seg.tri.support {pcds}

The auxiliary triangle to define the support of type I segregation

Description

Returns the triangle whose intersection with a general triangle gives the support for type I segregation given the delta (i.e., \delta 100 % area of a triangle around the vertices is chopped off). See the plot in the examples.

Caveat: the vertices of this triangle may be outside the triangle, tri, depending on the value of delta (i.e., for small values of delta).

Usage

seg.tri.support(delta, tri)

Arguments

delta

A positive real number between 0 and 1 that determines the percentage of area of the triangle around the vertices forbidden for point generation.

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

Value

the vertices of the triangle (stacked row-wise) whose intersection with a general triangle gives the support for type I segregation for the given delta

Author(s)

Elvan Ceyhan

See Also

rseg.std.tri and rseg.multi.tri

Examples

#for a general triangle
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
delta<-.3  #try also .5,.75,.85
Tseg<-seg.tri.support(delta,Tr)

Xlim<-range(Tr[,1],Tseg[,1])
Ylim<-range(Tr[,2],Tseg[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

oldpar <- par(pty="s")
plot(Tr,pch=".",xlab="",ylab="",
main="segregation support is the intersection\n of these two triangles",
axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
polygon(Tseg,lty=2)

txt<-rbind(Tr,Tseg)
xc<-txt[,1]+c(-.03,.03,.03,.06,.04,-.04)
yc<-txt[,2]+c(.02,.02,.04,-.03,0,0)
txt.str<-c("A","B","C","T1","T2","T3")
text(xc,yc,txt.str)
par(oldpar)