# Proximity Catch Digraphs and Their Applications

## Documentation for package ‘pcds’ version 0.1.1

- DESCRIPTION file.

## Help Pages

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

## -- A --

angle.str2end | The angles to draw arcs between two line segments
angle3pnts | The angle between two line segments
ArcsASMT | 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
ArcsCS1D | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case
ArcsCSend1D | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end interval case
ArcsCSMI | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case
ArcsCSmid1D | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle intervals case
ArcsCSMT | The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data - multiple triangle case
ArcsCStri | The arcs of Central Similarity Proximity Catch Digraphs (CS-PCD) for 2D data - one triangle case
ArcsPE1D | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case
ArcsPEend1D | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case
ArcsPEMI | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case
ArcsPEmid1D | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle intervals case
ArcsPEMT | The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - multiple triangle 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.bastri | The labels of the vertices of a triangle in the (unscaled) basic triangle form
ASarcdens.tri | Arc density of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case
asyvarCS1D | Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case
asyvarCS2D | Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D uniform data in one triangle
asyvarCSend1D | Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end interval case
asyvarPE1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case
asyvarPE2D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle
asyvarPEend1D | 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
cent.nondeg | Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs)
centersMc | Parameterized centers of intervals
centMc | Parameterized center of an interval
circ.cent.bastri | Circumcenter of a basic triangle
circ.cent.tetra | Circumcenter of a general tetrahedron
circ.cent.tri | Circumcenter of a general triangle
cl2CC.TbVR | The closest points to circumcenter in each CC-vertex region in a basic triangle
cl2CC.VR | The closest points to circumcenter in each CC-vertex region in a triangle
cl2edgesTe | The closest points in a data set to edges in the standard equilateral triangle
cl2eTbVRcent | The closest points among a data set in the vertex regions to the corresponding edges in a basic triangle
cl2eVRCC | The closest points in a data set to edges in each CC-vertex region in a triangle
cl2eVRcent | The closest points among a data set in the vertex regions to the respective edges in a triangle
cl2eVRcent.alt | 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
cl2eVRCM | The closest points in a data set to edges in each CM-vertex region in a triangle
cl2fVRth | 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
cp2e.bastri | Projections of a point inside the basic triangle to its edges
cp2e.tri | Projections of a point inside a triangle to its edges
cp2edges.nd | Projections of Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs) to its edges
CSarcdens.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.pt2set | Distance from a point to a set of finite cardinality
dom.exact | Exact domination number (i.e. domination number by the exact algorithm)
dom.greedy | Approximate domination number and approximate dominating set by the greedy algorithm
dp2l | The distance from a point to a line
dp2pl | The distance from a point to a plane

## -- F --

fr2eTeER | The furthest points in a data set from edges in each CM-edge region in the standard equilateral triangle
fr2vTbVRCC | The furthest points from vertices in each CC-vertex region in a basic triangle
fr2vVRCC | The furthest points in a data set from vertices in each CC-vertex region in a 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 '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
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
funsMuVarCSend1D | 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
funsMuVarPEend1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case
funsPG2PE1D | 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 'lD1CCinTb' and 'lD2CCinTb' which are of class "TriLines" - The lines joining the midpoints of edges to the circumcenter (CC) in the 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

## -- G --

Gam1ASbastri | The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - basic triangle case
Gam1AStri | 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
Gam1CS1D | The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) for an interval
Gam1CSTe | The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case
Gam1CSTet1 | The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with t=1
Gam1PE1D | The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) for an interval
Gam1PEbastri | The indicator for a point being a dominating point or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - basic triangle case
Gam1PEstdTetra | The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case
Gam1PEtetra | The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Gam1PEtri | The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
Gam2ASbastri | The indicator for two points being a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - basic triangle case
Gam2AStri | The indicator for two points constituting a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one 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
Gam2CSTe | 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
Gam2PEbastri | The indicator for two points being a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - basic triangle case
Gam2PEstdTetra | The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case
Gam2PEtetra | The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Gam2PEtri | The indicator for two points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
Gam3CSTe | 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
Gam3PEstdTetra | The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case
Gam3PEtetra | The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
Gam4CSTe | 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
Gam5CSTe | 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
Gam6CSTe | 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

