# The plot of the Proportional Edge (PE) Proximity Regions for a 3D data set - standard regular tetrahedron case Plots the points in and outside of the standard regular tetrahedron $T_h=T((0,0,0),(1,0,0),(1/2,\sqrt{3}/2,0),(1/2,\sqrt{3}/6,\sqrt{6}/3))$ and also the PE proximity regions for points in data set `Xp`. PE proximity regions are defined with respect to the standard regular tetrahedron $T_h$ with expansion parameter $r \ge 1$, so PE proximity regions are defined only for points inside $T_h$. Vertex regions are based on circumcenter (which is equivalent to the center of mass for the standard regular tetrahedron) of $T_h$. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:comp-geo-2010;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r plotPEregs.std.tetra( Xp, r, main = NULL, xlab = NULL, ylab = NULL, zlab = NULL, xlim = NULL, ylim = NULL, zlim = NULL, ... ) ``` ## Arguments - `Xp`: A set of 3D points for which PE proximity regions are constructed. - `r`: A positive real number which serves as the expansion parameter in PE proximity region; must be $\ge 1$. - `main`: An overall title for the plot (default=`NULL`). - `xlab, ylab, zlab`: titles for the $x$, $y$, and $z$ axes, respectively (default=`NULL` for all). - `xlim, ylim, zlim`: Two `numeric` vectors of length 2, giving the $x$-, $y$-, and $z$-coordinate ranges (default=`NULL` for all). - ``...``: Additional `scatter3D` parameters. ## Returns Plot of the PE proximity regions for points inside the standard regular tetrahedron $T_h$ (and just the points outside $T_h$) ## Examples ```r A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0); D<-c(1/2,sqrt(3)/6,sqrt(6)/3) tetra<-rbind(A,B,C,D) r<-1.5 n<-3 #try also n<-20 Xp<-runif.std.tetra(n)$g #try also Xp[,1]<-Xp[,1]+1 plotPEregs.std.tetra(Xp[1:3,],r) P1<-c(.1,.1,.1) plotPEregs.std.tetra(rbind(P1,P1),r) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `plotPEregs`, `plotASregs.tri`, `plotASregs`, `plotCSregs.tri`, and `plotCSregs` ## Author(s) Elvan Ceyhan

plotPEregs.std.tetra function