Triangulation Operations

Locking and Unlocking the Convex Hull

For unconstrained triangulations, the only boundary is the convex hull of the point set, but the boundary_nodes field is empty because it is reserved for a constrained boundary. There may be cases where you want to treat the convex hull as if it were a constrained boundary. For example, this is done internally inside refine! when providing an unconstrained triangulation for mesh refinement. Let us give an example of how this can be done, in case you want to do this for your own application.

using DelaunayTriangulation
using CairoMakie

points = rand(2, 50)
tri = triangulate(points)
get_boundary_nodes(tri)

Int64[]

As you can see, the boundary nodes field is empty. We can lock the convex hull using lock_convex_hull!:

lock_convex_hull!(tri)
get_boundary_nodes(tri)

12-element Vector{Int64}:
 14
  6
  1
 20
 43
  7
 32
 41
 40
 33
 23
 14

Now the boundary nodes field is not empty. Note that if you try and lock the convex hull again, you will get an error because DelaunayTriangulation.has_boundary_nodes(tri) is now true. To now unlock the convex hull, we use unlock_convex_hull!:

unlock_convex_hull!(tri)
get_boundary_nodes(tri)

Int64[]

This function will error if it detects that the existing boundary isn't actually equal to the convex hull.

Note that this locking/unlocking doesn't actually change anything about the triangulation, it just adds information into tri to treat it as if you had provided the convex hull as a constrained boundary to start with.

Just the code

An uncommented version of this example is given below. You can view the source code for this file here.

using DelaunayTriangulation
using CairoMakie

points = rand(2, 50)
tri = triangulate(points)
get_boundary_nodes(tri)

lock_convex_hull!(tri)
get_boundary_nodes(tri)

unlock_convex_hull!(tri)
get_boundary_nodes(tri)

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