## -- I --

in.circle | Check whether a point is inside a circle
in.tetrahedron | Check whether a point is inside a tetrahedron
in.triangle | Check whether a point is inside a triangle
IncMatASMT | Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case
IncMatAStri | Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case
IncMatCS1D | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case
IncMatCSMT | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - multiple triangle case
IncMatCSTe | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case
IncMatCStri | Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case
IncMatPE1D | Incidence matrix for Proportiona-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - multiple interval case
IncMatPEMT | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - multiple triangle case
IncMatPETe | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case
IncMatPEtetra | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case
IncMatPEtri | Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
ind.Del.tri | Functions provide the indices of the Delaunay triangles where the points reside
ind.int.set | Indices of the intervals where the 1D point(s) reside
IndASdomUBtri | Indicator for an upper bound for the domination number of Arc Slice Proximity Catch Digraph (AS-PCD) by the exact algorithm - one triangle 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
IndCSdomUBTe | 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
IndCSdomUBtri | Indicator for an upper bound for the domination number of Central Similarity Proximity Catch Digraph (CS-PCD) by the exact algorithm - one triangle case
IndCSTe | 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
IndCSTe.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
IndCSTeRAB | 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
IndCSTeRABt1 | 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
IndCSTeRAC | 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
IndCSTeRACt1 | 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
IndCSTeRBC | 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
IndCSTeRBCt1 | 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
IndCSTeSet | 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
IndCSTet1 | 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
indices.Del.tri | Functions provide the indices of the Delaunay triangles where the points reside
IndNASbastri | The indicator for the presence of an arc from a point to another for Arc Slice Proximity Catch Digraphs (AS-PCDs) - basic triangle case
IndNAStri | The indicator for the presence of an arc from a point to another for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one 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
IndNAStriSet | 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
IndNCSend1D | The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end interval case
IndNCSint | The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case
IndNCSmid1D | The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case
IndNCStri | The indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs)
IndNCStri.alt | 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)
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
IndNCStriSet | 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
IndNPEbastri | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - basic triangle case
IndNPEend1D | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case
IndNPEint | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one interval case
IndNPEmid1D | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
IndNPEstdtetra | 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
IndNPETe | 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
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
IndNPETeSet | 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
IndNPEtetra | The indicator for the presence of an arc from one 3D point to another 3D point for Proportional Edge Proximity Catch Digraphs (PE-PCDs)
IndNPEtri | The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
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
IndNPEtriSet | 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
IndUBdom | Indicator for an upper bound for the domination number by the exact algorithm
int.2lines | The point of intersection of two lines
int.circ.line | The points of intersection of a line and a circle
int.line.plane | The point of intersection of a line and a plane
inTriAll | Check whether all points in a data set are inside the triangle
is.in.data | Check a point belong to a given data set
is.point | Check the argument is a point of a given dimension
isStdEqTri | Check whether a triangle is a standard equilateral triangle

## -- K --

Kfr2vTbVRCC | The 'k' furthest points from vertices in each CC-vertex region in a basic triangle
Kfr2vVRCC | The 'k' furthest points in a data set from vertices in each CC-vertex region in a triangle

## -- L --

lA_CM.Te | The lines joining two vertices to the center of mass in standard equilateral triangle
lA_M.Te | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
lB_CM.Te | The lines joining two vertices to the center of mass in standard equilateral triangle
lB_M.Te | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
lC_M.Te | The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it
lD1CCinTb | 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.
lD2CCinTb | 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.
Line | The line joining two distinct 2D points 'a' and 'b'
Line3D | The line crossing 3D point 'r0' in the direction of vector 'v' (or if 'v' is a point, in direction of v-r0)

## -- 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
muCSend1D | 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
muPEend1D | Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case

## -- N --

NASbastri | The vertices of the Arc Slice (AS) Proximity Region in the 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
NPEbastri | The vertices of the Proportional Edge (PE) Proximity Region in a basic triangle
NPEint | The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case
NPEstdtetra | 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
NumArcsASMT | Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case
NumArcsAStri | Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case
NumArcsCSend1D | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - end interval case
NumArcsCSint | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case
NumArcsCSmid1D | Number of Arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case
NumArcsCSMT | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - multiple triangle case
NumArcsCSTe | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case
NumArcsCStri | Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case
NumArcsPEend1D | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case
NumArcsPEint | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one interval case
NumArcsPEmid1D | Number of Arcs for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
NumArcsPEMT | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - multiple triangle case
NumArcsPETe | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case
NumArcsPEtri | Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
NumDelTri | Number of Delaunay triangles based on a 2D data set

## -- O --

order.d2e.Te | Returns the ranks and orders of points in decreasing distance to the edges of the triangle

## -- P --

paraline | The line paralel 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 paralel to the plane spanned by three distinct 3D points 'a', 'b', and 'c'
pcds | pcds: A package for Proximity Catch Digraphs and Their Applications
PEarcdens.tri | Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case
PEdom.tetra | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one tetrahedron case
PEdom1D | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data
PEdomMT | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - multiple triangle case
PEdomMTnd | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) with non-degeneracy centers - multiple triangle case
PEdomtri | The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one triangle case
perp.ln2pl | The line crossing the 3D point 'P' and perpendicular to the plane spanned by 3D points 'A', 'B', and 'C'
perpline | The line passing thru a point and perpendicular to the line segment joining two points
PG2A | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2AI | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2AII | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2AIII | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2AIV | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2Asym | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2B | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2BIII | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2Bsym | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2C | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2CIV | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2Csym | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2PE1D | The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2PE1D.asy | The asymptotic probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
PG2PEtri | 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
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.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
plotASarcsMT | The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case
plotASarcsTri | The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - one triangle case
plotASregsMT | The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - multiple triangle case
plotASregsTri | The plot of the Arc Slice (AS) Proximity Regions 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
plotCSarcsMT | The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - multiple triangle case
plotCSarcsTri | The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - one triangle case
plotCSregsInt | The plot of the Central Similarity (CS) Proximity Regions for a general interval (vertices jittered along y-coordinate) - one interval case
plotCSregsMI | The plot of the Central Similarity (CS) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case
plotCSregsMT | The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - multiple triangle case
plotCSregsTri | 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.
plotDeltri | 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
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
plotPEarcsMT | The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case
plotPEarcsTri | The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - one triangle case
plotPEregsInt | The plot of the Proportional Edge (PE) Proximity Regions for a general interval (vertices jittered along y-coordinate) - one interval case
plotPEregsMI | The plot of the Proportional Edge (PE) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case
plotPEregsMT | 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
plotPEregsTH | The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - one tetrahedron case
plotPEregsTri | The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - one triangle case
print.Extrema | Print a 'Extrema' object
print.Lines | Print a 'Lines' object
print.Lines3D | Print a 'Lines3D' 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.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

