the M-vertex regions in a triangle that contains the points in a give data set

Generation of Uniform Points in a Triangle

Generation of Uniform Points in a tetrahedron

Generation of points segregated (in a Type I fashion) from the vertices of \(T_e\)

runif.multi.tri

Generation of Uniform Points in the Convex Hull of Points

prj.cent2edges.basic.tri

Projections of a point inside the standard basic triangle form to its edges

rel.vert.end.int

The index of the vertex region in an end-interval that contains a given point

summary.NumArcs

Return a summary of a NumArcs object

runif.std.tetra

Generation of Uniform Points in the Standard Regular Tetrahedron \(T_h\)

Return a summary of a PCDs object

seg.tri.support

The auxiliary triangle to define the support of type I segregation

The closest points among a data set in the standard equilateral triangle to the median lines in the six half edge regions

summary.Extrema

Return a summary of a Extrema object

The slope of a line

Tree Species in a Swamp Forest

Return a summary of a Planes object

Generation of points segregated (in a Type I fashion) from the vertices of a triangle

summary.Patterns

Return a summary of a Patterns object

rel.vert.mid.int

The index of the vertex region in a middle interval that contains a given point

runif.basic.tri

Generation of Uniform Points in the standard basic triangle

summary.TriLines

Return a summary of a TriLines object

The index of the \(CC\)-vertex region in a triangle that contains a point

The index of the vertex region in a triangle that contains a given point

Generation of points segregated (in a Type II fashion) from the vertices of \(T_e\)

tri2std.basic.tri

Converting a triangle to the standard basic triangle form form

rel.edge.basic.triCM

The index of the \(CM\)-edge region in a standard basic triangle form that contains a point

rel.edge.basic.tri

The index of the edge region in a standard basic triangle form that contains a point

prj.nondegPEcent2edges

Projections of Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs) to its edges

rel.vert.std.tri

The index of the vertex region in the standard equilateral triangle that contains a given point

rel.vert.std.triCM

The index of the \(CM\)-vertex region in the standard equilateral triangle that contains a given point

rel.verts.tri.nondegPE

The indices of the vertex regions in a triangle that contains the points in a give data set

summary.Lines3D

Return a summary of a Lines3D object

Generation of Uniform Points in the Standard Equilateral Triangle

Return a summary of a Lines object

runif.std.tri.onesixth

Generation of Uniform Points in the first one-sixth of standard equilateral triangle

rel.verts.triCC

The indices of the \(CC\)-vertex regions in a triangle that contains the points in a give data set.

summary.Uniform

Return a summary of a Uniform object