# Generation of points segregated (in a Type I fashion) from the vertices of a triangle An object of class `"Patterns"`. Generates `n` points uniformly in the support for Type I segregation in a given triangle, `tri`. `delta` is the parameter of segregation (that is, $\delta 100$ % of the area around each vertex in the triangle is forbidden for point generation). `delta` corresponds to `eps` in the standard equilateral triangle $T_e$ as $delta=4 eps^2/3$ (see `rseg.std.tri` function). See (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:arc-density-PE,ceyhan:arc-density-CS,ceyhan:dom-num-NPE-Spat2011;textual",package="pcds",cached_env=.Rdpack.currefs) ) for more on the segregation pattern. ```r rseg.tri(n, tri, delta) ``` ## Arguments - `n`: A positive integer representing the number of points to be generated from the segregation pattern in the triangle, `tri`. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `delta`: A positive real number in $(0,1)$. `delta` is the parameter of segregation (that is, $\delta 100$ % area around vertices of each Delaunay triangle is forbidden for point generation). ## Returns A `list` with the elements - **type**: The type of the pattern from which points are to be generated - **mtitle**: The `"main"` title for the plot of the point pattern - **parameters**: Exclusion parameter, `delta`, of the Type I segregation pattern. `delta` is in $(0,1)$ and $\delta 100$ % area around vertices of the triangle `tri` is forbidden for point generation. - **ref.points**: The input set of points, i.e., vertices of `tri`; reference points, i.e., points from which generated points are segregated. - **gen.points**: The output set of generated points segregated from the vertices of `tri`. - **tri.Y**: Logical output, if `TRUE` the triangle `tri` is also plotted when the corresponding plot function from the `Patterns` object is called. - **desc.pat**: Description of the point pattern - **num.points**: The `vector` of two numbers, which are the number of generated points and the number of reference (i.e., vertex of `tri`, which is 3 here). - **xlimit,ylimit**: The ranges of the $x$- and $y$-coordinates of the reference points, which are the vertices of the triangle `tri` ## Examples ```r n<-100 A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C) del<-.4 Xdt<-rseg.tri(n,Tr,del) Xdt summary(Xdt) plot(Xdt) Xp<-Xdt$g Xlim<-range(Tr[,1]) Ylim<-range(Tr[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(Tr,pch=".",xlab="",ylab="", main="Points from Type I Segregation \n in one Triangle", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) points(Xp) xc<-Tr[,1]+c(-.02,.02,.02) yc<-Tr[,2]+c(.02,.02,.03) txt.str<-c("A","B","C") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rassoc.tri`, `rseg.std.tri`, `rsegII.std.tri`, and `rseg.multi.tri` ## Author(s) Elvan Ceyhan

rseg.tri function