pcds (version 0.1.8)

prj.cent2edges: Projections of a point inside a triangle to its edges

Description

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 (ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).

Usage

prj.cent2edges(tri, M)

Value

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 \(i=1,2,3\).

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.

Author

Elvan Ceyhan

References

See Also

prj.cent2edges.basic.tri and prj.nondegPEcent2edges

Examples

# \donttest{
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)
# }