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We describe new methods for the construction of spiral toolpaths forhigh-speed machining. In the simplest case, our method takes a polygon as inputand a number $\delta>0$ and returns a spiral starting at a central point in thepolygon, going around towards the boundary while morphing to the shape of thepolygon. The spiral consists of linear segments and circular arcs, it is $G^1$continuous, it has no self-intersections, and the distance from each point onthe spiral to each of the neighboring revolutions is at most $\delta$. Ourmethod has the advantage over previously described methods that it is easilyadjustable to the case where there is an island in the polygon to be avoided bythe spiral. In that case, the spiral starts at the island and morphs the islandto the outer boundary of the polygon. It is shown how to apply that method tomake significantly shorter spirals in polygons with no islands. Finally, weshow how to make a spiral in a polygon with multiple islands by connecting theislands into one island.

Spiral Toolpaths for High-Speed Machining of 2D Pockets with or without Islands