Technology Of Generating NC Tool Path For Subdivision Surfaces Based On Catmull-Clark Scheme

Subdivision scheme is a new discrete modeling technology which describes the modeling surface through controlling mesh and subdivision rules. It has many advantages such as localness and affine-invariance of traditional B-spline surface and adaptability to arbitrary topology which parameter surfaces do not have, and is becoming one of the most powerful geometric modeling tools. Subdivision scheme for surface is a gradual subdivision which obtains final surface by discrete-to-discrete method, and the disadvantage of conventional method from discrete to continuous and then from continuous to discrete is avoided. The Catmull-Clark subdivision scheme is generalization of B-spline surfaces, which can be blent with NURBS surfaces easily and be unified with the NC processing commendably. Numerical Control of subdivision surface is the base of subdivision surface applied to industry manufacture. And an accurate programming method of Numerical Control tool path is a soul of Numerical Control.The paper focuses on the Catmull-Clark subdivision surfaces. Based on the Catmull-Clark subdivision scheme , a new approach to generate NC tool path for subdivision surfaces is presented. The aim is to apply subdivision surfaces to product manufacture, and to make preparations for development of subdivision surfaces in industry field. The main contents are as follows:1. Based on the Catmull-Clark subdivision scheme, a new approach to generate NC tool path for subdivision surfaces is presented: First calculate the limit points and the normal vectors at these points from the initial control mesh . Second generate offset surface with controlling accuracy by using the limit points, the normal vectors and the radius of the ball end milling cutter. Next generate NC cutting tool path from the offset subdivision surface. This method applies subdivision surfaces to CAD/ CAM system , and adapts to quadrilateral models of arbitrary topology.2. Catmull-Clark subdivision scheme is implemented by developing tool Visual C++ 6.0 and OpenGL; Offset surface of Catmull-Clark subdivision surface is implemented by combinative method of Quadtree structure and Winged Edge structure; NC tool path of Catmull-Clark subdivision surface is generated by section plane method.3. Offset error, which is a basis problem in subdivision suifaces, is also analyzed in the paper. And two methods about analysis and control are presented. The first one is to control precision of offset surfaces by criterion based on angle between normal vectors of two neighbor vertexes. The second one is to obtain offset surfaces whose precision has been given by criterion based on distance between control mesh vertexes and non-control mesh vertexes.