Subdivision surface-based finish machining

Subdivision surfaces combine smooth spline surfaces and polygonal meshes together, therefore, a smooth design model and discrete machining models may be unified and subdivision surfaces may be used as a common representation for geometric design and machining. Motivated by the idea, this paper presents the study of finish machining of objects represented by subdivision surfaces with emphasis on geometric error control involved in tool-path generation. First, given a design model, chordal error is controlled during finishing model building. A chordal error-driven adaptive subdivision method is used to build finishing models with less data. Second, a surface decomposition machining strategy is used to control the cusp height error. A simple iso-slope curve tracing and surface decomposition algorithm is presented to partition the model into flat and steep regions. Contour-map tool-paths are generated in the steep regions while iso-planar tool-paths are generated in the flat regions. The gouge problem is easily handled through two-dimensional (2D) tool-path correction algorithms. The implementation results demonstrate that subdivision is capable of serving as a unified representation for both geometric modelling and machining.