runif.std.tri.onesixth {pcds}

Generation of Uniform Points in the first one-sixth of standard equilateral triangle

Description

An object of class "Uniform". Generates n points uniformly in the first 1/6th of the standard equilateral triangle T_e=(A,B,C) with vertices with A=(0,0); B=(1,0), C=(1/2,\sqrt{3}/2) (see the examples below). The first 1/6th of the standard equilateral triangle is the triangle with vertices A=(0,0), (1/2,0), C=(1/2,\sqrt{3}/6).

Usage

runif.std.tri.onesixth(n)

Arguments

n

a positive integer representing number of uniform points to be generated in the first one-sixth of T_e.

Value

A list with the elements

type

The type of the point pattern

mtitle

The "main" title for the plot of the point pattern

support

The vertices of the support of the uniformly generated points

gen.points

The output set of uniformly generated points in the first 1/6th of the standard equilateral triangle.

out.region

The outer region for the one-sixth of T_e, which is just T_e here.

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 vertices of the support (i.e., Y) points.

txt4pnts

Description of the two numbers in num.points.

xlimit, ylimit

The ranges of the x- and y-coordinates of the generated, support and outer region points

Author(s)

Elvan Ceyhan

See Also

runif.std.tri, runif.basic.tri, runif.tri, and runif.multi.tri

Examples

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
CM<-(A+B+C)/3;
D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2;
Ds<-rbind(D1,D2,D3)
nx<-100  #try also nx<-1000

#data generation step
set.seed(1)
Xdt<-runif.std.tri.onesixth(nx)
Xdt
summary(Xdt)
plot(Xdt,asp=1)

Xd<-Xdt$gen.points

#plot of the data with the regions in the equilateral triangle
Xlim<-range(Te[,1])
Ylim<-range(Te[,2])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]

plot(Te,asp=1,pch=".",xlim=Xlim+xd*c(-.01,.01),
ylim=Ylim+yd*c(-.01,.01),xlab=" ",ylab=" ",
     main="first 1/6th of the \n standard equilateral triangle")
polygon(Te)
L<-Te; R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty=2)
polygon(rbind(A,D3,CM),col=5)
points(Xd)

#letter annotation of the plot
txt<-rbind(A,B,C,CM,D1,D2,D3)
xc<-txt[,1]+c(-.02,.02,.02,.04,.05,-.03,0)
yc<-txt[,2]+c(.02,.02,.02,.03,0,.03,-.03)
txt.str<-c("A","B","C","CM","D1","D2","D3")
text(xc,yc,txt.str)