Abstract G-surf is a method for defining and machining the compound curvature surfaces encountered in many engineering applications. The surfaces are defined by orthogonal grids of B-spline space curves and machined with a cylindrical end-milling cutter inclined at predetermined angles to the surface normals. The approach proves to be very flexible and, as the cutter operates at a full and select cutting speed, gives an efficient means of material removal. Surface finish and cutter interference are both affected by cutter inclination to the surface normal and can be adjusted for optimum conditions. The interactive menu-driven package fits onto microcomputer installations and is suitable for small- to medium-size manufacturing companies.