# tri.find

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##### Locate a point in a triangulation

This subroutine locates a point P=(x,y) relative to a triangulation created by tri.mesh. If P is contained in a triangle, the three vertex indexes are returned. Otherwise, the indexes of the rightmost and leftmost visible boundary nodes are returned.

##### Usage
tri.find(tri.obj,x,y)
##### Arguments
tri.obj
an triangulation object
x
x-coordinate of the point
y
y-coordinate of the point
##### Value

• A list with elements i1,i2,code{i3} containing nodal indexes, in counterclockwise order, of the vertices of a triangle containing P=(x,y), or, if P is not contained in the convex hull of the nodes, i1 indexes the rightmost visible boundary node, i2 indexes the leftmost visible boundary node, and i3 = 0. Rightmost and leftmost are defined from the perspective of P, and a pair of points are visible from each other if and only if the line segment joining them intersects no triangulation arc. If P and all of the nodes lie on a common line, then i1=i2=i3 = 0 on output.

##### References

R. J. Renka (1996). Algorithm 751: TRIPACK: a constrained two-dimensional {Delaunay} triangulation package. ACM Transactions on Mathematical Software. 22, 1-8.

tri, print.tri, plot.tri, summary.tri, triangles, convex.hull

• tri.find
##### Examples
data(tritest)
tritest.tr<-tri.mesh(tritest$x,tritest$y)
plot(tritest.tr)
pnt<-list(x=0.3,y=0.4)
triangle.with.pnt<-tri.find(tritest.tr,pnt$x,pnt$y)
attach(triangle.with.pnt)
lines(tritest$x[c(i1,i2,i3,i1)],tritest$y[c(i1,i2,i3,i1)],col="red")
points(pnt$x,pnt$y)
Documentation reproduced from package tripack, version 1.0-1, License: R functions: GPL, Fortran code: available at netlib

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