{ "_id": "6a156601acfb0bcc41d61b1c", "Package": "pcds", "Type": "Package", "Title": "Proximity Catch Digraphs and Their Applications", "Version": "0.1.7", "Author": "Elvan Ceyhan", "Maintainer": "Elvan Ceyhan ", "Description": "Contains the functions for construction and visualization\nof various families of the proximity catch digraphs (PCDs) (see\n(Ceyhan (2005) ISBN:978-3-639-19063-2), for computing the graph\ninvariants for testing the patterns of segregation and\nassociation against complete spatial randomness (CSR) or\nuniformity in one, two and three dimensional cases. The package\nalso has tools for generating points from these spatial\npatterns. The graph invariants used in testing spatial point\ndata are the domination number (Ceyhan (2011)\n) and arc density (Ceyhan et al.\n(2006) ; Ceyhan et al. (2007)\n). The PCD families considered are\nArc-Slice PCDs, Proportional-Edge PCDs, and Central Similarity\nPCDs.", "License": "GPL-2", "Encoding": "UTF-8", "LazyData": "TRUE", "RdMacros": "Rdpack", "RoxygenNote": "7.2.3", "VignetteBuilder": "knitr", "Language": "en-US", "Config/pak/sysreqs": "cmake libfreetype6-dev libglu1-mesa-dev make\ntexlive libicu-dev libpng-dev libuv1-dev libgl1-mesa-dev\nzlib1g-dev", "Repository": "https://elvanceyhan.r-universe.dev", "Date/Publication": "2023-06-16 15:50:46 UTC", "RemoteUrl": "https://github.com/elvanceyhan/pcds", "RemoteRef": "HEAD", "RemoteSha": "00331843a0670e7cd9a62b7bca70df06d4629212", "NeedsCompilation": "no", "Packaged": { "Date": "2026-05-26 09:14:48 UTC", "User": "root" }, "MD5sum": "3a76b776d1dd8a9338e075a2820f9b6e", "_user": "elvanceyhan", "_type": "src", "_file": "pcds_0.1.7.tar.gz", "_fileid": "11e8cc8f053bd2819ec398b5a05b9591be16732080ade659f4b4e16dc753b9fa", "_filesize": 5559379, "_sha256": "11e8cc8f053bd2819ec398b5a05b9591be16732080ade659f4b4e16dc753b9fa", "_created": "2026-05-26T09:14:48.000Z", "_published": "2026-05-26T09:21:05.211Z", "_distro": "noble", "_jobs": [ { "job": 77843705959, "time": 285, "config": "linux-devel-x86_64", "r": "4.7.0", "check": "WARNING", "artifact": "7213345651" }, { "job": 77843706046, "time": 269, "config": "linux-release-x86_64", "r": "4.6.0", "check": "WARNING", "artifact": "7213340129" }, { "job": 77843706084, "time": 261, "config": "macos-oldrel-arm64", "r": "4.5.3", "check": "WARNING", "artifact": "7213321371" }, { "job": 77843705968, "time": 206, "config": "macos-release-arm64", "r": "4.6.0", "check": "WARNING", "artifact": "7213303419" }, { "job": 77842772651, "time": 337, "config": "source", "r": "4.6.0", "check": "OK", "artifact": "7213244474" }, { "job": 77843705908, "time": 177, "config": "wasm-release", "r": "4.6.0", "check": "OK", "artifact": "7213307560" }, { "job": 77843706194, "time": 227, "config": "windows-devel", "r": "4.7.0", "check": "WARNING", "artifact": "7213325943" }, { "job": 77843706187, "time": 208, "config": "windows-oldrel", "r": "4.5.3", "check": "WARNING", "artifact": "7213318637" }, { "job": 77843705963, "time": 269, "config": "windows-release", "r": "4.6.0", "check": "WARNING", "artifact": "7213341288" } ], "_buildurl": "https://github.com/r-universe/elvanceyhan/actions/runs/26443211765", "_status": "success", "_host": "GitHub-Actions", "_upstream": "https://github.com/elvanceyhan/pcds", "_commit": { "id": "00331843a0670e7cd9a62b7bca70df06d4629212", "author": "elvanceyhan ", "committer": "elvanceyhan ", "message": "made the following changes:\n-renamed functions to follow a consistent naming convention\n-changed some of the print() functions to cat() in the print methods of the objects\n-added NumArcs object for num.arcs* functions\n", "time": 1686930646 }, "_maintainer": { "name": "Elvan Ceyhan", "email": "elvanceyhan@gmail.com", "login": "elvanceyhan", "description": "Associate professor at the Dept of Mathematics and Statistics of Auburn University. 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(AS-PCD) for a 2D data set - multiple triangle case", "topics": [ "arcsAS" ] }, { "page": "ArcsAStri", "title": "The arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for 2D data - one triangle case", "topics": [ "arcsAStri" ] }, { "page": "ArcsCS", "title": "The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data - multiple triangle case", "topics": [ "arcsCS" ] }, { "page": "ArcsCS1D", "title": "The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case", "topics": [ "arcsCS1D" ] }, { "page": "ArcsCSend.int", "title": "The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end interval case", "topics": [ "arcsCSend.int" ] }, { "page": "ArcsCSint", "title": "The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - one interval case", "topics": [ "arcsCSint" ] }, { "page": "ArcsCSmid.int", "title": "The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle intervals case", "topics": [ "arcsCSmid.int" ] }, { "page": "ArcsCStri", "title": "The arcs of Central Similarity Proximity Catch Digraphs (CS-PCD) for 2D data - one triangle case", "topics": [ "arcsCStri" ] }, { "page": "ArcsPE", "title": "The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - multiple triangle case", "topics": [ "arcsPE" ] }, { "page": "ArcsPE1D", "title": "The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - multiple interval case", "topics": [ "arcsPE1D" ] }, { "page": "ArcsPEend.int", "title": "The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case", "topics": [ "arcsPEend.int" ] }, { "page": "ArcsPEint", "title": "The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - one interval case", "topics": [ "arcsPEint" ] }, { "page": "ArcsPEmid.int", "title": "The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle intervals case", "topics": [ "arcsPEmid.int" ] }, { "page": "ArcsPEtri", "title": "The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - one triangle case", "topics": [ "arcsPEtri" ] }, { "page": "area.polygon", "title": "The area of a polygon in R^2", "topics": [ "area.polygon" ] }, { "page": "as.basic.tri", "title": "The labels of the vertices of a triangle in the basic triangle form", "topics": [ "as.basic.tri" ] }, { "page": "ASarc.dens.tri", "title": "Arc