We present a geometric problem that arises in browsing and solve it in constant time per query without using exhaustive tables. This result has practical application in "query previewers" which have been developed and user-tested at the Human--Computer Interface Lab at U. Maryland. Unfortunately, we prove that several closely related problems require exhaustive tables, no matter how much time we allow per query. Joint work with Ben Shneiderman, Egemen Tanin, and Catherine Plaisant