| angle.str2end |
The angles to draw arcs between two line segments - Gives the two pairs of angles in radians or degrees to draw arcs between two vectors or line segments for the 'draw.arc' function in the plotrix package. The angles are provided with respect to the x-axis in the coordinate system. The line segments are [ba] and [bc] when the argument is given as 'a, b, c' in the function. 'radian' is a logical argument (default='TRUE') which yields the angle in radians if 'TRUE', and in degrees if 'FALSE'. The first pair of angles is for drawing arcs in the smaller angle between [ba] and [bc] and the second pair of angles is for drawing arcs in the counter-clockwise order from [ba] to [bc]. |
| angle3pnts |
The angle between two line segments |
| ArcsASMT |
An object of class "PCDs": The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case |
| ArcsAStri |
An object of class "PCDs": The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - one triangle case |
| ArcsCS1D |
An object of class "PCDs": The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case |
| ArcsCSend1D |
An object of class "PCDs": The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end interval case |
| ArcsCSMI |
An object of class "PCDs": The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case |
| ArcsCSmid1D |
An object of class "PCDs": The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle intervals case |
| ArcsCSMT |
An object of class "PCDs": The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data - multiple triangle case |
| ArcsCStri |
An object of class "PCDs": The arcs of Central Similarity Proximity Catch Digraphs (CS-PCD) for 2D data - one triangle case |
| ArcsPE1D |
An object of class "PCDs": The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case |
| ArcsPEend1D |
An object of class "PCDs": The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case |
| ArcsPEMI |
An object of class "PCDs": The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case |
| ArcsPEmid1D |
An object of class "PCDs": The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle intervals case |
| ArcsPEMT |
An object of class "PCDs": The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - multiple triangle case |
| ArcsPEtri |
An object of class "PCDs": 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 |
Two functions: 'muCS1D' and '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 |
Two functions: 'muCS2D' and '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 |
Two functions: 'muCSend1D' and '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 |
The functions 'muPE1D' and 'asyvarPE1D' and their auxiliary functions - Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case. |
| asyvarPE2D |
Two functions: 'muPE2D' and '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 |
Two functions: 'muPEend1D' and 'asyvarPEend1D' - Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case |
| cart2bary |
Two functions: 'cart2bary' and 'bary2cart' - 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 |
An object of class "Extrema": The closest points to circumcenter in each CC-vertex region in a basic triangle |
| cl2CC.VR |
An object of class "Extrema": The closest points to circumcenter in each CC-vertex region in a triangle |
| cl2edgesTe |
An object of class "Extrema": The closest points in a data set to edges in the standard equilateral triangle |
| cl2eTbVRcent |
An object of class "Extrema": The closest points among a data set in the vertex regions to the corresponding edges in a basic triangle |
| cl2eVRCC |
An object of class "Extrema": The closest points in a data set to edges in each CC-vertex region in a triangle |
| cl2eVRcent |
An object of class "Extrema": The closest points among a data set in the vertex regions to the respective edges in a triangle |
| cl2eVRcent.alt |
An object of class "Extrema": 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 |
An object of class "Extrema": The closest points in a data set to edges in each CM-vertex region in a triangle |
| cl2fVRth |
An object of class "Extrema": The closest points among a data set in the vertex regions to the respective faces in a tetrahedron |
| cl2Mc.int |
An object of class "Extrema": 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 |
| fr2eTeER |
An object of class "Extrema": The furthest points in a data set from edges in each CM-edge region in the standard equilateral triangle |
| fr2vTbVRCC |
An object of class "Extrema": The furthest points from vertices in each CC-vertex region in a basic triangle |
| fr2vVRCC |
An object of class "Extrema": The furthest points in a data set from vertices in each CC-vertex region in a triangle |
| funsAB2CMTe |
Two functions, 'lA_CM.Te' and 'lB_CM.Te' of class "TriLines" - The lines joining two vertices to the center of mass in standard equilateral triangle. |
| funsAB2MTe |
Three functions, 'lA_M.Te', 'lB_M.Te' and 'lC_M.Te' of class "TriLines" - The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it. |
| funsCartBary |
Two functions: 'cart2bary' and 'bary2cart' - Converts of a point in Cartesian coordinates to Barycentric coordinates and vice versa. |
| funsCSEdgeRegs |
Three indicator functions: 'IndCSTeRAB', 'IndCSTeRBC' and '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. |
| funsCSGamTe |
Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe - 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 |
Three indicator functions: 'IndCSTeRABt1', 'IndCSTeRBCt1' and '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 |
| funsIndDelTri |
Two functions: ind.Del.tri and indices.Del.tri - Functions provide the indices of the Delaunay triangles where the points reside. |
| funsMuVarCS1D |
Two functions: 'muCS1D' and 'asyvarCS1D' - Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case |
| funsMuVarCS2D |
Two functions: 'muCS2D' and '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 |
| funsMuVarCSend1D |
Two functions: 'muCSend1D' and 'asyvarCSend1D' - Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end interval case |
| funsMuVarPE1D |
The functions 'muPE1D' and 'asyvarPE1D' and their auxiliary functions - Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case. |
| funsMuVarPE2D |
Two functions: 'muPE2D' and '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 |
| funsMuVarPEend1D |
Two functions: 'muPEend1D' and 'asyvarPEend1D' - 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 function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| funsRankOrderTe |
Two functions: 'rank.d2e.Te' and 'order.d2e.Te' - 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 |
The functions 'muPE1D' and 'asyvarPE1D' and their auxiliary functions - Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case. |
| fvar2 |
The functions 'muPE1D' and 'asyvarPE1D' and their auxiliary functions - Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case. |