density of Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case", "topics": [ "ASarc.dens.tri" ] }, { "page": "center.nondegPE", "title": "Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs)", "topics": [ "center.nondegPE" ] }, { "page": "centerMc", "title": "Parameterized center of an interval", "topics": [ "centerMc" ] }, { "page": "centersMc", "title": "Parameterized centers of intervals", "topics": [ "centersMc" ] }, { "page": "circumcenter.basic.tri", "title": "Circumcenter of a standard basic triangle form", "topics": [ "circumcenter.basic.tri" ] }, { "page": "circumcenter.tetra", "title": "Circumcenter of a general tetrahedron", "topics": [ "circumcenter.tetra" ] }, { "page": "circumcenter.tri", "title": "Circumcenter of a general triangle", "topics": [ "circumcenter.tri" ] }, { "page": "cl2CCvert.reg", "title": "The closest points to circumcenter in each CC-vertex region in a triangle", "topics": [ "cl2CCvert.reg" ] }, { "page": "cl2CCvert.reg.basic.tri", "title": "The closest points to circumcenter in each CC-vertex region in a standard basic triangle", "topics": [ "cl2CCvert.reg.basic.tri" ] }, { "page": "cl2edges.std.tri", "title": "The closest points in a data set to edges in the standard equilateral triangle", "topics": [ "cl2edges.std.tri" ] }, { "page": "cl2edges.vert.reg.basic.tri", "title": "The closest points among a data set in the vertex regions to the corresponding edges in a standard basic triangle", "topics": [ "cl2edges.vert.reg.basic.tri" ] }, { "page": "cl2edgesCCvert.reg", "title": "The closest points in a data set to edges in each CC-vertex region in a triangle", "topics": [ "cl2edgesCCvert.reg" ] }, { "page": "cl2edgesCMvert.reg", "title": "The closest points in a data set to edges in each CM-vertex region in a triangle", "topics": [ "cl2edgesCMvert.reg" ] }, { "page": "cl2edgesMvert.reg", "title": "The closest points among a data set in the vertex regions to the respective edges in a triangle", "topics": [ "cl2edgesMvert.reg" ] }, { "page": "cl2faces.vert.reg.tetra", "title": "The closest points among a data set in the vertex regions to the respective faces in a tetrahedron", "topics": [ "cl2faces.vert.reg.tetra" ] }, { "page": "cl2Mc.int", "title": "The closest points to center in each vertex region in an interval", "topics": [ "cl2Mc.int" ] }, { "page": "CSarc.dens.test", "title": "A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D data", "topics": [ "CSarc.dens.test" ] }, { "page": "CSarc.dens.test.int", "title": "A test of uniformity of 1D data in a given interval based on Central Similarity Proximity Catch Digraph (CS-PCD)", "topics": [ "CSarc.dens.test.int" ] }, { "page": "CSarc.dens.test1D", "title": "A test of segregation/association based on arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data", "topics": [ "CSarc.dens.test1D" ] }, { "page": "CSarc.dens.tri", "title": "Arc density of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case", "topics": [ "CSarc.dens.tri" ] }, { "page": "dimension", "title": "The dimension of a 'vector' or matrix or a data frame", "topics": [ "dimension" ] }, { "page": "Dist", "title": "The distance between two vectors, matrices, or data frames", "topics": [ "Dist" ] }, { "page": "dist.point2line", "title": "The distance from a point to a line defined by two points", "topics": [ "dist.point2line" ] }, { "page": "dist.point2plane", "title": "The distance from a point to a plane spanned by three 3D points", "topics": [ "dist.point2plane" ] }, { "page": "dist.point2set", "title": "Distance from a point to a set of finite cardinality", "topics": [ "dist.point2set" ] }, { "page": "dom.num.exact", "title": "Exact domination number (i.e., domination number by the exact algorithm)", "topics": [ "dom.num.exact" ] }, { "page": "dom.num.greedy", "title": "Approximate domination number and approximate dominating set by the greedy algorithm", "topics": [ "dom.num.greedy" ] }, { "page": "edge.reg.triCM", "title": "The vertices of the CM-edge region in a triangle that contains the point", "topics": [ "edge.reg.triCM" ] }, { "page": "fr2edgesCMedge.reg.std.tri", "title": "The furthest points in a data set from edges in each CM-edge region in the standard equilateral triangle", "topics": [ "fr2edgesCMedge.reg.std.tri" ] }, { "page": "fr2vertsCCvert.reg", "title": "The furthest points in a data set from vertices in each CC-vertex region in a triangle", "topics": [ "fr2vertsCCvert.reg" ] }, { "page": "fr2vertsCCvert.reg.basic.tri", "title": "The furthest points from vertices in each CC-vertex region in a standard basic triangle", "topics": [ "fr2vertsCCvert.reg.basic.tri" ] }, { "page": "funsAB2CMTe", "title": "The lines joining two vertices to the center of mass in standard equilateral triangle", "topics": [ "funsAB2CMTe", "lineA2CMinTe", "lineB2CMinTe" ] }, { "page": "funsAB2MTe", "title": "The lines joining the three vertices of the standard equilateral triangle to a center, 'M', of it", "topics": [ "funsAB2MTe", "lineA2MinTe", "lineB2MinTe", "lineC2MinTe" ] }, { "page": "funsCartBary", "title": "Converts of a point in Cartesian coordinates to Barycentric coordinates and vice versa", "topics": [ "bary2cart", "cart2bary", "funsCartBary" ] }, { "page": "funsCSEdgeRegs", "title": "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", "topics": [ "funsCSEdgeRegs", "IarcCSstd.triRAB", "IarcCSstd.triRAC", "IarcCSstd.triRBC" ] }, { "page": "funsCSGamTe", "title": "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", "topics": [ "funsCSGamTe", "Idom.num2CSstd.tri", "Idom.num3CSstd.tri", "Idom.num4CSstd.tri", "Idom.num5CSstd.tri", "Idom.num6CSstd.tri" ] }, { "page": "funsCSt1EdgeRegs", "title": "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", "topics": [ "funsCSt1EdgeRegs", "IarcCSt1.std.triRAB", "IarcCSt1.std.triRAC", "IarcCSt1.std.triRBC" ] }, { "page": "funsIndDelTri", "title": "Functions provide the indices of the Delaunay triangles where the points reside", "topics": [ "funsIndDelTri", "index.delaunay.tri", "indices.delaunay.tri" ] }, { "page": "funsMuVarCS1D", "title": "Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case", "topics": [ "asyvarCS1D", "funsMuVarCS1D", "muCS1D" ] }, { "page": "funsMuVarCS2D", "title": "Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D uniform data in one triangle", "topics": [ "asyvarCS2D", "funsMuVarCS2D", "muCS2D" ] }, { "page": "funsMuVarCSend.int", "title": "Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end interval case", "topics": [ "asyvarCSend.int", "funsMuVarCSend.int", "muCSend.int" ] }, { "page": "funsMuVarPE1D", "title": "Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case", "topics": [ "asyvarPE1D", "funsMuVarPE1D", "fvar1", "fvar2", "mu1PE1D", "muPE1D" ] }, { "page": "funsMuVarPE2D", "title": "Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle", "topics": [ "asyvarPE2D", "funsMuVarPE2D", "muPE2D" ] }, { "page": "funsMuVarPEend.int", "title": "Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case", "topics": [ "asyvarPEend.int", "funsMuVarPEend.int", "muPEend.int" ] }, { "page": "funsPDomNum2PE1D", "title": "The functions for probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case", "topics": [ "funsPDomNum2PE1D", "Pdom.num2A", "Pdom.num2AI", "Pdom.num2AII", "Pdom.num2AIII", "Pdom.num2AIV", "Pdom.num2Asym", "Pdom.num2B", "Pdom.num2BIII", "Pdom.num2Bsym", "Pdom.num2C", "Pdom.num2CIV", "Pdom.num2Csym", "Pdom.num2PE1D" ] }, { "page": "funsRankOrderTe", "title": "Returns the ranks and orders of points in decreasing distance to the edges of the triangle", "topics": [ "funsRankOrderTe", "order.dist2edges.std.tri", "rank.dist2edges.std.tri" ] }, { "page": "funsTbMid2CC", "title": "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.", "topics": [ "funsTbMid2CC", "lineD1CCinTb", "lineD2CCinTb" ] }, { "page": "IarcASbasic.tri", "title": "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", "topics": [ "IarcASbasic.tri" ] }, { "page": "IarcASset2pnt.tri", "title": "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", "topics": [ "IarcASset2pnt.tri" ] }, { "page": "IarcAStri", "title": "The indicator for the presence of an arc from a point to another for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case", "topics": [ "IarcAStri" ] }, { "page": "IarcCS.Te.onesixth", "title": "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", "topics": [ "IarcCS.Te.onesixth" ] }, { "page": "IarcCSbasic.tri", "title": "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", "topics": [ "IarcCSbasic.tri" ] }, { "page": "IarcCSedge.reg.std.tri", "title": "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", "topics": [ "IarcCSedge.reg.std.tri" ] }, { "page": "IarcCSend.int", "title": "The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end interval case", "topics": [ "IarcCSend.int" ] }, { "page": "IarcCSint", "title": "The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case", "topics": [ "IarcCSint" ] }, { "page": "IarcCSmid.int", "title": "The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case", "topics": [ "IarcCSmid.int" ] }, { "page": "IarcCSset2pnt.std.tri", "title": "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", "topics": [ "IarcCSset2pnt.std.tri" ] }, { "page": "IarcCSset2pnt.tri", "title": "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", "topics": [ "IarcCSset2pnt.tri" ] }, { "page": "IarcCSstd.tri", "title": "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", "topics": [ "IarcCSstd.tri" ] }, { "page": "IarcCSt1.std.tri", "title": "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", "topics": [ "IarcCSt1.std.tri" ] }, { "page": "IarcCStri", "title": "The indicator for the presence of an arc from one point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs)", "topics": [ "IarcCStri" ] }, { "page": "IarcCStri.alt", "title": "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)", "topics": [ "IarcCStri.alt" ] }, { "page": "IarcPEbasic.tri", "title": "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", "topics": [ "IarcPEbasic.tri" ] }, { "page": "IarcPEend.int", "title": "The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case", "topics": [ "IarcPEend.int" ] }, { "page": "IarcPEint", "title": "The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one interval case", "topics": [ "IarcPEint" ] }, { "page": "IarcPEmid.int", "title": "The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case", "topics": [ "IarcPEmid.int" ] }, { "page": "IarcPEset2pnt.std.tri", "title": "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", "topics": [ "IarcPEset2pnt.std.tri" ] }, { "page": "IarcPEset2pnt.tri", "title": "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", "topics": [ "IarcPEset2pnt.tri" ] }, { "page": "IarcPEstd.tetra", "title": "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", "topics": [ "IarcPEstd.tetra" ] }, { "page": "IarcPEstd.tri", "title": "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", "topics": [ "IarcPEstd.tri" ] }, { "page": "IarcPEtetra", "title": "The indicator for the presence of an arc from one 3D point to another 3D point for Proportional Edge Proximity Catch Digraphs (PE-PCDs)", "topics": [ "IarcPEtetra" ] }, { "page": "IarcPEtri", "title": "The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case", "topics": [ "IarcPEtri" ] }, { "page": "Idom.num.up.bnd", "title": "Indicator for an upper bound for the domination number by the exact algorithm", "topics": [ "Idom.num.up.bnd" ] }, { "page": "Idom.num1ASbasic.tri", "title": "The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - standard basic triangle case", "topics": [ "Idom.num1ASbasic.tri" ] }, { "page": "Idom.num1AStri", "title": "The indicator for a point being a dominating point for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case", "topics": [ "Idom.num1AStri" ] }, { "page": "Idom.num1CS.Te.onesixth", "title": "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", "topics": [ "Idom.num1CS.Te.onesixth" ] }, { "page": "Idom.num1CSint", "title": "The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) for an interval", "topics": [ "Idom.num1CSint" ] }, { "page": "Idom.num1CSstd.tri", "title": "The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case", "topics": [ "Idom.num1CSstd.tri" ] }, { "page": "Idom.num1CSt1std.tri", "title": "The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case with t=1", "topics": [ "Idom.num1CSt1std.tri" ] }, { "page": "Idom.num1PEbasic.tri", "title": "The indicator for a point being a dominating point or not for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard basic triangle case", "topics": [ "Idom.num1PEbasic.tri" ] }, { "page": "Idom.num1PEint", "title": "The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) for an interval", "topics": [ "Idom.num1PEint" ] }, { "page": "Idom.num1PEstd.tetra", "title": "The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case", "topics": [ "Idom.num1PEstd.tetra" ] }, { "page": "Idom.num1PEtetra", "title": "The indicator for a 3D point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case", "topics": [ "Idom.num1PEtetra" ] }, { "page": "Idom.num1PEtri", "title": "The indicator for a point being a dominating point for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case", "topics": [ "Idom.num1PEtri" ] }, { "page": "Idom.num2ASbasic.tri", "title": "The indicator for two points being a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - standard basic triangle case", "topics": [ "Idom.num2ASbasic.tri" ] }, { "page": "Idom.num2AStri", "title": "The indicator for two points constituting a dominating set for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case", "topics": [ "Idom.num2AStri" ] }, { "page": "Idom.num2CS.Te.onesixth", "title": "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", "topics": [ "Idom.num2CS.Te.onesixth" ] }, { "page": "Idom.num2PEbasic.tri", "title": "The indicator for two points being a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard basic triangle case", "topics": [ "Idom.num2PEbasic.tri" ] }, { "page": "Idom.num2PEstd.tetra", "title": "The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case", "topics": [ "Idom.num2PEstd.tetra" ] }, { "page": "Idom.num2PEtetra", "title": "The indicator for two 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case", "topics": [ "Idom.num2PEtetra" ] }, { "page": "Idom.num2PEtri", "title": "The indicator for two points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case", "topics": [ "Idom.num2PEtri" ] }, { "page": "Idom.num3PEstd.tetra", "title": "The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard regular tetrahedron case", "topics": [ "Idom.num3PEstd.tetra" ] }, { "page": "Idom.num3PEtetra", "title": "The indicator for three 3D points constituting a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case", "topics": [ "Idom.num3PEtetra" ] }, { "page": "Idom.numASup.bnd.tri", "title": "Indicator for an upper bound for the domination number of Arc Slice Proximity Catch Digraph (AS-PCD) by the exact algorithm - one triangle case", "topics": [ "Idom.numASup.bnd.tri" ] }, { "page": "Idom.numCSup.bnd.std.tri", "title": "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", "topics": [ "Idom.numCSup.bnd.std.tri" ] }, { "page": "Idom.numCSup.bnd.tri", "title": "Indicator for an upper bound for the domination number of Central Similarity Proximity Catch Digraph (CS-PCD) by the exact algorithm - one triangle case", "topics": [ "Idom.numCSup.bnd.tri" ] }, { "page": "Idom.setAStri", "title": "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", "topics": [ "Idom.setAStri" ] }, { "page": "Idom.setCSstd.tri", "title": "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", "topics": [ "Idom.setCSstd.tri" ] }, { "page": "Idom.setCStri", "title": "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", "topics": [ "Idom.setCStri" ] }, { "page": "Idom.setPEstd.tri", "title": "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", "topics": [ "Idom.setPEstd.tri" ] }, { "page": "Idom.setPEtri", "title": "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", "topics": [ "Idom.setPEtri" ] }, { "page": "in.circle", "title": "Check whether a point is inside a circle", "topics": [ "in.circle" ] }, { "page": "in.tetrahedron", "title": "Check whether a point is inside a tetrahedron", "topics": [ "in.tetrahedron" ] }, { "page": "in.tri.all", "title": "Check whether all points in a data set are inside the triangle", "topics": [ "in.tri.all" ] }, { "page": "in.triangle", "title": "Check whether a point is inside a triangle", "topics": [ "in.triangle" ] }, { "page": "inci.matAS", "title": "Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case", "topics": [ "inci.matAS" ] }, { "page": "inci.matAStri", "title": "Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - one triangle case", "topics": [ "inci.matAStri" ] }, { "page": "inci.matCS", "title": "Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - multiple triangle case", "topics": [ "inci.matCS" ] }, { "page": "inci.matCS1D", "title": "Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case", "topics": [ "inci.matCS1D" ] }, { "page": "inci.matCSint", "title": "Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - one interval case", "topics": [ "inci.matCSint" ] }, { "page": "inci.matCSstd.tri", "title": "Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case", "topics": [ "inci.matCSstd.tri" ] }, { "page": "inci.matCStri", "title": "Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case", "topics": [ "inci.matCStri" ] }, { "page": "inci.matPE", "title": "Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - multiple triangle case", "topics": [ "inci.matPE" ] }, { "page": "inci.matPE1D", "title": "Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - multiple interval case", "topics": [ "inci.matPE1D" ] }, { "page": "inci.matPEint", "title": "Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - one interval case", "topics": [ "inci.matPEint" ] }, { "page": "inci.matPEstd.tri", "title": "Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard equilateral triangle case", "topics": [ "inci.matPEstd.tri" ] }, { "page": "inci.matPEtetra", "title": "Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case", "topics": [ "inci.matPEtetra" ] }, { "page": "inci.matPEtri", "title": "Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case", "topics": [ "inci.matPEtri" ] }, { "page": "index.six.Te", "title": "Region index inside the Gamma-1 region", "topics": [ "index.six.Te" ] }, { "page": "intersect.line.circle", "title": "The points of intersection of a line and a circle", "topics": [ "intersect.line.circle" ] }, { "page": "intersect.line.plane", "title": "The point of intersection of a line and a plane", "topics": [ "intersect.line.plane" ] }, { "page": "intersect2lines", "title": "The point of intersection of two lines defined by two pairs of points", "topics": [ "intersect2lines" ] }, { "page": "interval.indices.set", "title": "Indices of the intervals where the 1D point(s) reside", "topics": [ "interval.indices.set" ] }, { "page": "is.in.data", "title": "Check a point belong to a given data set", "topics": [ "is.in.data" ] }, { "page": "is.point", "title": "Check the argument is a point of a given dimension", "topics": [ "is.point" ] }, { "page": "is.std.eq.tri", "title": "Check whether a triangle is a standard equilateral triangle", "topics": [ "is.std.eq.tri" ] }, { "page": "kfr2vertsCCvert.reg", "title": "The 'k' furthest points in a data set from vertices in each CC-vertex region in a triangle", "topics": [ "kfr2vertsCCvert.reg" ] }, { "page": "Line", "title": "The line joining two distinct 2D points 'a' and 'b'", "topics": [ "Line" ] }, { "page": "Line3D", "title": "The line crossing 3D point 'p' in the direction of 'vector' 'v' (or if 'v' is a point, in direction of v-r_0)", "topics": [ "Line3D" ] }, { "page": "NASbasic.tri", "title": "The vertices of the Arc Slice (AS) Proximity Region in the standard basic triangle", "topics": [ "NASbasic.tri" ] }, { "page": "NAStri", "title": "The vertices of the Arc Slice (AS) Proximity Region in a general triangle", "topics": [ "NAStri" ] }, { "page": "NCSint", "title": "The end points of the Central Similarity (CS) Proximity Region for a point - one interval case", "topics": [ "NCSint" ] }, { "page": "NCStri", "title": "The vertices of the Central Similarity (CS) Proximity Region in a general triangle", "topics": [ "NCStri" ] }, { "page": "NPEbasic.tri", "title": "The vertices of the Proportional Edge (PE) Proximity Region in a standard basic triangle", "topics": [ "NPEbasic.tri" ] }, { "page": "NPEint", "title": "The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case", "topics": [ "NPEint" ] }, { "page": "NPEstd.tetra", "title": "The vertices of the Proportional Edge (PE) Proximity Region in the standard regular tetrahedron", "topics": [ "NPEstd.tetra" ] }, { "page": "NPEtetra", "title": "The vertices of the Proportional Edge (PE) Proximity Region in a tetrahedron", "topics": [ "NPEtetra" ] }, { "page": "NPEtri", "title": "The vertices of the Proportional Edge (PE) Proximity Region in a general triangle", "topics": [ "NPEtri" ] }, { "page": "num.arcsAS", "title": "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", "topics": [ "num.arcsAS" ] }, { "page": "num.arcsAStri", "title": "Number of arcs of Arc Slice Proximity Catch Digraphs (AS-PCDs) and quantities related to the triangle - one triangle case", "topics": [ "num.arcsAStri" ] }, { "page": "num.arcsCS", "title": "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", "topics": [ "num.arcsCS" ] }, { "page": "num.arcsCS1D", "title": "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", "topics": [ "num.arcsCS1D" ] }, { "page": "num.arcsCSend.int", "title": "Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - end interval case", "topics": [ "num.arcsCSend.int" ] }, { "page": "num.arcsCSint", "title": "Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the interval - one interval case", "topics": [ "num.arcsCSint" ] }, { "page": "num.arcsCSmid.int", "title": "Number of Arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case", "topics": [ "num.arcsCSmid.int" ] }, { "page": "num.arcsCSstd.tri", "title": "Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the triangle - standard equilateral triangle case", "topics": [ "num.arcsCSstd.tri" ] }, { "page": "num.arcsCStri", "title": "Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and quantities related to the triangle - one triangle case", "topics": [ "num.arcsCStri" ] }, { "page": "num.arcsPE", "title": "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", "topics": [ "num.arcsPE" ] }, { "page": "num.arcsPE1D", "title": "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", "topics": [ "num.arcsPE1D" ] }, { "page": "num.arcsPEend.int", "title": "Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case", "topics": [ "num.arcsPEend.int" ] }, { "page": "num.arcsPEint", "title": "Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the interval - one interval case", "topics": [ "num.arcsPEint" ] }, { "page": "num.arcsPEmid.int", "title": "Number of Arcs for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case", "topics": [ "num.arcsPEmid.int" ] }, { "page": "num.arcsPEstd.tri", "title": "Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - standard equilateral triangle case", "topics": [ "num.arcsPEstd.tri" ] }, { "page": "num.arcsPEtetra", "title": "Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the tetrahedron - one tetrahedron case", "topics": [ "num.arcsPEtetra" ] }, { "page": "num.arcsPEtri", "title": "Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - one triangle case", "topics": [ "num.arcsPEtri" ] }, { "page": "num.delaunay.tri", "title": "Number of Delaunay triangles based on a 2D data set", "topics": [ "num.delaunay.tri" ] }, { "page": "paraline", "title": "The line at a point 'p' parallel to the line segment joining two distinct 2D points 'a' and 'b'", "topics": [ "paraline" ] }, { "page": "paraline3D", "title": "The line crossing the 3D point 'p' and parallel to line joining 3D points 'a' and 'b'", "topics": [ "paraline3D" ] }, { "page": "paraplane", "title": "The plane at a point and parallel to the plane spanned by three distinct 3D points 'a', 'b', and 'c'", "topics": [ "paraplane" ] }, { "page": "pcds", "title": "pcds: A package for Proximity Catch Digraphs and Their Applications", "topics": [ "pcds" ] }, { "page": "Pdom.num2PE1Dasy", "title": "The asymptotic probability of domination number = 2 for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case", "topics": [ "Pdom.num2PE1Dasy" ] }, { "page": "Pdom.num2PEtri", "title": "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", "topics": [ "Pdom.num2PEtri" ] }, { "page": "PEarc.dens.test", "title": "A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data", "topics": [ "PEarc.dens.test" ] }, { "page": "PEarc.dens.test.int", "title": "A test of uniformity of 1D data in a given interval based on Proportional Edge Proximity Catch Digraph (PE-PCD)", "topics": [ "PEarc.dens.test.int" ] }, { "page": "PEarc.dens.test1D", "title": "A test of segregation/association based on arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data", "topics": [ "PEarc.dens.test1D" ] }, { "page": "PEarc.dens.tetra", "title": "Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one tetrahedron case", "topics": [ "PEarc.dens.tetra" ] }, { "page": "PEarc.dens.tri", "title": "Arc density of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case", "topics": [ "PEarc.dens.tri" ] }, { "page": "PEdom.num", "title": "The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - multiple triangle case", "topics": [ "PEdom.num" ] }, { "page": "PEdom.num.binom.test", "title": "A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Binomial Approximation", "topics": [ "PEdom.num.binom.test" ] }, { "page": "PEdom.num.binom.test1D", "title": "A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - Binomial Approximation", "topics": [ "PEdom.num.binom.test1D" ] }, { "page": "PEdom.num.binom.test1Dint", "title": "A test of uniformity for 1D data based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - Binomial Approximation", "topics": [ "PEdom.num.binom.test1Dint" ] }, { "page": "PEdom.num.nondeg", "title": "The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) with non-degeneracy centers - multiple triangle case", "topics": [ "PEdom.num.nondeg" ] }, { "page": "PEdom.num.norm.test", "title": "A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Normal Approximation", "topics": [ "PEdom.num.norm.test" ] }, { "page": "PEdom.num.tetra", "title": "The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one tetrahedron case", "topics": [ "PEdom.num.tetra" ] }, { "page": "PEdom.num.tri", "title": "The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) - one triangle case", "topics": [ "PEdom.num.tri" ] }, { "page": "PEdom.num1D", "title": "The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data", "topics": [ "PEdom.num1D" ] }, { "page": "PEdom.num1Dnondeg", "title": "The domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) with non-degeneracy centers - multiple interval case", "topics": [ "PEdom.num1Dnondeg" ] }, { "page": "perpline", "title": "The line passing through a point and perpendicular to the line segment joining two points", "topics": [ "perpline" ] }, { "page": "perpline2plane", "title": "The line crossing the 3D point 'p' and perpendicular to the plane spanned by 3D points 'a', 'b', and 'c'", "topics": [ "perpline2plane" ] }, { "page": "Plane", "title": "The plane passing through three distinct 3D points 'a', 'b', and 'c'", "topics": [ "Plane" ] }, { "page": "plot.Extrema", "title": "Plot an 'Extrema' 'object'", "topics": [ "plot.Extrema" ] }, { "page": "plot.Lines", "title": "Plot a 'Lines' 'object'", "topics": [ "plot.Lines" ] }, { "page": "plot.Lines3D", "title": "Plot a 'Lines3D' 'object'", "topics": [ "plot.Lines3D" ] }, { "page": "plot.NumArcs", "title": "Plot a 'NumArcs' 'object'", "topics": [ "plot.NumArcs" ] }, { "page": "plot.Patterns", "title": "Plot a 'Patterns' 'object'", "topics": [ "plot.Patterns" ] }, { "page": "plot.PCDs", "title": "Plot a 'PCDs' 'object'", "topics": [ "plot.PCDs" ] }, { "page": "plot.Planes", "title": "Plot a 'Planes' 'object'", "topics": [ "plot.Planes" ] }, { "page": "plot.TriLines", "title": "Plot a 'TriLines' 'object'", "topics": [ "plot.TriLines" ] }, { "page": "plot.Uniform", "title": "Plot a 'Uniform' 'object'", "topics": [ "plot.Uniform" ] }, { "page": "plotASarcs", "title": "The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - multiple triangle case", "topics": [ "plotASarcs" ] }, { "page": "plotASarcs.tri", "title": "The plot of the arcs of Arc Slice Proximity Catch Digraph (AS-PCD) for a 2D data set - one triangle case", "topics": [ "plotASarcs.tri" ] }, { "page": "plotASregs", "title": "The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - multiple triangle case", "topics": [ "plotASregs" ] }, { "page": "plotASregs.tri", "title": "The plot of the Arc Slice (AS) Proximity Regions for a 2D data set - one triangle case", "topics": [ "plotASregs.tri" ] }, { "page": "plotCSarcs", "title": "The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - multiple triangle case", "topics": [ "plotCSarcs" ] }, { "page": "plotCSarcs.int", "title": "The plot of the arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data (vertices jittered along y-coordinate) - one interval case", "topics": [ "plotCSarcs.int" ] }, { "page": "plotCSarcs.tri", "title": "The plot of the arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for a 2D data set - one triangle case", "topics": [ "plotCSarcs.tri" ] }, { "page": "plotCSarcs1D", "title": "The plot of the arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data (vertices jittered along y-coordinate) - multiple interval case", "topics": [ "plotCSarcs1D" ] }, { "page": "plotCSregs", "title": "The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - multiple triangle case", "topics": [ "plotCSregs" ] }, { "page": "plotCSregs.int", "title": "The plot of the Central Similarity (CS) Proximity Regions for a general interval (vertices jittered along y-coordinate) - one interval case", "topics": [ "plotCSregs.int" ] }, { "page": "plotCSregs.tri", "title": "The plot of the Central Similarity (CS) Proximity Regions for a 2D data set - one triangle case", "topics": [ "plotCSregs.tri" ] }, { "page": "plotCSregs1D", "title": "The plot of the Central Similarity (CS) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case", "topics": [ "plotCSregs1D" ] }, { "page": "plotDelaunay.tri", "title": "The scatterplot of points from one class and plot of the Delaunay triangulation of the other class", "topics": [ "plotDelaunay.tri" ] }, { "page": "plotIntervals", "title": "The plot of the subintervals based on 'Yp' points together with 'Xp' points", "topics": [ "plotIntervals" ] }, { "page": "plotPEarcs", "title": "The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - multiple triangle case", "topics": [ "plotPEarcs" ] }, { "page": "plotPEarcs.int", "title": "The plot of the arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) for 1D data (vertices jittered along y-coordinate) - one interval case", "topics": [ "plotPEarcs.int" ] }, { "page": "plotPEarcs.tri", "title": "The plot of the arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for a 2D data set - one triangle case", "topics": [ "plotPEarcs.tri" ] }, { "page": "plotPEarcs1D", "title": "The plot of the arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) for 1D data (vertices jittered along y-coordinate) - multiple interval case", "topics": [ "plotPEarcs1D" ] }, { "page": "plotPEregs", "title": "The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - multiple triangle case", "topics": [ "plotPEregs" ] }, { "page": "plotPEregs.int", "title": "The plot of the Proportional Edge (PE) Proximity Regions for a general interval (vertices jittered along y-coordinate) - one interval case", "topics": [ "plotPEregs.int" ] }, { "page": "plotPEregs.std.tetra", "title": "The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - standard regular tetrahedron case", "topics": [ "plotPEregs.std.tetra" ] }, { "page": "plotPEregs.tetra", "title": "The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - one tetrahedron case", "topics": [ "plotPEregs.tetra" ] }, { "page": "plotPEregs.tri", "title": "The plot of the Proportional Edge (PE) Proximity Regions for a 2D data set - one triangle case", "topics": [ "plotPEregs.tri" ] }, { "page": "plotPEregs1D", "title": "The plot of the Proportional Edge (PE) Proximity Regions (vertices jittered along y-coordinate) - multiple interval case", "topics": [ "plotPEregs1D" ] }, { "page": "print.Extrema", "title": "Print a 'Extrema' 'object'", "topics": [ "print.Extrema" ] }, { "page": "print.Lines", "title": "Print a 'Lines' 'object'", "topics": [ "print.Lines" ] }, { "page": "print.Lines3D", "title": "Print a 'Lines3D' 'object'", "topics": [ "print.Lines3D" ] }, { "page": "print.NumArcs", "title": "Print a 'NumArcs' 'object'", "topics": [ "print.NumArcs" ] }, { "page": "print.Patterns", "title": "Print a 'Patterns' 'object'", "topics": [ "print.Patterns" ] }, { "page": "print.PCDs", "title": "Print a 'PCDs' 'object'", "topics": [ "print.PCDs" ] }, { "page": "print.Planes", "title": "Print a 'Planes' 'object'", "topics": [ "print.Planes" ] }, { "page": "print.summary.Extrema", "title": "Print a summary of a 'Extrema' 'object'", "topics": [ "print.summary.Extrema" ] }, { "page": "print.summary.Lines", "title": "Print a summary of a 'Lines' 'object'", "topics": [ "print.summary.Lines" ] }, { "page": "print.summary.Lines3D", "title": "Print a summary of a 'Lines3D' 'object'", "topics": [ "print.summary.Lines3D" ] }, { "page": "print.summary.NumArcs", "title": "Print a summary of a 'NumArcs' 'object'", "topics": [ "print.summary.NumArcs" ] }, { "page": "print.summary.Patterns", "title": "Print a summary of a 'Patterns' 'object'", "topics": [ "print.summary.Patterns" ] }, { "page": "print.summary.PCDs", "title": "Print a summary of a 'PCDs' 'object'", "topics": [ "print.summary.PCDs" ] }, { "page": "print.summary.Planes", "title": "Print a summary of a 'Planes' 'object'", "topics": [ "print.summary.Planes" ] }, { "page": "print.summary.TriLines", "title": "Print a summary of a 'TriLines' 'object'", "topics": [ "print.summary.TriLines" ] }, { "page": "print.summary.Uniform", "title": "Print a summary of a 'Uniform' 'object'", "topics": [ "print.summary.Uniform" ] }, { "page": "print.TriLines", "title": "Print a 'TriLines' 'object'", "topics": [ "print.TriLines" ] }, { "page": "print.Uniform", "title": "Print a 'Uniform' 'object'", "topics": [ "print.Uniform" ] }, { "page": "prj.cent2edges", "title": "Projections of a point inside a triangle to its edges", "topics": [ "prj.cent2edges" ] }, { "page": "prj.cent2edges.basic.tri", "title": "Projections of a point inside the standard basic triangle form to its edges", "topics": [ "prj.cent2edges.basic.tri" ] }, { "page": "prj.nondegPEcent2edges", "title": "Projections of Centers for non-degenerate asymptotic distribution of domination number of Proportional Edge Proximity Catch Digraphs (PE-PCDs) to its edges", "topics": [ "prj.nondegPEcent2edges" ] }, { "page": "radii", "title": "The radii of points from one class with respect to points from the other class", "topics": [ "radii" ] }, { "page": "radius", "title": "The radius of a point from one class with respect to points from the other class", "topics": [ "radius" ] }, { "page": "rassoc.circular", "title": "Generation of points associated (in a radial or circular fashion) with a given set of points", "topics": [ "rassoc.circular" ] }, { "page": "rassoc.matern", "title": "Generation of points associated (in a Matern-like fashion) to a given set of points", "topics": [ "rassoc.matern" ] }, { "page": "rassoc.multi.tri", "title": "Generation of points associated (in a Type I fashion) with a given set of points", "topics": [ "rassoc.multi.tri" ] }, { "page": "rassoc.std.tri", "title": "Generation of points associated (in a Type I fashion) with the vertices of T_e", "topics": [ "rassoc.std.tri" ] }, { "page": "rassoc.tri", "title": "Generation of points associated (in a Type I fashion) with the vertices of a triangle", "topics": [ "rassoc.tri" ] }, { "page": "rassocII.std.tri", "title": "Generation of points associated (in a Type II fashion) with the edges of T_e", "topics": [ "rassocII.std.tri" ] }, { "page": "rel.edge.basic.tri", "title": "The index of the edge region in a standard basic triangle form that contains a