runif.basic.tri: Generation of Uniform Points in the standard basic triangle

In pcds: Proximity Catch Digraphs and Their Applications

Generation of Uniform Points in the standard basic triangle

Description

An object of class "Uniform". Generates n points uniformly in the standard basic triangle T_b=T((0,0),(1,0),(c_1,c_2)) where c_1 is in [0,1/2], c_2>0 and (1-c_1)^2+c_2^2 \le 1.

Any given triangle can be mapped to the basic triangle by a combination of rigid body motions (i.e., translation, rotation and reflection) and scaling, preserving uniformity of the points in the original triangle (\insertCiteceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:arc-density-PE;textualpcds). Hence, standard basic triangle is useful for simulation studies under the uniformity hypothesis.

Usage

runif.basic.tri(n, c1, c2)

Arguments

n	A positive integer representing the number of uniform points to be generated in the standard basic triangle.
c1, c2	Positive real numbers representing the top vertex in standard basic triangle T_b=T((0,0),(1,0),(c_1,c_2)), c_1 must be in [0,1/2], c_2>0 and (1-c_1)^2+c_2^2 \le 1.

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 of the uniformly generated points, it is the standard basic triangle T_b for this function
gen.points	The output set of generated points uniformly in the standard basic triangle
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, Tb

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

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

Examples

c1<-.4; c2<-.6
A<-c(0,0); B<-c(1,0); C<-c(c1,c2);
Tb<-rbind(A,B,C);
n<-100

set.seed(1)
runif.basic.tri(1,c1,c2)
Xdt<-runif.basic.tri(n,c1,c2)
Xdt
summary(Xdt)
plot(Xdt)

Xp<-runif.basic.tri(n,c1,c2)$g

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

plot(Tb,xlab="",ylab="",xlim=Xlim+xd*c(-.01,.01),
ylim=Ylim+yd*c(-.01,.01),type="n")
polygon(Tb)
points(Xp)

pcds documentation built on May 29, 2024, 9:36 a.m.