pcds (version 0.1.4)

funsCSEdgeRegs: Each function is for the presence of an arc from a point in one of the edge regions to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

Description

Three indicator functions: IndCSTeRAB, IndCSTeRBC and IndCSTeRAC.

The function IndCSTeRAB returns I(pt2 is in \(N_{CS}(pt1,t)\) for pt1 in \(RAB\) (edge region for edge \(AB\), i.e., edge 3) in the standard equilateral triangle \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\);

IndCSTeRBC returns I(pt2 is in \(N_{CS}(pt1,t)\) for pt1 in \(RBC\) (edge region for edge \(BC\), i.e., edge 1) in \(T_e\); and

IndCSTeRAC returns I(pt2 is in \(N_{CS}(pt1,t)\) for pt1 in \(RAC\) (edge region for edge \(AC\), i.e., edge 2) in \(T_e\). That is, each function returns 1 if pt2 is in \(N_{CS}(pt1,t)\), returns 0 otherwise.

CS proximity region is defined with respect to \(T_e\) whose vertices are also labeled as \(T_e=T(v=1,v=2,v=3)\) with expansion parameter \(t>0\) and edge regions are based on the center \(M=(m_1,m_2)\) in Cartesian coordinates or \(M=(\alpha,\beta,\gamma)\) in barycentric coordinates in the interior of \(T_e\)

If pt1 and pt2 are distinct and pt1 is outside the corresponding edge region and pt2 is outside \(T_e\), it returns 0, but if they are identical, then it returns 1 regardless of their location (i.e., it allows loops).

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010;textualpcds).

Usage

IndCSTeRAB(pt1, pt2, t, M)
IndCSTeRBC(pt1, pt2, t, M)
IndCSTeRAC(pt1, pt2, t, M)

Value

Each function returns \(I(\)pt2 is in \(N_{CS}(pt1,t))\) for pt1, that is, returns 1 if pt2 is in \(N_{CS}(pt1,t)\), returns 0 otherwise

Arguments

pt1

A 2D point whose CS proximity region is constructed.

pt2

A 2D point. The function determines whether pt2 is inside the CS proximity region of pt1 or not.

t

A positive real number which serves as the expansion parameter in CS proximity region.

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the standard equilateral triangle \(T_e\).

Author

Elvan Ceyhan

See Also

IndCSTeRABt1, IndCSTeRBCt1 and IndCSTeRACt1

Examples

#Examples for IndCSTeRAB
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
CM<-(A+B+C)/3
T3<-rbind(A,B,CM);

set.seed(1)
dat3<-runif.tri(10,T3)$g
dat<-runifTe(10)$gen.points

M<-as.numeric(runifTe(1)$g)  #try also M<-c(.6,.2)

t<-1

IndCSTeRAB(dat3[1,],dat[2,],t,M)
IndCSTeRAB(dat3[1,],dat3[1,],t,M)
IndCSTeRAB(dat[1,],dat[1,],t,M)

IndCSTeRAB(dat3[1,],dat[2,],t=20,M)
IndCSTeRAB(dat3[1,],dat3[3,],t,M)
IndCSTeRAB(c(.2,.5),dat[2,],t,M)

IndCSTeRAB(dat[1,],dat[2,],t,M)

#Examples for IndCSTeRBC
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
CM<-(A+B+C)/3
T1<-rbind(B,C,CM);

set.seed(1)
dat1<-runif.tri(10,T1)$g
dat<-runifTe(10)$gen.points

M<-as.numeric(runifTe(1)$g)  #try also M<-c(.6,.2)

t<-1

IndCSTeRBC(dat1[1,],dat[2,],t,M)
IndCSTeRBC(dat1[1,],dat1[1,],t,M)

IndCSTeRBC(dat[2,],dat[2,],t,M)
IndCSTeRBC(dat1[1,],dat[2,],t=20,M)
IndCSTeRBC(dat1[1,],dat1[3,],t,M)
IndCSTeRBC(c(.2,.5),dat[2,],t,M)

IndCSTeRBC(c(.2,.5),c(.2,.5),t,M)

IndCSTeRBC(dat[1,],dat[2,],t,M)

#Examples for IndCSTeRAC
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
CM<-(A+B+C)/3
T2<-rbind(A,C,CM);

set.seed(1)
dat2<-runif.tri(10,T2)$g
dat<-runifTe(10)$gen.points

M<-as.numeric(runifTe(1)$g)  #try also M<-c(.6,.2)

t<-1

IndCSTeRAC(dat2[1,],dat[2,],t,M)
IndCSTeRAC(dat2[1,],dat2[1,],t,M)
IndCSTeRAC(dat[1,],dat[1,],t,M)

IndCSTeRAC(dat2[1,],dat2[3,],t,M)
IndCSTeRAC(dat2[1,],dat2[3,],t=20,M)
IndCSTeRAC(c(.2,.5),dat[2,],t,M)

IndCSTeRAC(c(.2,.5),c(.2,.5),t,M)

IndCSTeRAC(dat[1,],dat[2,],t,M)