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This is an R package that contains the functions for generating patterns of segregation, association, complete spatial randomness (CSR) and Uniform data in one, two, and three dimensional cases, for testing these patterns based on domination number and arc density of the proximity catch digraphs (PCDs) for two-dimensional data, for visualization of 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.

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

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Install

install.packages('pcds')

Monthly Downloads

201

Version

0.1.1

License

GPL-2

Maintainer

Elvan Ceyhan

Last Published

March 25th, 2020

Functions in pcds (0.1.1)

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

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 2D data - multiple triangle case

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

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

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

Gam1CS.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

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

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

The distance between two vectors, matrices, or data frames

The indicator for a 3D point being a dominating point 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 two points being a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - basic triangle case

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

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

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

t = 1

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

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

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

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

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

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

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

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

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

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

IndCS.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

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

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 Central Similarity Proximity Catch Digraphs (CS-PCDs) for an interval

Gam2CS.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

IndNAStri.domset

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

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

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

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

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

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

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

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

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

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

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

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

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

The indicator for the presence of an arc from a point in set S to the point pt 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) - standard equilateral triangle case with

t = 1

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

Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron 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 in set S to the point pt for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one 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

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

An alternative function to the function IndNCStri 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 a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case

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

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

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

IndNCStri.domset

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

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

The k furthest points from vertices in each CC-vertex region in a basic triangle

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

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

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

IndNPEtri.domset

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

IndNPETe.domset

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

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case

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

Number of arcs of 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) - end interval case

The line crossing 3D point r0 in the direction of vector v (or if v is a point, in direction of

v - r 0

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - multiple triangle case

The line joining two distinct 2D points a and b

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

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

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

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

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

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

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

The angles to draw arcs between two line segments

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

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

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

Number of Delaunay triangles based on a 2D data set

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

The angle between two line segments

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

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

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

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

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

Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case

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

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

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

The area of a polygon in

R^{2}

Circumcenter of a general triangle

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

The closest points to circumcenter in each CC-vertex region in a basic triangle

Projections of a point inside the basic triangle to its edges

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

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

The furthest points from vertices in each CC-vertex region in a basic triangle

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

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

An alternative function to the function cl2eVRcent which finds the closest points among a data set in the vertex regions to the respective edges in a triangle

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - multiple triangle case

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

The labels of the vertices of a triangle in the (unscaled) basic triangle form

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

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

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

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

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

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

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

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

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

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

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

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

Projections of a point inside a triangle to its edges

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

circ.cent.tetra

Circumcenter of a general tetrahedron

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

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

circ.cent.bastri

Circumcenter of a basic triangle

funsMuVarCSend1D

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

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

Approximate domination number and approximate dominating set by the greedy algorithm

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

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

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

Check whether a point is inside a tetrahedron

Check whether a point is inside a triangle

pcds: A package for Proximity Catch Digraphs and Their Applications

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

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

Plot a TriLines object

funsMuVarPEend1D

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

Parameterized centers of intervals

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

Parameterized center of an interval

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

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

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

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

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

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

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

funsRankOrderTe

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

The line crossing the 3D point P and parallel to line joining 3D points A and B

Plot a Patterns object

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

Check the argument is a point of a given dimension

The line paralel to the line segment joining two distinct 2D points a and b

Check whether a triangle is a standard equilateral triangle

Plot a Lines3D object

Plot a PCDs object

The dimension of a vector or matrix or a data frame

Plot a Planes object

Distance from a point to a set of finite cardinality

.onLoad getOption package settings

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

The distance from a point to a line

.onAttach start message

Plot a Uniform object

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

The plot of the Arc Slice (AS) Proximity Regions 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

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

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

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

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

The distance from a point to a plane

The function GamkCSTe 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

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

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

Print a Patterns object

Two functions lD1CCinTb and lD2CCinTb which are of class "TriLines" --- The lines joining the midpoints of edges to the circumcenter (CC) in the basic triangle.

The point of intersection of a line and a plane

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

Check whether a point is inside a circle

The point of intersection of two lines

The line crossing the 3D point P and perpendicular to the plane spanned by 3D points A, B, and C

The points of intersection of a line and a circle

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

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

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

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

plotPEregsStdTH

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

Print a PCDs object

print.summary.PCDs

Print a summary of a PCDs object

Print a Lines3D object

print.summary.Lines3D

Print a summary of a Lines3D object

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

Check a point belong to a given data set

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

T_{e}

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

redges.tri.cent

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

Plot an Extrema object

runifTe.onesixth

Generation of Uniform Points in a part of standard equilateral triangle

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

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

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

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

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 Proportional Edge (PE) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case

Plot a Lines object

Return a summary of a Lines object

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

The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - one triangle case Plots the points in and outside of the triangle tri and also the CS proximity regions which are also triangular for points inside the triangle tri with edge regions are based on the center of mass CM.

Print a Extrema object

Print a Planes object

Print a Lines object

print.summary.Planes

Print a summary of a Planes object

print.summary.Patterns

Print a summary of a Patterns object

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

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

Tree Species in a Swamp Forest

summary.Lines3D

Return a summary of a Lines3D object

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

Generation of Uniform Points in a tetrahedron

summary.Uniform

Return a summary of a Uniform object

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

T_{e}

Generation of Uniform Points in a triangle

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

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

print.summary.Uniform

Print a summary of a Uniform object

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

T_{e}

print.summary.TriLines

Print a summary of a TriLines object

Generation of Uniform Points in the Standard Equilateral Triangle

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

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

T_{e}

Generation of Uniform Points in the Convex Hull of Points

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

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

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

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

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

The auxiliary triangle to define the support of type I segregation

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

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

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

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

The closest points among a data set in the standard equilateral triangle to the median lines in 6 half edge regions

summary.Patterns

Return a summary of a Patterns object

Return a summary of a PCDs object

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

Print a TriLines object

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

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

Generation of Uniform Points in the basic triangle

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

Region index inside the Gamma-1 region

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

rverts.tri.cent

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

Generation of Uniform Points in the Standard Regular Tetrahedron

T_{h}

Print a Uniform object

rverts.tri.cent.alt

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

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

print.summary.Extrema

Print a summary of a Extrema object

print.summary.Lines

Print a summary of a Lines object

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

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

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

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

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

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

The index of the CC-vertex region in a basic triangle that contains a point

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

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

The slope of a line

The index of the CM-vertex region in a basic triangle that contains a point

summary.Extrema

Return a summary of a Extrema object

summary.TriLines

Return a summary of a TriLines object

Return a summary of a Planes object

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 1D data - end interval case

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

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

The arcs of Central Similarity Proximity Catch Digraphs (CS-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

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

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

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