point", "topics": [ "rel.edge.basic.tri" ] }, { "page": "rel.edge.basic.triCM", "title": "The index of the CM-edge region in a standard basic triangle form that contains a point", "topics": [ "rel.edge.basic.triCM" ] }, { "page": "rel.edge.std.triCM", "title": "The index of the edge region in the standard equilateral triangle that contains a point", "topics": [ "rel.edge.std.triCM" ] }, { "page": "rel.edge.tri", "title": "The index of the edge region in a triangle that contains the point", "topics": [ "rel.edge.tri" ] }, { "page": "rel.edge.triCM", "title": "The index of the CM-edge region in a triangle that contains the point", "topics": [ "rel.edge.triCM" ] }, { "page": "rel.edges.tri", "title": "The indices of the 'M'-edge regions in a triangle that contains the points in a give data set", "topics": [ "rel.edges.tri" ] }, { "page": "rel.edges.triCM", "title": "The indices of the CM-edge regions in a triangle that contains the points in a give data set", "topics": [ "rel.edges.triCM" ] }, { "page": "rel.vert.basic.tri", "title": "The index of the vertex region in a standard basic triangle form that contains a given point", "topics": [ "rel.vert.basic.tri" ] }, { "page": "rel.vert.basic.triCC", "title": "The index of the CC-vertex region in a standard basic triangle form that contains a point", "topics": [ "rel.vert.basic.triCC" ] }, { "page": "rel.vert.basic.triCM", "title": "The index of the CM-vertex region in a standard basic triangle form that contains a point", "topics": [ "rel.vert.basic.triCM" ] }, { "page": "rel.vert.end.int", "title": "The index of the vertex region in an end-interval that contains a given point", "topics": [ "rel.vert.end.int" ] }, { "page": "rel.vert.mid.int", "title": "The index of the vertex region in a middle interval that contains a given point", "topics": [ "rel.vert.mid.int" ] }, { "page": "rel.vert.std.tri", "title": "The index of the vertex region in the standard equilateral triangle that contains a given point", "topics": [ "rel.vert.std.tri" ] }, { "page": "rel.vert.std.triCM", "title": "The index of the CM-vertex region in the standard equilateral triangle that contains a given point", "topics": [ "rel.vert.std.triCM" ] }, { "page": "rel.vert.tetraCC", "title": "The index of the CC-vertex region in a tetrahedron that contains a point", "topics": [ "rel.vert.tetraCC" ] }, { "page": "rel.vert.tetraCM", "title": "The index of the CM-vertex region in a tetrahedron that contains a point", "topics": [ "rel.vert.tetraCM" ] }, { "page": "rel.vert.tri", "title": "The index of the vertex region in a triangle that contains a given point", "topics": [ "rel.vert.tri" ] }, { "page": "rel.vert.triCC", "title": "The index of the CC-vertex region in a triangle that contains a point", "topics": [ "rel.vert.triCC" ] }, { "page": "rel.vert.triCM", "title": "The index of the CM-vertex region in a triangle that contains a given point", "topics": [ "rel.vert.triCM" ] }, { "page": "rel.verts.tri", "title": "The indices of the vertex regions in a triangle that contains the points in a give data set", "topics": [ "rel.verts.tri" ] }, { "page": "rel.verts.tri.nondegPE", "title": "The indices of the vertex regions in a triangle that contains the points in a give data set", "topics": [ "rel.verts.tri.nondegPE" ] }, { "page": "rel.verts.triCC", "title": "The indices of the CC-vertex regions in a triangle that contains the points in a give data set.", "topics": [ "rel.verts.triCC" ] }, { "page": "rel.verts.triCM", "title": "The indices of the CM-vertex regions in a triangle that contains the points in a give data set", "topics": [ "rel.verts.triCM" ] }, { "page": "rel.verts.triM", "title": "The alternative function for the indices of the M-vertex regions in a triangle that contains the points in a give data set", "topics": [ "rel.verts.triM" ] }, { "page": "rseg.circular", "title": "Generation of points segregated (in a radial or circular fashion) from a given set of points", "topics": [ "rseg.circular" ] }, { "page": "rseg.multi.tri", "title": "Generation of points segregated (in a Type I fashion) from a given set of points", "topics": [ "rseg.multi.tri" ] }, { "page": "rseg.std.tri", "title": "Generation of points segregated (in a Type I fashion) from the vertices of T_e", "topics": [ "rseg.std.tri" ] }, { "page": "rseg.tri", "title": "Generation of points segregated (in a Type I fashion) from the vertices of a triangle", "topics": [ "rseg.tri" ] }, { "page": "rsegII.std.tri", "title": "Generation of points segregated (in a Type II fashion) from the vertices of T_e", "topics": [ "rsegII.std.tri" ] }, { "page": "runif.basic.tri", "title": "Generation of Uniform Points in the standard basic triangle", "topics": [ "runif.basic.tri" ] }, { "page": "runif.multi.tri", "title": "Generation of Uniform Points in the Convex Hull of Points", "topics": [ "runif.multi.tri" ] }, { "page": "runif.std.tetra", "title": "Generation of Uniform Points in the Standard Regular Tetrahedron T_h", "topics": [ "runif.std.tetra" ] }, { "page": "runif.std.tri", "title": "Generation of Uniform Points in the Standard Equilateral Triangle", "topics": [ "runif.std.tri" ] }, { "page": "runif.std.tri.onesixth", "title": "Generation of Uniform Points in the first one-sixth of standard equilateral triangle", "topics": [ "runif.std.tri.onesixth" ] }, { "page": "runif.tetra", "title": "Generation of Uniform Points in a tetrahedron", "topics": [ "runif.tetra" ] }, { "page": "runif.tri", "title": "Generation of Uniform Points in a Triangle", "topics": [ "runif.tri" ] }, { "page": "seg.tri.support", "title": "The auxiliary triangle to define the support of type I segregation", "topics": [ "seg.tri.support" ] }, { "page": "six.extremaTe", "title": "The closest points among a data set in the standard equilateral triangle to the median lines in the six half edge regions", "topics": [ "six.extremaTe" ] }, { "page": "slope", "title": "The slope of a line", "topics": [ "slope" ] }, { "page": "summary.Extrema", "title": "Return a summary of a 'Extrema' 'object'", "topics": [ "summary.Extrema" 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