问题
I'm using a triangulation library to compute the Constrained Delaunay Triangulation of a set of rectangles within some large boundary. The algorithm returns all the edges, but also adds edges inside of the rectangles that define the constraints.
I want to be able to create a graph without the edges within any of the rectangles that are the constraints (with the exception of the large boundary of course) but removing these edges in the triangulation that is given to me takes longer than O(nlog(n)) time at least and that's not good for what I need.
What I'm asking is, is there any quick way to get a CDT to keep edges from appearing within some polygon? I want the rectangles to be empty of edges but I'm not sure how to quickly do that.
In case this helps, the library I'm using is TriPath by Marcello Kallmann, and it is written in c++ (http://graphics.ucmerced.edu/software/tripath/). My application is in Java and I'm using JNI.
EDIT: As requested, here's some images to help you visualize what I'm trying to describe. This CDT is built with the black lines being constraints. As you can see, each constrained edge is part of a rectangle. The blue lines are unconstrained Delaunay edges. I am trying to remove any blue unconstrained Delaunay edges from within the black constrained rectangles.
回答1:
In case constrained rectangles cannot overlap or contain each other, I suggest putting a slightly smaller rectangle inside every original rectangle. The gap between inner and original rectangle should be small enough that no unconstrained edge could possibly fit inside an original rectangle without intersecting a smaller rectangle. Then, after triangulation is done, delete every edge that is adjacent to any of the vertices of those smaller rectangles. That way you'll be able to find out whether an edge should be deleted in O(1) time, and so the whole procedure will take O(E).
One way to choose a small enough gap is to evaluate the triangulation without smaller rectangles, find the edge of minimum length, and take, say, 1/3 of that length as a gap.
来源：https://stackoverflow.com/questions/21706947/rectangular-constraints-in-delaunay-triangulation-without-edges-within