runif.std.tri.onesixth: 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)

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

Arguments

n: a positive integer representing number of uniform points to be generated in the first one-sixth of \(T_e\).

Author

Elvan Ceyhan

Examples

Run this code

# \donttest{
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)
# }