Abstract: A method, apparatus, and computer program product provide the ability to construct a spiral toolpath for machining solid material. A polygon with a polygonal hole in an interior is obtained. A Voronoi diagram of a set of line segments is obtained and modified to provide a modified Voronoi diagram (VD) having a cycle with one or more trees growing out. For each of the trees, a wave model is defined for a wave that starts at time t=0 on leaves on a boundary of the hole and moves through the tree to hit leaves on a boundary of the polygon at time t=1. A polyline spiral curve toolpath is created by travelling around the wave as it moves towards the boundary of the polygon. A pocket is milled in a solid piece of material by following the polyline spiral curve toolpath.

Abstract: A method, apparatus, and computer program product provide the ability to construct a spiral toolpath for machining solid material. A polygon with a polygonal hole in an interior is obtained. A Voronoi diagram of a set of line segments is obtained and modified to provide a modified Voronoi diagram (VD) having a cycle with one or more trees growing out. For each of the trees, a wave model is defined for a wave that starts at time t=0 on leaves on a boundary of the hole and moves through the tree to hit leaves on a boundary of the polygon at time t=1. A polyline spiral curve toolpath is created by travelling around the wave as it moves towards the boundary of the polygon. A pocket is milled in a solid piece of material by following the polyline spiral curve toolpath.