We propose a novel method to generate a small set of ruled surfaces that do not collide with the input shape for linear hot-wire rough machining. Central to our technique is a new observation: ruled surfaces constructed by vertical extrusion from planar smooth curves that approach the input shape's outer contour lines without collisions can effectively remove material during rough machining. Accordingly, we develop an iterative algorithm that alternates in each iteration between computing a viewpoint to determine an outer contour line and optimizing a smooth curve to approximate that contour line under the collision-free constraint. Specifically, a view selection approach based on a genetic algorithm is used to optimize the viewpoint for removing materials as much as possible, and an adaptive fitting algorithm is presented to find the constrained curves. The feasibility and practicability of our method are demonstrated through 10 physical examples. Compared with manual designs, our method obtains lower errors with the same number of cuts.
Zhang et al. (2026) studied this question.