pcds (version 0.1.4)

as.bastri: The labels of the vertices of a triangle in the (unscaled) basic triangle form

Description

Labels the vertices of triangle, tri, as \(ABC\) so that \(AB\) is the longest edge, \(BC\) is the second longest and \(AC\) is the shortest edge (the order is as in the basic triangle). The new triangle \(T(A,B,C)\) is unscaled, i.e., the longest edge \(AB\) may not be of unit length.

The basic triangle is \(T_b=T((0,0),(1,0),(c_1,c_2))\) 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. Hence basic triangle is useful for simulation studies under the uniformity hypothesis.

Usage

as.bastri(tri)

Value

A list with two elements

tri

The vertices of the triangle stacked row-wise and labeled row-wise as \(A\), \(B\), \(C\).

desc

Description of the edges based on the vertices, i.e., "Edges (in decreasing length are) AB, BC, and AC".

orig.order

Row order of the input triangle, tri, when converted to the scaled version of the basic triangle

Arguments

tri

Three 2D points, stacked row-wise, each row representing a vertex of the triangle.

Author

Elvan Ceyhan

Examples

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

as.bastri(rbind(A,B,C))

as.bastri(rbind(B,C,A))

as.bastri(rbind(B,A,C))
as.bastri(rbind(A,C,B))

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
as.bastri(rbind(A,B,C))
as.bastri(rbind(A,C,B))
as.bastri(rbind(B,A,C))

A<-runif(2); B<-runif(2); C<-runif(2)
as.bastri(rbind(A,B,C))

dat.fr<-data.frame(a=rbind(A,B,C))
as.bastri(dat.fr)