| 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 |
Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe - 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 |
Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe - 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 |
Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe - 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 |
Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe - 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 |
Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe - 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 |
| 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 |
Two functions: ind.Del.tri and indices.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 |
Three indicator functions: 'IndCSTeRAB', 'IndCSTeRBC' and '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. |
| IndCSTeRABt1 |
Three indicator functions: 'IndCSTeRABt1', 'IndCSTeRBCt1' and '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 |
| IndCSTeRAC |
Three indicator functions: 'IndCSTeRAB', 'IndCSTeRBC' and '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 |
Three indicator functions: 'IndCSTeRABt1', 'IndCSTeRBCt1' and '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 |
Three indicator functions: 'IndCSTeRAB', 'IndCSTeRBC' and '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. |
| IndCSTeRBCt1 |
Three indicator functions: 'IndCSTeRABt1', 'IndCSTeRBCt1' and '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 |
| 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 |
Two functions: ind.Del.tri and 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 |
| lA_CM.Te |
Two functions, 'lA_CM.Te' and 'lB_CM.Te' of class "TriLines" - The lines joining two vertices to the center of mass in standard equilateral triangle. |
| lA_M.Te |
Three functions, 'lA_M.Te', 'lB_M.Te' and 'lC_M.Te' of class "TriLines" - The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it. |
| lB_CM.Te |
Two functions, 'lA_CM.Te' and 'lB_CM.Te' of class "TriLines" - The lines joining two vertices to the center of mass in standard equilateral triangle. |
| lB_M.Te |
Three functions, 'lA_M.Te', 'lB_M.Te' and 'lC_M.Te' of class "TriLines" - The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it. |
| lC_M.Te |
Three functions, 'lA_M.Te', 'lB_M.Te' and 'lC_M.Te' of class "TriLines" - 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 |
An object of class "Lines": The line joining two distinct 2D points 'a' and 'b' |
| Line3D |
An object of class "Lines3D": The line crossing 3D point 'r0' in the direction of vector 'v' (or if 'v' is a point, in direction of v-r0) |
| 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 |
| paraline |
An object of class "Lines": The line paralel to the line segment joining two distinct 2D points 'a' and 'b' |
| paraline3D |
An object of class "Lines3D": The line crossing the 3D point 'P' and parallel to line joining 3D points 'A' and 'B' |
| paraplane |
An object of class "Planes": The plane paralel to the plane spanned by three distinct 3D points 'a', 'b', and 'c' |
| 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 |
An object of class "Lines3D": The line crossing the 3D point 'P' and perpendicular to the plane spanned by 3D points 'A', 'B', and 'C' |
| perpline |
An object of class "Lines": The line passing thru a point and perpendicular to the line segment joining two points |
| PG2A |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2AI |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2AII |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2AIII |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2AIV |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2Asym |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2B |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2BIII |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2Bsym |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2C |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2CIV |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| PG2Csym |
The function 'Pg2PE1D' and its auxiliary functions - The functions for probability of domination number=2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case |
| Pg2PE1D |
The function 'Pg2PE1D' and its auxiliary functions - 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 |
An object of class "Planes": 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 |
| 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 |
Two functions: 'rank.d2e.Te' and 'order.d2e.Te' - Returns the ranks and orders of points in decreasing distance to the edges of the triangle. |
| rasc.disc |
An object of class "Patterns": Generation of points associated (in a radial or circular fashion) with a given set of points |
| rasc.matern |
An object of class "Patterns": Generation of points associated (in a Matern-like fashion) to a given set of points |
| rasc.tri |
An object of class "Patterns": Generation of points associated (in a Type I fashion) with the vertices of a triangle |
| rascIITe |
An object of class "Patterns": Generation of points associated (in a Type II fashion) with the edges of T_e |
| rascMT |
An object of class "Patterns": Generation of points associated (in a Type I fashion) with a given set of points |
| rascTe |
An object of class "Patterns": 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 |
An object of class "Patterns": Generation of points segregated (in a radial or circular fashion) from a given set of points |
| rseg.tri |
An object of class "Patterns": Generation of points segregated (in a Type I fashion) from the vertices of a triangle |
| rsegIITe |
An object of class "Patterns": Generation of points segregated (in a Type II fashion) from the vertices of T_e |
| rsegMT |
An object of class "Patterns": Generation of points segregated (in a Type I fashion) from a given set of points. |
| rsegTe |
An object of class "Patterns": Generation of points segregated (in a Type I fashion) from the vertices of T_e |
| runif.bastri |
An object of class "Uniform": Generation of Uniform Points in the basic triangle |
| runif.stdtetra |
An object of class "Uniform": Generation of Uniform Points in the Standard Regular Tetrahedron T_h |
| runif.tetra |
An object of class "Uniform": Generation of Uniform Points in a tetrahedron |
| runif.tri |
An object of class "Uniform": Generation of Uniform Points in a triangle |
| runifMT |
An object of class "Uniform": Generation of Uniform Points in the convex hull of points |
| runifTe |
An object of class "Uniform": Generation of Uniform Points in the Standard Equilateral Triangle |
| runifTe.onesixth |
An object of class "Uniform": 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 |
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