# Incidence matrix for Arc Slice Proximity Catch Digraphs (AS-PCDs) - multiple triangle case Returns the incidence matrix for the AS-PCD whose vertices are a given 2D numerical data set, `Xp`, in the convex hull of `Yp` which is partitioned by the Delaunay triangles based on `Yp` points. AS proximity regions are defined with respect to the Delaunay triangles based on `Yp` points and vertex regions are based on the center `M="CC"` for circumcenter of each Delaunay triangle or $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of each Delaunay triangle; default is `M="CC"` i.e., circumcenter of each triangle. Each Delaunay triangle is first converted to an (nonscaled) basic triangle so that `M` will be the same type of center for each Delaunay triangle (this conversion is not necessary when `M` is $CM$). Convex hull of `Yp` is partitioned by the Delaunay triangles based on `Yp` points (i.e., multiple triangles are the set of these Delaunay triangles whose union constitutes the convex hull of `Yp` points). For the incidence matrix loops are allowed, so the diagonal entries are all equal to 1. See (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textual",package="pcds",cached_env=.Rdpack.currefs) ) for more on AS-PCDs. Also see (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="okabe:2000,ceyhan:comp-geo-2010,sinclair:2016;textual",package="pcds",cached_env=.Rdpack.currefs) ) for more on Delaunay triangulation and the corresponding algorithm. ```r inci.matAS(Xp, Yp, M = "CC") ``` ## Arguments - `Xp`: A set of 2D points which constitute the vertices of the AS-PCD. - `Yp`: A set of 2D points which constitute the vertices of the Delaunay triangles. - `M`: The center of the triangle. `"CC"` stands for circumcenter of each Delaunay triangle or 3D point in barycentric coordinates which serves as a center in the interior of each Delaunay triangle; default is `M="CC"` i.e., the circumcenter of each triangle. ## Returns Incidence matrix for the AS-PCD whose vertices are the 2D data set, `Xp`, and AS proximity regions are defined in the Delaunay triangles based on `Yp` points. ## Examples ```r #nx is number of X points (target) and ny is number of Y points (nontarget) nx<-15; ny<-5; #try also nx<-40; ny<-10 or nx<-1000; ny<-10; set.seed(1) Xp<-cbind(runif(nx,0,1),runif(nx,0,1)) Yp<-cbind(runif(ny,0,.25),runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1)) #try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1)) M<-"CC" #try also M<-c(1,1,1) IM<-inci.matAS(Xp,Yp,M) IM dom.num.greedy(IM) #try also dom.num.exact(IM) #this might take a long time for large nx IM<-inci.matAS(Xp,Yp[1:3,],M) inci.matAS(Xp,rbind(Yp,Yp)) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `inci.matAStri`, `inci.matPE`, and `inci.matCS` ## Author(s) Elvan Ceyhan

inci.matAS function