Metapost/fontbase numeric problems with botip
The tip() macro of the font-base macros we inherited, as accessed through our set_botip() interface, has trouble making sharp corners in the case where control points are close together. We would want to set "tip" to a large number in order to extend the edges significantly further than the distance between successive control points, but setting it any larger than 1 is likely to trigger a numeric overflow in Metapost's fixed-point arithmetic. Ideally, when set to 1 it should be effectively infinite (extend the edges as far as necessary to make them intersect). We very rarely use any values other than 1 and 0. But at the very least, we should be able to extend edges further than the amount that the current 1.0 means.
Maybe the current font-base macros can be changed to allow longer, and even unlimited, extension without overflow. Maybe now is the time to switch to using one of the fancier numeric formats permitted by current versions of Metapost.