Today compound sculptured surfaces have been widely used to design complicated shapes and details of mechanical parts in the automotive, aeronautical, die and mold industries. The technology of machining these surfaces with high quality and efficiency is badly needed in the manufacturing industry. In Computer numerical control (CNC) finish machining of compound sculptured surface parts, local gouging is a major concern due to the geometric mismatch between the engaged regions of the cutting surface and the part surfaces. Specifically, local gouging will occur at a cutter contact point along the tangent direction, in which the normal curvature of the cutting surface is less than that of the part surface. In the past years, some researchers have applied curvature analysis techniques to local gouging detection for a single surface patch;​ however, a practicable, reliable approach to evaluating the geometric mis/match between the cutting and part surfaces has not yet been available. My research originally proposes an improved approach to detecting potential local gouging for compound surface patches and to determine an optimum tool size for local gouge free machining. This approach applies comprehensive curvature analysis to the engaged regions between the cutting and part surfaces in 3-axis finish machining by using different standard cutters. This research contributes to the research on sculptured surface machining with in-depth understanding about the geometric mis/match between the cutting and part surfaces and has great potential impact to advance CNC machining technique in the manufacturing industry.