Research On Minor Adjustment Of Freeform Curves & Surfaces And Its Applications

This paper briefly reviews the research history and current status of freeform curve and surface techniques. And we discuss the characters, applications and representative work on shape modification methods and related techniques of curves and surfaces. A new concept that minor adjustment of freeform curves and surfaces is presented to solve a series of typical problems in engineering. We set up the basic framework of minor adjustment, which includes the theoretical basis, key techniques and its applications.After summarizing the deficiencies in shape modification techniques of freeform curve and surface, we present the concept of minor adjustment for the first time. And on the basis thought of "from the engineering and to the engineering", a theoretical framework is set up.The most important class A surfaces are those representing hoods, roofs, etc. of automobiles. The design of class A surfaces thus involves not only functional criteria but also subjective ones relating to style and appearance. We give a smooth minor adjustment method to Bezier curves based on the control vertexes addition and modification of feature curves. On the one hand, the interactive vertex addition can make the control polygon shape of feature curve approximate the space points. And on the other hand, the iterative minor adjustment of control vertexes can guarantee the fitting precision.The geometric models of vehicle headlamp reflectors have strict criteria, which are related of photometric characteristics. We present a rapid modeling method by minor adjustment of surfaces, which is based on iterative fitting. The reflector surfaces can be created rapidly by minor adjusting the section curves iteratively. And the whole process is under error control. The function module that we developed by UG GRIP has been applied in a famous headlamp enterprise in Taiwan. It has been proofed effective in reverse engineering.In certain EDM operations, electrode orbiting is used to improve flushingconditions and to achieve fine finishing. And the orbital motion makes the dimension of cavity in the workpiece deviate from the design objective. This paper presents a compensation method for electrode orbiting in EDM which is based on surface minor adjustment of general offset. The presented techniques are used to modify the geometry of free-form electrode, so as to eliminate the effect of orbital motions. A lot of examples and machining results show that the developed techniques can improve the machining precision effectively.At last many assistant techniques are studied to help realize all kinds of key algorithm. A standard IGES data interface is developed to guarantee the information exchange between CAD/CAM systems. And a recognition method of discrete points on trimmed surface is presented, which is based on the plane domain of surface parameter. The approach changes the recognition from the complex 3D space to the simple parameter plane artfully. The discrete point of a full NURBS is on the trimmed surface only when its NURBS parameters are in the domain of trimmed surface. The method solves the problem of the recognition for large numbers of discrete points.