You don't seem to have grokked the main feature that makes Slug interesting. The algorithm handles every single possible case uniformly through the use of a very fast classification and root eligibility determination technique. On some GPUs (including all NV from the last 10+ years), handling the full set of cases shown on the poster reduces to a single instruction (LOP3). The algorithm also eliminates all numerical precision issues -- provably -- making it the most robust of all time. There are no valid inputs for which the algorithm fails, so to say Loop-Blinn is somehow more robust is incorrect.