Spline paths in NC machining are advantageous over linear and circular paths due to their smoothness and compact representation, thus are highly desirable in high-speed machining (HSM) where frequent change of tool position and orientation may lead to inefficient machining, tool wear, and chatter. This paper presents an approach for calculating spline NC paths directly from discrete points with controlled accuracy. Part geometry is represented by discrete points via an implicit point set surface (PSS). Cutter location (CL) points are generated directly from implicit part surfaces and interpolated by B-spline curves. A computing procedure for calculating maximum scallop height is given. The procedure is general and suitable for part surfaces in various surface representations provided that the closest distance from a point to the part surface can be calculated. Our results affirm that the proposed approach can produce high-quality B-spline NC paths directly from discrete points. The resulting spline paths make it possible for directly importing discrete points into Computer Numerical Control (CNC) machines for high-speed machining.