# Proximity Catch Digraphs and Their Applications

## Documentation for package ‘pcds’ version 0.1.8

- DESCRIPTION file
- User guides, package vignettes and other documentation
- Package README

## Help Pages

A B C D E F I K L M N O P R S T X misc

pcds-package | pcds: A package for Proximity Catch Digraphs and Their Applications

## -- A --

angle.str2end | The angles to draw arcs between two line segments
angle3pnts | The angle between two line segments
arcsAS | The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case
arcsAStri | The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - one triangle case
arcsCS | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data - multiple triangle case
arcsCS1D | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case
arcsCSend.int | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case
arcsCSint | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - one interval case
arcsCSmid.int | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle intervals case
arcsCStri | The arcs of Central Similarity Proximity Catch Digraphs (CS-PCD) for 2D data - one triangle case
arcsPE | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - multiple triangle case
arcsPE1D | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case
arcsPEend.int | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end-interval case
arcsPEint | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - one interval case
arcsPEmid.int | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle intervals case
arcsPEtri | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - one triangle case
area.polygon | The area of a polygon in R^2
as.basic.tri | The labels of the vertices of a triangle in the basic triangle form
ASarc.dens.tri | Arc density of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case
asy.varCS1D | Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case
asy.varCS2D | Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D uniform data in one triangle
asy.varCSend.int | Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case
asy.varPE1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case
asy.varPE2D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle
asy.varPEend.int | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end-interval case

## -- B --

bary2cart | Converts of a point in Cartesian coordinates to Barycentric coordinates and vice versa

## -- C --

cart2bary | Converts of a point in Cartesian coordinates to Barycentric coordinates and vice versa
center.nondegPE | Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs)
centerMc | Parameterized center of an interval
centersMc | Parameterized centers of intervals
circumcenter.basic.tri | Circumcenter of a standard basic triangle form
circumcenter.tetra | Circumcenter of a general tetrahedron
circumcenter.tri | Circumcenter of a general triangle
cl2CCvert.reg | The closest points to circumcenter in each CC-vertex region in a triangle
cl2CCvert.reg.basic.tri | The closest points to circumcenter in each CC-vertex region in a standard basic triangle
cl2edges.std.tri | The closest points in a data set to edges in the standard equilateral triangle
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
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
cl2faces.vert.reg.tetra | The closest points among a data set in the vertex regions to the respective faces in a tetrahedron
cl2Mc.int | The closest points to center in each vertex region in an interval
CSarc.dens.test | A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data
CSarc.dens.test.int | A test of uniformity of 1D data in a given interval based on Central Similarity Proximity Catch Digraph (CS-PCD)
CSarc.dens.test1D | A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data
CSarc.dens.tri | Arc density of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

## -- D --

dimension | The dimension of a 'vector' or matrix or a data frame
Dist | The distance between two vectors, matrices, or data frames
dist.point2line | The distance from a point to a line defined by two points
dist.point2plane | The distance from a point to a plane spanned by three 3D points
dist.point2set | Distance from a point to a set of finite cardinality
dom.num.exact | Exact domination number (i.e., domination number by the exact algorithm)
dom.num.greedy | Approximate domination number and approximate dominating set by the greedy algorithm

## -- E --

edge.reg.triCM | The vertices of the CM-edge region in a triangle that contains the point

## -- F --

fr2edgesCMedge.reg.std.tri | The furthest points in a data set from edges in each CM-edge region in the standard equilateral triangle
fr2vertsCCvert.reg | The furthest points in a data set from vertices in each CC-vertex region in a triangle
fr2vertsCCvert.reg.basic.tri | The furthest points from vertices in each CC-vertex region in a standard basic triangle
funsAB2CMTe | The lines joining two vertices to the center of mass in standard equilateral triangle
funsAB2MTe | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
funsCartBary | Converts of a point in Cartesian coordinates to Barycentric coordinates and vice versa
funsCSEdgeRegs | 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
funsCSGamTe | 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
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
funsIndDelTri | Functions provide the indices of the Delaunay triangles where the points reside
funsMuVarCS1D | Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case
funsMuVarCS2D | 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
funsMuVarPE1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case
funsMuVarPE2D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle
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
funsPDomNum2PE1D | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
funsRankOrderTe | Returns the ranks and orders of points in decreasing distance to the edges of the triangle
funsTbMid2CC | 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.
fvar1 | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case
fvar2 | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case

