In exemplary implementations of this invention, a computer-assisted, handheld machining tool allows even an inexperienced user to carve a complex 3D object, while maintaining artistic freedom to modify the sculpture from an initial CAD design. The tool prevents the user from unintentionally removing material from a volume defined by the CAD design. It does so by slowing or halting spindle rotation as the bit approaches or penetrates the protected volume. The user can override this protective feature. The tool may operate in at least three interaction modes: (i) a static mode in which a static CAD model is used, where the computer assists by preventing the user from damaging the static model; (ii) a dynamic mode where the computer dynamically modifies the CAD model during the sculpting process; and (iii) an autonomous mode where the computer can operate independently of the user, for tasks such as semi-automatic texture rendering.