circumcenter.tri {pcds}

Circumcenter of a general triangle

Description

Returns the circumcenter a given triangle, tri, with vertices stacked row-wise. See (Weisstein (2019); Ceyhan (2010)) for triangle centers.

Usage

circumcenter.tri(tri)

Arguments

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

Value

circumcenter of the triangle tri

Author(s)

Elvan Ceyhan

References

Ceyhan E (2010). “Extension of One-Dimensional Proximity Regions to Higher Dimensions.” Computational Geometry: Theory and Applications, 43(9), 721-748.

Weisstein EW (2019). “Triangle Centers.” From MathWorld — A Wolfram Web Resource, http://mathworld.wolfram.com/TriangleCenter.html.

See Also

circumcenter.basic.tri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);  #the vertices of the triangle Tr

CC<-circumcenter.tri(Tr)  #the circumcenter
CC

D1<-(B+C)/2; D2<-(A+C)/2; D3<-(A+B)/2; #midpoints of the edges
Ds<-rbind(D1,D2,D3)

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

plot(A,asp=1,pch=".",xlab="",ylab="",main="Circumcenter of a triangle",
axes=TRUE,xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05))
polygon(Tr)
points(rbind(CC))
L<-matrix(rep(CC,3),ncol=2,byrow=TRUE); R<-Ds
segments(L[,1], L[,2], R[,1], R[,2], lty = 2)

txt<-rbind(Tr,CC,Ds)
xc<-txt[,1]+c(-.08,.08,.08,.12,-.09,-.1,-.09)
yc<-txt[,2]+c(.02,-.02,.03,-.06,.02,.06,-.04)
txt.str<-c("A","B","C","CC","D1","D2","D3")
text(xc,yc,txt.str)

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);  #the vertices of the equilateral triangle Te
circumcenter.tri(Te)  #the circumcenter

A<-c(0,0); B<-c(0,1); C<-c(2,0);
Tr<-rbind(A,B,C);  #the vertices of the triangle T
circumcenter.tri(Tr)  #the circumcenter