## -- I --

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
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
IarcAStri | The indicator for the presence of an arc from a point to another for Arc Slice Proximity Catch Digraphs (AS-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
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
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
IarcCSend.int | The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end-interval case
IarcCSint | The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case
IarcCSmid.int | 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.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
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
IarcCSstd.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
IarcCSstd.triRAB | 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
IarcCSstd.triRAC | 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
IarcCSstd.triRBC | 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
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
IarcCSt1.std.triRAB | 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
IarcCSt1.std.triRAC | 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
IarcCSt1.std.triRBC | 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
IarcCStri | The indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs)
IarcCStri.alt | 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)
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
IarcPEend.int | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end-interval case
IarcPEint | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one interval case
IarcPEmid.int | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval 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
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
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
IarcPEstd.tri | 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
IarcPEtetra | The indicator for the presence of an arc from one 3D point to another 3D point for Proportional Edge Proximity Catch Digraphs (PE-PCDs)
IarcPEtri | 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.num.up.bnd | Indicator for an upper bound for the domination number by the exact algorithm
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.num1AStri | The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one 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
Idom.num1CSint | The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) for an interval
Idom.num1CSstd.tri | The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral 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
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.num1PEint | The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) for an interval
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
Idom.num1PEtetra | The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Idom.num1PEtri | 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
Idom.num2AStri | The indicator for two points constituting a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle 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.num2CSstd.tri | 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
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.num2PEstd.tetra | The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case
Idom.num2PEtetra | The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Idom.num2PEtri | The indicator for two points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
Idom.num3CSstd.tri | 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
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.num3PEtetra | The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Idom.num4CSstd.tri | 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
Idom.num5CSstd.tri | 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
Idom.num6CSstd.tri | 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
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
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
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.setAStri | 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.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
Idom.setCStri | 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
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
Idom.setPEtri | 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
in.circle | Check whether a point is inside a circle
in.tetrahedron | Check whether a point is inside a tetrahedron
in.tri.all | Check whether all points in a data set are inside the triangle
in.triangle | Check whether a point is inside a triangle
inci.matAS | Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case
inci.matAStri | Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case
inci.matCS | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - multiple triangle case
inci.matCS1D | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case
inci.matCSint | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - one interval case
inci.matCSstd.tri | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case
inci.matCStri | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case
inci.matPE | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - multiple triangle case
inci.matPE1D | Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - multiple interval case
inci.matPEint | Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - one interval case
inci.matPEstd.tri | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case
inci.matPEtetra | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
inci.matPEtri | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
index.delaunay.tri | Functions provide the indices of the Delaunay triangles where the points reside
index.six.Te | Region index inside the Gamma-1 region
indices.delaunay.tri | Functions provide the indices of the Delaunay triangles where the points reside
intersect.line.circle | The points of intersection of a line and a circle
intersect.line.plane | The point of intersection of a line and a plane
intersect2lines | The point of intersection of two lines defined by two pairs of points
interval.indices.set | Indices of the intervals where the 1D point(s) reside
is.in.data | Check a point belong to a given data set
is.point | Check the argument is a point of a given dimension
is.std.eq.tri | Check whether a triangle is a standard equilateral triangle

## -- K --

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

## -- L --

Line | The line joining two distinct 2D points 'a' and 'b'
Line3D | The line crossing 3D point 'p' in the direction of 'vector' 'v' (or if 'v' is a point, in direction of v-r_0)
lineA2CMinTe | The lines joining two vertices to the center of mass in standard equilateral triangle
lineA2MinTe | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
lineB2CMinTe | The lines joining two vertices to the center of mass in standard equilateral triangle
lineB2MinTe | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
lineC2MinTe | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
lineD1CCinTb | 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.
lineD2CCinTb | 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.

