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This paper presents a new method to efficiently update workpiece and determine cutter-workpiece engagement (CWE) in multi-axis milling simulation based on a uniform voxel modeling space. At each cutter location, a novel algorithm named direct voxel tracing is developed and used to generate a functional cutter surface voxel model to reliably establish the internal space of the milling cutter. The cutter internal space is represented by its voxel boundary with small memory usage. Through the Boolean subtraction between two successive voxel boundaries of the cutter internal space, a minimal voxel deactivation region is attained within which all active workpiece voxels are deactivated (removed) to update the workpiece model. To determine the associated CWE map, a 3D circle voxelization algorithm is employed. By slicing the cutter surface by a sequence of planes perpendicular to and along the cutter axis, CWE can be determined as the sliced 3D circles are voxelized. Quantitative comparisons of the proposed method against existing voxel modeling and vector modeling-based methods have been made. The results have demonstrated much improved computational efficiency of the proposed method in simulating the complex multi-axis milling operations. [ABSTRACT FROM AUTHOR]