## -- 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.d2e.Te | Returns the ranks and orders of points in decreasing distance to the edges of the triangle
rasc.disc | Generation of points associated (in a radial or circular fashion) with a given set of points
rasc.matern | Generation of points associated (in a Matern-like fashion) to a given set of points
rasc.tri | Generation of points associated (in a Type I fashion) with the vertices of a triangle
rascIITe | Generation of points associated (in a Type II fashion) with the edges of T_e
rascMT | Generation of points associated (in a Type I fashion) with a given set of points
rascTe | Generation of points associated (in a Type I fashion) with the vertices of T_e
re.bastri.cent | The index of the edge region in a basic triangle that contains a point
re.bastriCM | The index of the CM-edge region in a basic triangle that contains a point
re.tri.cent | The index of the edge region in a triangle that contains the point
re.triCM | The index of the CM-edge region in a triangle that contains the point
redge.triCM | The vertices of the CM-edge region in a triangle that contains the point
redges.tri.cent | The indices of the 'M'-edge regions in a triangle that contains the points in a give data set
redges.triCM | The indices of the CM-edge regions in a triangle that contains the points in a give data set
rel.six.Te | Region index inside the Gamma-1 region
reTeCM | The index of the edge region in the standard equilateral triangle that contains a point
rseg.disc | Generation of points segregated (in a radial or circular fashion) from a given set of points
rseg.tri | Generation of points segregated (in a Type I fashion) from the vertices of a triangle
rsegIITe | Generation of points segregated (in a Type II fashion) from the vertices of T_e
rsegMT | Generation of points segregated (in a Type I fashion) from a given set of points
rsegTe | Generation of points segregated (in a Type I fashion) from the vertices of T_e
runif.bastri | Generation of Uniform Points in the basic triangle
runif.stdtetra | Generation of Uniform Points in the Standard Regular Tetrahedron T_h
runif.tetra | Generation of Uniform Points in a tetrahedron
runif.tri | Generation of Uniform Points in a triangle
runifMT | Generation of Uniform Points in the Convex Hull of Points
runifTe | Generation of Uniform Points in the Standard Equilateral Triangle
runifTe.onesixth | Generation of Uniform Points in a part of standard equilateral triangle
rv.bastri.cent | The index of the vertex region in a basic triangle that contains a given point
rv.bastriCC | The index of the CC-vertex region in a basic triangle that contains a point
rv.bastriCM | The index of the CM-vertex region in a basic triangle that contains a point
rv.end.int | The index of the vertex region in an end-interval that contains a given point
rv.mid.int | The index of the vertex region in a middle interval that contains a given point
rv.tetraCC | The index of the CC-vertex region in a tetrahedron that contains a point
rv.tetraCM | The index of the CM-vertex region in a tetrahedron that contains a point
rv.tri.cent | The index of the vertex region in a triangle that contains a given point
rv.triCC | The index of the CC-vertex region in a triangle that contains a point
rv.triCM | The index of the CM-vertex region in a 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
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
rverts.tri.nd | The indices of the vertex regions in a triangle that contains the points in a give data set
rverts.triCC | The indices of the CC-vertex regions in a triangle that contains the points in a give data set.
rverts.triCM | The indices of the CM-vertex regions in a triangle that contains the points in a give data set
rvTe.cent | The index of the vertex region in the standard equilateral triangle that contains a given point
rvTeCM | The index of the CM-vertex region in the standard equilateral triangle that contains a given point

## -- S --

seg.tri.supp | The auxiliary triangle to define the support of type I segregation
six.ext | The closest points among a data set in the standard equilateral triangle to the median lines in 6 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.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 --

TSArcDensCS1D | A test of uniformity of 1D data in a given interval based on Central Similarity Proximity Catch Digraph (CS-PCD)
TSArcDensCSMT | A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data
TSArcDensPE1D | A test of uniformity of 1D data in a given interval based on Proportional Edge Proximity Catch Digraph (PE-PCD)
TSArcDensPEMT | A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data
TSDomPEBin | A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Binomial Approximation
TSDomPEBin1D | A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - Binomial Approximation
TSDomPENor | A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Normal Approximation

## -- X --

XinCHY | 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