## -- M --

mu1PE1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case
muCS1D | Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case
muCS2D | Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D uniform data in one triangle
muCSend.int | Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case
muPE1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case
muPE2D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle
muPEend.int | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end-interval case

## -- N --

NASbasic.tri | The vertices of the Arc Slice (AS) Proximity Region in the standard basic triangle
NAStri | The vertices of the Arc Slice (AS) Proximity Region in a general triangle
NCSint | The end points of the Central Similarity (CS) Proximity Region for a point - one interval case
NCStri | The vertices of the Central Similarity (CS) Proximity Region in a general triangle
NPEbasic.tri | The vertices of the Proportional Edge (PE) Proximity Region in a standard basic triangle
NPEint | The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case
NPEstd.tetra | The vertices of the Proportional Edge (PE) Proximity Region in the standard regular tetrahedron
NPEtetra | The vertices of the Proportional Edge (PE) Proximity Region in a tetrahedron
NPEtri | The vertices of the Proportional Edge (PE) Proximity Region in a general triangle
num.arcsAS | 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
num.arcsAStri | Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) and quantities related to the triangle - one triangle case
num.arcsCS | 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
num.arcsCS1D | 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
num.arcsCSend.int | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - end-interval case
num.arcsCSint | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the interval - one interval case
num.arcsCSmid.int | Number of Arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle 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
num.arcsCStri | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the triangle - one triangle case
num.arcsPE | 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
num.arcsPE1D | 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
num.arcsPEint | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the interval - one interval case
num.arcsPEmid.int | Number of Arcs for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
num.arcsPEstd.tri | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - standard equilateral triangle case
num.arcsPEtetra | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the tetrahedron - one tetrahedron case
num.arcsPEtri | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - one triangle case
num.delaunay.tri | Number of Delaunay triangles based on a 2D data set

## -- O --

order.dist2edges.std.tri | Returns the ranks and orders of points in decreasing distance to the edges of the triangle

