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.
tri.find(tri.obj,x,y)
tri.obj |
an triangulation object |
x |
x-coordinate of the point |
y |
y-coordinate of the point |
A list with elements i1,i2,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.
A. Gebhardt
R. J. Renka (1996). Algorithm 751: TRIPACK: a constrained two-dimensional Delaunay triangulation package. ACM Transactions on Mathematical Software. 22, 1-8.
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)
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