Research On The Direct Interpolation Of Free Form Curve And Surface

With the development of the manufacture, auto control, micro-electronics, data processing and etc, the new opened numerical control technology will take the place of the conventional one. In the system of numerical control, the function of the interpolation affects the appraisement of the whole system of CNC. In the modern manufacturing, the request of the quality and the quantity in the free form curve and surface grows, so it is necessary to research the directly interpolation of the free form curve and surface, not only to improve the efficiency and the quality, but to adapt the development of the modern numerical control technology.NURBS(Non-Uniform Rational B_Spline) was be ordered to be a international standard for the exchange of product model date by ISO thanks to its good mathematic feature, and what's more, in the field of CAD, NURBS has been well used. So, it's necessary to research the interpolation of NURBS as the representation of the free form curve and surface.Based on the study of the method of construct and the feature with NURBS curve and surface, this paper introduced the method in which to confirming the parametrical vector and to get the control points, disposes the base-function, and this paper gives a dynamic interpolation for NURBS with the feature of real-time look ahead, which can get the continuous step lengths under the considering of the precision and the characteristic of the motor and the direction change of the curve, and it also can look ahead the begin of deceleration, which used to decrease the current speed to zero for avoiding the over-cut and the machine's jounce.During the manufacturing of the free form feature, it is impossible for the tool to extend all over the surface, so it only to move along some limited curve. So we should to firm the position of the curves. This paper gives the several method to confirm the tool path, and compares them with each other. For two different surfaces, this paper used two different methods to solve the problem. For the 2.5D surface, we used the conventional method to get the tool path; for the 3D surface, different curvature gets different excursion distance. Based the request of the precision, the upper two methods can get the best tool path because of the least time.On the introduced methods, a system programmed with Visual C++ be used to get the tool points from inputted through points, and with the help of Matlab, its feasibility and correctness was be validated.