Tick Talk on EsoxRepublic.com

Offset entities in a sketch is a very handy sketch tool. It comes in handy in so many ways: shelling parts, creating slots, scaling geometry, making sheet-like profiles. Not much more need be said.

Offsetting sketch entities creates a set of entities that are a constant distance from the original selected entities. For the simplest geometry, arcs and lines, the resulting entities are the same type: an offset of a line is a parallel line, an offset of an arc is a concentric arc. Splines, well, are still splines, no surprise there.

Offsets of conics are not conics

The surprise for some is the result of offsetting conics, eliipses and parbolae. The obvious assumption from experience is that the offset of an ellipse is an ellipse, and the offset of a parabola is a parabola. This assumption would be a mistake.

The offset of an ellipse is not an ellipse. The result looks like an ellipse, and is certainly oval-shaped, but is not a true ellipse.

Pictured below is the result of a quick experiment. Sketch A (green) is an ellipse. Sketch B (black) is an offset of the ellipse. Sketch C (red) is an ellipse with the same major and minor diameters as the offset. They do not match.

Offset of ellipse vs. ellipse of same major & minor diameter. Green = original 1 x 3 ellipse; black = 0.25 offset; red = ellipse w/ same major/minor diameters as offset. Click image for larger version.

Try the same experiment with a parabola and see what happens.

The Implications

I first started this article simply as a brief academic discussions of the results of offsets. While googling arond to see what else is out there, I found this subject does have some relevance beyond curiosity, especially for toolpaths in CNC programming.

For CNC programmers the important fact is that the toolpath to create a 2D ellipse is not a true ellipse. Creating a toolpath by scaling an ellipse or by creating a second ellipse with major/minor diameters increased by half a tool diameter will yield erroneous results. An offset must be used, and the offset is not an ellipse.