Researchers commonly develop notched drill points with secondary cutting edges that have unusual specifications; however, mathematical models cannot comprehensively specify these thinned/notched drill points. In an earlier work (Lin, P. D., and Tzeng, C. S., 2007, “New Method for Determination of the Pose of the Grinding Wheel for Thinning Drill Points,” Int. J. Mach. Tools Manuf., 47(15), pp. 2218–2229), precise mathematical modeling for drill design and one-wheel grinding of ISO-standard drills with linear secondary cutting edges was presented. That model is expanded herein to drill points with a specifiable secondary cutting edge and characteristic angle distribution. Optionally, the entire cutting edge (primary, secondary, and chisel edges) can be provided with continuity to eliminate stress concentration points. The mathematical background and modeling are summarized in this study. Experimental drills are produced and tested for verification and demonstration. The presented modeling technique allows subsequent researchers to exactly duplicate the drills, including the thinning/notching drill points, a capability that was previously unavailable. This system is useful for improved drill CAD and CNC software for the design, manufacture, reconditioning, and research of novel point design.