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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

256

Version

0.1.6

License

GPL-2

Maintainer

Elvan Ceyhan

Last Published

April 29th, 2023

Functions in pcds (0.1.6)

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 2D data - multiple 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 2D data - one triangle case

Arc density of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle 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 1D data - multiple interval case

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

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

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

The distance between two vectors, matrices, or data frames

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

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

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

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

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

The indicator for a point being a dominating point 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) - standard basic triangle case

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

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

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

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

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 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 for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with \(t=1\)

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) - one triangle case

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

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

Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-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

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

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

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

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 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) - one tetrahedron case

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

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

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

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

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

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

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

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 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 p 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) - standard equilateral triangle case with \(t=1\)

IndNCS.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

IndNCSTe.domset

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

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 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

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

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

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) - middle interval case

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

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

IndNCSedge.regTe

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 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) - end interval 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

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

An alternative 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 in set S to the point p for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral 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

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 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) - standard basic triangle case

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

IndNPEstd.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 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

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 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

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

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

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

The line joining two distinct 2D points a and b

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

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

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

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

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

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

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

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case

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

NumArcsCSmid.int

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

NumArcsPEend.int

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

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

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

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

NumArcsPEmid.int

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

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

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

NumArcsCSend.int

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

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

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

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

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

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

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

PEarcdens.tetra

Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron 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) with non-degeneracy centers - multiple interval case

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

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

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

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

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

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

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

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

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

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 arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data

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

cent.ndPE2edges

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

The angle between two line segments

The angles to draw arcs between two line segments

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

TSDomPEBin1Dint

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

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

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

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

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

Parameterized centers of intervals

Circumcenter of a general triangle

Projections of a point inside a triangle to its edges

Parameterized center of an interval

cl2CC.VRbas.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

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

cent2edges.bas.tri

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

circ.cent.bas.tri

Circumcenter of a standard basic triangle form

circ.cent.tetra

Circumcenter of a general tetrahedron

cl2edges.std.tri

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

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

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

cl2facesVRtetra

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

cl2edgesVRbas.tri

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

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

The dimension of a vector or matrix or a data frame

dist.point2line

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

fr2vertsCC_VRbas.tri

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

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

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

Approximate domination number and approximate dominating set by the greedy algorithm

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

.onAttach start message

.onLoad getOption package settings

fr2edgesCM_ERstd.tri

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

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

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

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

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

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 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

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 \(t=1\)

dist.point2plane

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

Distance from a point to a set of finite cardinality

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

funsRankOrderTe

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

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

Check whether a point is inside a circle

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

Check whether a point is inside a tetrahedron

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

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

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

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

kfr2vertsCC_VRbas.tri

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

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

Check whether a point is inside a triangle

The points of intersection of a line and a circle

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

Check whether a triangle is a standard equilateral triangle

Check the argument is a point of a given dimension

Check a point belong to a given data set

The function to round to n decimals or to the nearest non-zero decimal place, if rounding to n yields zero.

Number of Delaunay triangles based on a 2D data set

Plot a PCDs object

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

Plot a Patterns object

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

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

Plot a Lines object

pcds: A package for Proximity Catch Digraphs and Their Applications

Plot a Lines3D object

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

Plot an Extrema object

The point of intersection of a line and a plane

Plot a Uniform object

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

Plot a TriLines object

Plot a Planes object

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

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

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

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 Arc Slice (AS) Proximity Regions 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

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 subintervals based on Yp points together with Xp 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

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

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

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

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

plotPEregs.tetra

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

Print a Lines object

Print a Lines3D object

plotPEregs.std.tetra

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

Print a PCDs object

Print a Patterns object

Print a TriLines object

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

Print a Planes object

Print a Uniform object

print.summary.PCDs

Print a summary of a PCDs object

Print a Extrema object

print.summary.Patterns

Print a summary of a Patterns object

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

print.summary.Extrema

Print a summary of a Extrema object

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

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 \(T_e\)

print.summary.TriLines

Print a summary of a TriLines object

print.summary.Planes

Print a summary of a Planes object

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

print.summary.Uniform

Print a summary of a Uniform object

print.summary.Lines

Print a summary of a Lines object

print.summary.Lines3D

Print a summary of a Lines3D object

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

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

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

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

rel.edges.triCM

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

Region index inside the Gamma-1 region

rel.verts.tri.cent

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

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

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

rel.edges.tri.cent

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

re.bas.tri.cent

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

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

rel.verts.tri.nd

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

rel.verts.triCC

The indices of the \(CC\)-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 points segregated (in a Type I fashion) from the vertices of \(T_e\)

rel.verts.triCM

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

Generation of Uniform Points in the standard basic triangle

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

runif.std.tri.onesixth

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

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

Generation of Uniform Points in a Triangle

rv.bas.tri.cent

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

Generation of Uniform Points in a tetrahedron

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

Generation of Uniform Points in the Convex Hull of Points

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

runif.std.tetra

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

Generation of Uniform Points in the Standard Equilateral Triangle

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

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

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

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

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

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

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

Return a summary of a Lines object

summary.Lines3D

Return a summary of a Lines3D object

The slope of a line

summary.TriLines

Return a summary of a TriLines object

Return a summary of a Planes object

summary.Extrema

Return a summary of a Extrema object

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

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

summary.Uniform

Return a summary of a Uniform object

Return a summary of a PCDs object

summary.Patterns

Return a summary of a Patterns object

The auxiliary triangle to define the support of type I segregation

Tree Species in a Swamp Forest

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

tri2std.bas.tri

Converting a triangle to the standard basic triangle form form