inTriAll: Check whether all points in a data set are inside the triangle

Description

Checks if all the data points in the 2D data set, Dt, lie in the triangle, tri, using the barycentric coordinates, generally denoted as \((\alpha,\beta,\gamma)\).

If all (normalized or non-normalized) barycentric coordinates of a point are positive then the point is inside the triangle, if all are nonnegative with one or more are zero, then the point falls in the boundary. If some of the barycentric coordinates are negative, then the point falls outside the triangle.

boundary is a logical argument (default=FALSE) to include boundary or not, so if it is TRUE, the function checks if a point lies in the closure of the triangle (i.e., interior and boundary combined) else it checks if the point lies in the interior of the triangle.

Usage

inTriAll(Dt, tri, boundary = FALSE)

Value

A logical output, if all data points in Dt are inside the triangle, tri, the output is TRUE, else it is FALSE.

Arguments

Dt: A set of 2D points representing the set of data points.
tri: Three 2D points, stacked row-wise, each row representing a vertex of the triangle.
boundary: A logical parameter (default=FALSE) to include boundary or not, so if it is TRUE, the function checks if a point lies in the closure of the triangle (i.e., interior and boundary combined) else it checks if the point lies in the interior of the triangle.

Author

Elvan Ceyhan

Examples

Run this code

A<-c(1,1); B<-c(2,0); C<-c(1.5,2); p<-c(1.4,1.2)

Tr<-rbind(A,B,C)

inTriAll(p,Tr)

#for the vertex A
inTriAll(A,Tr)
inTriAll(A,Tr,boundary=TRUE)

#for a point on the edge AB
D3<-(A+B)/2
inTriAll(D3,Tr)
inTriAll(D3,Tr,boundary=TRUE)

#data set
n<-10
dat<-cbind(runif(n),runif(n))
inTriAll(dat,Tr,boundary=TRUE)

dat<-runifTe(n)$gen.points
inTriAll(dat,Tr)
inTriAll(dat,Tr,boundary=TRUE)

dat<-runif.tri(n,Tr)$g
inTriAll(dat,Tr)
inTriAll(dat,Tr,boundary=TRUE)

dat.fr<-data.frame(a=dat)
inTriAll(dat.fr,Tr)

dat.fr<-data.frame(a=Tr)
inTriAll(dat,dat.fr)