runif.std.tri: Generation of Uniform Points in the Standard Equilateral Triangle

Description

An object of class "Uniform". Generates n points uniformly in the standard equilateral triangle \(T_e=T(A,B,C)\) with vertices \(A=(0,0)\), \(B=(1,0)\), and \(C=(1/2,\sqrt{3}/2)\).

Usage

runif.std.tri(n)

Value

A list with the elements

type: The type of the pattern from which points are to be generated
mtitle: The "main" title for the plot of the point pattern
tess.points: The vertices of the support region of the uniformly generated points, it is the standard equilateral triangle \(T_e\) for this function
gen.points: The output set of generated points uniformly in the standard equilateral triangle \(T_e\).
out.region: The outer region which contains the support region, NULL for this function.
desc.pat: Description of the point pattern from which points are to be generated
num.points: The vector of two numbers, which are the number of generated points and the number of vertices of the support points (here it is 3).
txt4pnts: Description of the two numbers in num.points
xlimit,ylimit: The ranges of the \(x\)- and \(y\)-coordinates of the support, \(T_e\)

Arguments

n: A positive integer representing the number of uniform points to be generated in the standard equilateral triangle \(T_e\).

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);
n<-100

set.seed(1)
Xdt<-runif.std.tri(n)
Xdt
summary(Xdt)
plot(Xdt,asp=1)

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

Xp<-runif.std.tri(n)$gen.points
plot(Te,asp=1,pch=".",xlab="",ylab="",xlim=Xlim+xd*c(-.01,.01),
ylim=Ylim+yd*c(-.01,.01))
polygon(Te)
points(Xp)
# }