Question/Request for Zero-area triangulations

[billdenney]

I have a scenario where I'd like to have zero-area triangulations when they apply. What I'm trying to do is to create a random number generator based on the n-dimensional equivalent of an empirical cumulative distribution function. For that, if I have repeated values, I want to be able to sample from that zero-area space as many times as is present in the original data.

For a one-dimensional example, if I have the data c(1, 2, 2, 3), I'd like to sample equally from the following regions:

• [1, 2]
• [2, 2]
• [2, 3]

With the current version, those are automatically filtered out of the output data.

In one dimension, it would be simple to simply find all equal points and then increase the sampling weights for them. For more than one dimension, I believe that degenerate spaces would be omitted (for example, in 3 dimensions, the non-degenerate triangulation defines a plane; but, I would like to be able to sample along the line that is a degenerate triangulation).

My questions (and implicit requests):

• Is my understanding of when zero-area triangulations are formed correct?
• If so, is there a way to get the information out for degenerate triangles now without modification of the package?
• If there is no way to get the information for degenerate triangles, could an option be added to allow them?