Offset surface transformations for generating CNC toolpaths

A computer numerical control (CNC) tool control system, comprising:

• a CNC tool;
• a computer-controlled CNC tool movement assembly configured to manufacture a three-dimensional (3D) part by moving the CNC tool along a CNC toolpath;
• a logic subsystem;
• and
• a storage subsystem holding instructions executable by the logic subsystem to:
• read a digital model of the 3D part within a first topological space;
• generate an offset surface for the digital model in the first topological space;
• transform the offset surface in the first topological space to a transformed offset surface in a second topological space embedded in the first topological space;
• identify a plurality of contours at which a corresponding plurality of embedded parallel planes intersect the transformed offset surface in the second topological space;
• transform the plurality of contours in the second topological space into a corresponding plurality of transformed contours in the first topological space;
• and
• generate the CNC toolpath that traces each of the plurality of transformed contours in the first topological space, such that the CNC toolpath is useable by the CNC tool control system to manufacture the 3D part by controlling the computer-controlled CNC tool movement assembly to move the CNC tool along the CNC toolpath.

A method for computer numerical control (CNC) manufacturing, comprising:

• computer-reading a digital model of a three-dimensional (3D) part within a Euclidean space;
• computer-generating an offset surface for the digital model in the Euclidean space;
• computer-transforming the offset surface in the Euclidean space to a transformed offset surface in a manifold space embedded in the Euclidean space;
• computer-identifying a plurality of contours at which a corresponding plurality of embedded Z-level planes intersect the transformed offset surface in the manifold space;
• computer-transforming the plurality of contours in the manifold space into a corresponding plurality of transformed contours in the Euclidean space;
• computer-generating a CNC toolpath that traces each of the plurality of transformed contours in the Euclidean space;
• and
• computer-controlling a CNC tool to follow the CNC toolpath and manufacture the 3D part.