## -- P --

paraline | The line at a point 'p' parallel to the line segment joining two distinct 2D points 'a' and 'b'
paraline3D | The line crossing the 3D point 'p' and parallel to line joining 3D points 'a' and 'b'
paraplane | The plane at a point and parallel to the plane spanned by three distinct 3D points 'a', 'b', and 'c'
pcds | pcds: A package for Proximity Catch Digraphs and Their Applications
Pdom.num2A | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2AI | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2AII | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2AIII | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2AIV | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2Asym | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2B | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2BIII | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2Bsym | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2C | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2CIV | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2Csym | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2PE1D | The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2PE1Dasy | The asymptotic probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Pdom.num2PEtri | 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
PEarc.dens.test | A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data
PEarc.dens.test.int | A test of uniformity of 1D data in a given interval based on Proportional Edge Proximity Catch Digraph (PE-PCD)
PEarc.dens.test1D | A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data
PEarc.dens.tetra | Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
PEarc.dens.tri | Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
PEdom.num | 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
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
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
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
PEdom.num.tetra | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one tetrahedron case
PEdom.num.tri | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one triangle case
PEdom.num1D | 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
perpline | The line passing through a point and perpendicular to the line segment joining two points
perpline2plane | The line crossing the 3D point 'p' and perpendicular to the plane spanned by 3D points 'a', 'b', and 'c'
Plane | The plane passing through three distinct 3D points 'a', 'b', and 'c'
plot.Extrema | Plot an 'Extrema' 'object'
plot.Lines | Plot a 'Lines' 'object'
plot.Lines3D | Plot a 'Lines3D' 'object'
plot.NumArcs | Plot a 'NumArcs' 'object'
plot.Patterns | Plot a 'Patterns' 'object'
plot.PCDs | Plot a 'PCDs' 'object'
plot.Planes | Plot a 'Planes' 'object'
plot.TriLines | Plot a 'TriLines' 'object'
plot.Uniform | Plot a 'Uniform' 'object'
plotASarcs | The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case
plotASarcs.tri | The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - one triangle case
plotASregs | The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - multiple triangle case
plotASregs.tri | The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - one triangle case
plotCSarcs | The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - multiple triangle case
plotCSarcs.int | The plot of the arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data (vertices jittered along y-coordinate) - one interval case
plotCSarcs.tri | The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - one triangle case
plotCSarcs1D | The plot of the arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data (vertices jittered along y-coordinate) - multiple interval case
plotCSregs | The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - multiple triangle case
plotCSregs.int | The plot of the Central Similarity (CS) Proximity Regions for a general interval (vertices jittered along y-coordinate) - one interval case
plotCSregs.tri | The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - one triangle case
plotCSregs1D | The plot of the Central Similarity (CS) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case
plotDelaunay.tri | The scatterplot of points from one class and plot of the Delaunay triangulation of the other class
plotIntervals | The plot of the subintervals based on 'Yp' points together with 'Xp' points
plotPEarcs | The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case
plotPEarcs.int | The plot of the arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) for 1D data (vertices jittered along y-coordinate) - one interval case
plotPEarcs.tri | The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - one triangle case
plotPEarcs1D | The plot of the arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) for 1D data (vertices jittered along y-coordinate) - multiple interval case
plotPEregs | The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - multiple triangle case
plotPEregs.int | The plot of the Proportional Edge (PE) Proximity Regions for a general interval (vertices jittered along y-coordinate) - one interval case
plotPEregs.std.tetra | The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - standard regular tetrahedron case
plotPEregs.tetra | The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - one tetrahedron case
plotPEregs.tri | The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - one triangle case
plotPEregs1D | The plot of the Proportional Edge (PE) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case
print.Extrema | Print a 'Extrema' 'object'
print.Lines | Print a 'Lines' 'object'
print.Lines3D | Print a 'Lines3D' 'object'
print.NumArcs | Print a 'NumArcs' 'object'
print.Patterns | Print a 'Patterns' 'object'
print.PCDs | Print a 'PCDs' 'object'
print.Planes | Print a 'Planes' 'object'
print.summary.Extrema | Print a summary of a 'Extrema' 'object'
print.summary.Lines | Print a summary of a 'Lines' 'object'
print.summary.Lines3D | Print a summary of a 'Lines3D' 'object'
print.summary.NumArcs | Print a summary of a 'NumArcs' 'object'
print.summary.Patterns | Print a summary of a 'Patterns' 'object'
print.summary.PCDs | Print a summary of a 'PCDs' 'object'
print.summary.Planes | Print a summary of a 'Planes' 'object'
print.summary.TriLines | Print a summary of a 'TriLines' 'object'
print.summary.Uniform | Print a summary of a 'Uniform' 'object'
print.TriLines | Print a 'TriLines' 'object'
print.Uniform | Print a 'Uniform' 'object'
prj.cent2edges | Projections of a point inside a triangle to its edges
prj.cent2edges.basic.tri | Projections of a point inside the standard basic triangle form to its edges
prj.nondegPEcent2edges | Projections of Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs) to its edges

