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##### Add a constraint to an triangulaion object

This subroutine provides for creation of a constrained Delaunay triangulation which, in some sense, covers an arbitrary connected region R rather than the convex hull of the nodes. This is achieved simply by forcing the presence of certain adjacencies (triangulation arcs) corresponding to constraint curves. The union of triangles coincides with the convex hull of the nodes, but triangles in R can be distinguished from those outside of R. The only modification required to generalize the definition of the Delaunay triangulation is replacement of property 5 (refer to tri.mesh by the following:

5') If a node is contained in the interior of the circumcircle of a triangle, then every interior point of the triangle is separated from the node by a constraint arc.

In order to be explicit, we make the following definitions. A constraint region is the open interior of a simple closed positively oriented polygonal curve defined by an ordered sequence of three or more distinct nodes (constraint nodes) P(1),P(2),...,P(K), such that P(I) is adjacent to P(I+1) for I = 1,...,K with P(K+1) = P(1). Thus, the constraint region is on the left (and may have nonfinite area) as the sequence of constraint nodes is traversed in the specified order. The constraint regions must not contain nodes and must not overlap. The region R is the convex hull of the nodes with constraint regions excluded.

Note that the terms boundary node and boundary arc are reserved for nodes and arcs on the boundary of the convex hull of the nodes.

The algorithm is as follows: given a triangulation which includes one or more sets of constraint nodes, the corresponding adjacencies (constraint arcs) are forced to be present (Fortran subroutine EDGE). Any additional new arcs required are chosen to be locally optimal (satisfy the modified circumcircle property).

##### Usage
add.constraint(tri.obj,cstx,csty,reverse=F)
##### Arguments
tri.obj
object of class "tri"
cstx
vector containing x coordinates of the constraint curve.
csty
vector containing y coordinates of the constraint curve.
reverse
if TRUE the orientation of the constraint curve is reversed.
##### Value

• An new object of class "tri".

#

##### 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.

##### Examples
# we will use the test data from library(akima):
library(akima)
data(akima)
akima.tr<-tri.mesh(akima$x,akima$y)
# include all points in a big triangle:
plot(akima.trc)