Motion based geometric modeling

This thesis deals with the problem of kinematics driven geometric modeling. The central idea of the research on Kinematics Driven Geometric Modeling is to use geometric features (such as lines, planes or cylindrical surfaces) of a physical object instead of simply points as basic elements for constructing or sculpting freeform surfaces. Since the rigidity of the object has to be preserved when parameterizing the geometric features, the desired freeform surface has to be parameterized with a rigid-body motion of the subject. This requires that the domain of geometric design problem include kinematics of geometric features. As a result, a freeform surface designed this way will have not only a geometric control structure but also an intrinsic kinematic surfaces for designing sculptured surfaces would greatly simplify the problem of tool motion generation for the manufacture of such surfaces, since rigid body motions of geometric features can be readily generated with coordinated motions of a CNC machine tool. The results include: (1) A method is represented for the exact analysis and representation of the swept volume of a circular cylinder undergoing one- and two-parameter rational Bézier and B-spline motions. Instead of the approach of analyzing the point trajectory of an object motion for swept volume analysis, we seek to develop a new approach to swept volume analysis by studying the plane trajectory of a rational motion. We seek to bring together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as tool path planning for 5-axis machining of freeform surfaces. (2) To develop a new method for synthesizing a Non-Uniform Rational B-Spline (or NURBS) motion such that the swept surface of such a motion with a cylindrical cutter closely approximates a given ruled surface. First a NURBS motion is used to interpolate or approximate a set of discrete cutter locations for the side milling of a given ruled surface. Then the de Bool control positions of the NURBS motion is fine-tuned to minimize the error between the swept surface of the cylindrical cutter under the NURBS motion and the desired ruled surface. In this way, the tool motion is represented by the set of deBoor control positions and associated knot sequence as opposed to a huge set of discrete cutter locations. (3) To present a new approach to 5-axis NC tool path generation for sculptured surface machining with a fiat-end cutter. Rational Bézier and B-spline motions are used to plan cutter motions so that an exact representation of the effective cutting shape can be obtained. The exact representation leads to an accurate computation of the scallop curve generated by two adjacent tool paths. Two examples are given to show how this result can be used to accurately plan and verify tool paths for 5-axis CNC milling of sculptured surfaces.; Besides theories, we also develop a framework for web-based client-sever applications. Through the website, users can input their requests from clients, the servers process the requests and get back to clients, then clients will display the results. Some technologies, such as CGI, Win32 Internet API, COM/ATL/ActiveX, are used.