A new milling strategy of an elliptic cylinder
11/07/2026
How it works:
At every iteration:
- look at all current vertices of the outer polygon,
- select one with the largest distance to the ellipse,
- from that vertex, compute its orthogonal projection P onto the ellipse,
- at point P, compute the tangent line to the ellipse,
- make a cut along the direction defined by that tangent.
Repeat until all vertexes are closer to the ellipse than a given threshold.
By the way, the computation of the distance from a point to the ellipse, that yields also its orthogonal projection on the ellipse is not straightforward. It was made by the same dichotomous algorithm described here.
However, theoretical approach must cope with real life constraints, as shown in the figure below:
The first cut in the example above would fail as the tool's length is too short to make it; the shaft holder (i.e. the white rectangle) would hit the stock.
Work in progress…