Geometries which can be easily modeled and cut, and those which can't

A while back, I tried to enumerate the 2D shapes with an eye towards what shapes one might encounter while automating cutting things out:

https://wiki.shapeoko.com/index.php/Design_into_3D#Geometric_shapes

Exending this into 3 dimensions arguably would be useful as well, though it does create further difficulties in terms of nomenclature.

Looking at typically available CAM tools we find that there are certain things which are usually readily cut in a CAM tool:

  • circles and rounded forms w/ flat bottoms:

  • rectangular forms w/ rounded points w/ flat bottoms:

  • arbitrary shapes which do not have any acute points which cannot be cut by a round endmill — obtuse points can be — consider a star shape, the points of the star cannot be cut w/ a round endmill, but the internal angles can be, since the endmill moves around the angle.

  • forms defined by the surface geometry and the angle of the V endmill used for V carving:

The pockets above may easily have rounded bottoms added by insetting the geometry as needed to allow for cutting the bottom of the perimeter w/ a ball-nosed endmill as seen in:

Cutting past the stock along two edges will allow flat bottom geometry w/ square edges as is needed for fingerjoints as is seen in:

(requiring a fixture for holding stock vertically)

Advanced V carving allows for flat bottomed pockets w/ angled edges which match those of the selected V endmill w/ a bit of additional rounding.

Other geometries either require special tooling and forgoing a 3D preview or 3D modeling them, e.g.,

and

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