This paper presents an approach for generating curvature-adaptive finishing tool paths with bounded error directly from massive point data in three-axis computer numerical control (CNC) milling. This approach uses the moving least-squares (MLS) surface as the underlying surface representation. A closed-form formula for normal curvature computation is derived from the implicit form of MLS surfaces. It enables the generation of curvature-adaptive tool paths from massive point data that is critical for balancing the trade-off between machining accuracy and speed. To ensure the path accuracy and robustness for arbitrary surfaces where there might be an abrupt curvature change, a novel guidance field algorithm is introduced. It overcomes potential excessive locality of curvature-adaptive paths by examining the neighboring points’ curvature within a self-updating search bound. Our results affirm that the combination of curvature-adaptive path generation and the guidance field algorithm produces high-quality numerical control (NC) paths from a variety of point cloud data with bounded error.