We present an automatic algorithm for subtractive manufacturing of freeform 3D objects using high-speed machining (HSM) via CNC. A CNC machine operates a cylindrical cutter to carve off material from a 3D shape stock, following a toolpath, to “expose” the target object. Our method decomposes the input object’s surface into a small number of patches each of which is fully accessible and machinable by the CNC machine, in continuous fashion, under a fixed cutter-object setup configuration. This is achieved by covering the input surface with a minimum number of accessibleregions and then extracting a set of machinable patches from each accessible region. For each patch obtained, we compute a continuous, space-filling, and iso-scallop tool path which conforms to the patch boundary, enabling efficientcarving with high-quality surface finishing. The tool path is generated in the form of connected Fermat spirals, which have been generalized from a 2D fill pattern for layered manufacturing to work for curved surfaces. Furthermore, we develop a novel method to control the spacing of Fermat spirals based on directional surface curvature and adapt the heat method to obtain isoscallop carving. We demonstrate automatic generation of accessible and machinable surfacedecompositions and iso-scallop Fermat spiral carving paths for freeform 3D objects. Comparisons are made to tool paths generated by commercial software in terms of real machining time and surface quality.