For spherical cutters (a.k.a. ball-nose), the vertex-test (green dots), and the facet-test (blue dots), are fairly trivial. The edge-test (red-dots) is slightly more involved. Here, unlike before, I tried doing it without too many calls to "expensive" functions like sin(), cos() and sqrt(). The final result of taking the maximum of all tests is shown in the "all" image which shows cutter-locations colour-coded based on the type of cutter-contact.
The logical next step is the toroidal, or bull-nose cutter. Again the edge-test is the most difficult, and I never really understood where the geometry of the offset-ellipse shows up... anyone care to explain?