tri2std.basic.tri {pcds} | R Documentation |
Converting a triangle to the standard basic triangle form form
Description
This function transforms any triangle, tri
,
to the standard basic triangle form.
The standard basic triangle form 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 standard basic triangle form 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, standard basic triangle form is useful for simulation studies under the uniformity hypothesis.
Usage
tri2std.basic.tri(tri)
Arguments
tri |
A |
Value
A list
with two elements
Cvec |
The nontrivial vertex |
orig.order |
Row order of the input triangle, |
Author(s)
Elvan Ceyhan
Examples
c1<-.4; c2<-.6
A<-c(0,0); B<-c(1,0); C<-c(c1,c2);
tri2std.basic.tri(rbind(A,B,C))
tri2std.basic.tri(rbind(B,C,A))
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
tri2std.basic.tri(rbind(A,B,C))
tri2std.basic.tri(rbind(A,C,B))
tri2std.basic.tri(rbind(B,A,C))