# Check whether all points in a data set are inside the triangle Checks if all the data points in the 2D data set, `Xp`, 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=`TRUE`) 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. ```r in.tri.all(Xp, tri, boundary = TRUE) ``` ## Arguments - `Xp`: A set of 2D points representing the set of data points. - `tri`: A $3 \times 2$ matrix with 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. ## Returns A logical output, if all data points in `Xp` are inside the triangle, `tri`, the output is `TRUE`, else it is `FALSE`. ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); p<-c(1.4,1.2) Tr<-rbind(A,B,C) in.tri.all(p,Tr) #for the vertex A in.tri.all(A,Tr) in.tri.all(A,Tr,boundary = FALSE) #for a point on the edge AB D3<-(A+B)/2 in.tri.all(D3,Tr) in.tri.all(D3,Tr,boundary = FALSE) #data set n<-10 Xp<-cbind(runif(n),runif(n)) in.tri.all(Xp,Tr,boundary = TRUE) Xp<-runif.std.tri(n)$gen.points in.tri.all(Xp,Tr) in.tri.all(Xp,Tr,boundary = FALSE) Xp<-runif.tri(n,Tr)$g in.tri.all(Xp,Tr) in.tri.all(Xp,Tr,boundary = FALSE) ``` ## See Also `in.triangle` and `on.convex.hull` from the `interp` package for documentation for `in.convex.hull` ## Author(s) Elvan Ceyhan

in.tri.all function