A simple explanation of the asymptotic decider

The asymptotic decider is one of the standard ways of removing ambiguities in Marching Cubes. It’s a neat trick that uses the fact that bilinear interpolation across a face always creates hyperbolas, and so we can pick the value of the interpolation on the asymptote to help decide which of the two possible cases we have. The times I taught SciVis or have seen people teach it, students have always had a hard time understanding it.

It just occurred to me a simple way to explain it that I haven’t heard before. What the asymptotic decider is really doing is performing a single data-driven subdivision of the domain into smaller rectangles, such that the cases inside each subrectangle are unambiguous. The right place to subdivide the domain so that all the cases are necessarily unambiguous for a bilinear interpolant is exactly the asymptote.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s