# Projections of a point inside a triangle to its edges Returns the projections from a general center $M=(m_1,m_2)$ in Cartesian coordinates or $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of a triangle to the edges on the extension of the lines joining `M` to the vertices (see the examples for an illustration). See also (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) ). ```r prj.cent2edges(tri, M) ``` ## Arguments - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `M`: A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle `tri`. ## Returns Three projection points (stacked row-wise) from a general center $M=(m_1,m_2)$ in Cartesian coordinates or $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of a triangle to the edges on the extension of the lines joining `M` to the vertices; row $i$ is the projection point into edge $i$, for $i=1,2,3$. ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.0) Ds<-prj.cent2edges(Tr,M) #try also prj.cent2edges(Tr,M=c(1,1)) Ds Xlim<-range(Tr[,1]) Ylim<-range(Tr[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] if (dimension(M)==3) {M<-bary2cart(M,Tr)} #need to run this when M is given in barycentric coordinates plot(Tr,pch=".",xlab="",ylab="", main="Projection of Center M on the edges of a triangle",axes=TRUE, xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) polygon(Tr) L<-rbind(M,M,M); R<-Ds segments(L[,1], L[,2], R[,1], R[,2], lty = 2) xc<-Tr[,1] yc<-Tr[,2] txt.str<-c("rv=1","rv=2","rv=3") text(xc,yc,txt.str) txt<-rbind(M,Ds) xc<-txt[,1]+c(-.02,.04,-.04,-.02) yc<-txt[,2]+c(-.02,.04,.04,-.06) txt.str<-c("M","D1","D2","D3") text(xc,yc,txt.str) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `prj.cent2edges.basic.tri` and `prj.nondegPEcent2edges` ## Author(s) Elvan Ceyhan

prj.cent2edges function