## -- R --

radii | The radii of points from one class with respect to points from the other class
radius | The radius of a point from one class with respect to points from the other class
rank.dist2edges.std.tri | Returns the ranks and orders of points in decreasing distance to the edges of the triangle
rassoc.circular | Generation of points associated (in a radial or circular fashion) with a given set of points
rassoc.matern | Generation of points associated (in a Matern-like fashion) to a given set of points
rassoc.multi.tri | Generation of points associated (in a Type I fashion) with a given set of points
rassoc.std.tri | Generation of points associated (in a Type I fashion) with the vertices of T_e
rassoc.tri | Generation of points associated (in a Type I fashion) with the vertices of a triangle
rassocII.std.tri | Generation of points associated (in a Type II fashion) with the edges of T_e
rel.edge.basic.tri | The index of the edge region in a standard basic triangle form that contains a point
rel.edge.basic.triCM | The index of the CM-edge region in a standard basic triangle form that contains a point
rel.edge.std.triCM | The index of the edge region in the standard equilateral triangle that contains a point
rel.edge.tri | The index of the edge region in a triangle that contains the point
rel.edge.triCM | The index of the CM-edge region in a triangle that contains the point
rel.edges.tri | The indices of the 'M'-edge regions in a triangle that contains the points in a give data set
rel.edges.triCM | The indices of the CM-edge regions in a triangle that contains the points in a give data set
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
rel.vert.basic.triCM | The index of the CM-vertex region in a standard basic triangle form that contains a point
rel.vert.end.int | The index of the vertex region in an end-interval that contains a given point
rel.vert.mid.int | The index of the vertex region in a middle interval that contains a given point
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.vert.tetraCC | The index of the CC-vertex region in a tetrahedron that contains a point
rel.vert.tetraCM | The index of the CM-vertex region in a tetrahedron that contains a point
rel.vert.tri | The index of the vertex region in a triangle that contains a given point
rel.vert.triCC | The index of the CC-vertex region in a triangle that contains a point
rel.vert.triCM | The index of the CM-vertex region in a triangle that contains a given point
rel.verts.tri | The indices of the vertex regions in a triangle that contains the points in a give data set
rel.verts.tri.nondegPE | 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.
rel.verts.triCM | The indices of the CM-vertex regions in a triangle that contains the points in a give data set
rel.verts.triM | The alternative function for the indices of the M-vertex regions in a triangle that contains the points in a give data set
rseg.circular | Generation of points segregated (in a radial or circular fashion) from a given set of points
rseg.multi.tri | Generation of points segregated (in a Type I fashion) from a given set of points
rseg.std.tri | Generation of points segregated (in a Type I fashion) from the vertices of T_e
rseg.tri | Generation of points segregated (in a Type I fashion) from the vertices of a triangle
rsegII.std.tri | Generation of points segregated (in a Type II fashion) from the vertices of T_e
runif.basic.tri | Generation of Uniform Points in the standard basic triangle
runif.multi.tri | Generation of Uniform Points in the Convex Hull of Points
runif.std.tetra | Generation of Uniform Points in the Standard Regular Tetrahedron T_h
runif.std.tri | Generation of Uniform Points in the Standard Equilateral Triangle
runif.std.tri.onesixth | Generation of Uniform Points in the first one-sixth of standard equilateral triangle
runif.tetra | Generation of Uniform Points in a tetrahedron
runif.tri | Generation of Uniform Points in a Triangle

## -- S --

seg.tri.support | The auxiliary triangle to define the support of type I segregation
six.extremaTe | The closest points among a data set in the standard equilateral triangle to the median lines in the six half edge regions
slope | The slope of a line
summary.Extrema | Return a summary of a 'Extrema' 'object'
summary.Lines | Return a summary of a 'Lines' 'object'
summary.Lines3D | Return a summary of a 'Lines3D' 'object'
summary.NumArcs | Return a summary of a 'NumArcs' 'object'
summary.Patterns | Return a summary of a 'Patterns' 'object'
summary.PCDs | Return a summary of a 'PCDs' 'object'
summary.Planes | Return a summary of a 'Planes' 'object'
summary.TriLines | Return a summary of a 'TriLines' 'object'
summary.Uniform | Return a summary of a 'Uniform' 'object'
swamptrees | Tree Species in a Swamp Forest

## -- T --

tri2std.basic.tri | Converting a triangle to the standard basic triangle form form

## -- X --

Xin.convex.hullY | Points from one class inside the convex hull of the points from the other class

## -- misc --

.onAttach | .onAttach start message
.onLoad | .onLoad getOption package settings