A Real-Time NURBS Curve Interpolation Algorithm Based On The De_Boor Recursive Algorithm

Now most NC systems in China only have the functions of line interpolation and arc interpolation, and they can do nothing to the NURBS curves real timely. In order to machine some complex curves or surfaces, Line-blocks or Arc-blocks must be obtained through complicated mathematic calculation for arbitrary free-form curves or surfaces firstly, and then sending to CNC device to interpolate. In this way, not only can it result in the discontinuous factors of velocity and acceleration, but also lead to the huge consumption of CNC memory and the rush of data transmission. Currently CAD modeling data is mostly expressed by parameter curves. Because of the strong shape representation and shape control ability, NURBS become the standard of geometric representation of CAD modeling. So it is very necessary to design a real time NURBS curve interpolation algorithm with high speed and high precision.In this paper, a high-speed and high-precision real-time NURBS curve interpolation algorithm is put forward. The algorithm mainly involves the following aspects:1). The determination of parameter densification method. By simulating and comparing the main methods of parameter densification, it is found that the current existing methods for parameter densification can not meet the demand of minimizing both in speed deviation and computation time. By justifying some parameters of the current existing methods, an algorithm named "Taylor Second Order and Correction" is put forward, simulating and comparing testing shows that both speed-tracking accuracy and interpolation time consumption have greatly improved.2). The determination of the method for solving the point vector and derivative vector corresponding to the parameter u. By analyzing the main methods of how to calculate the point vector and derivative vector of NURBS curve, the De_Boor recursive algorithm, which has a small amount of computation relatively, is selected as the method for calculating the point vector and derivative vector of NURBS curve in this paper.3). The control of Velocity, acceleration and chord error. Taking into account the constrains of machine acceleration performance and the requirement of processing precision, a improved feedrate adaptive algorithm is put forward by the author, which involves the control of acceleration based on the original feedrate adaptive algorithm, and can ensure the velocity, acceleration and chord-error meet the demand of machining simultaneously.4). The implementation of real-time. Taking into account the requirements of real-time processing, the algorithm uses the segment of velocity as a unit of interpolation calculation. By inverse interpolation, including the selecting of the termination conditions, the approximation of intersection point, and the correction of the deceleration point and the maximum possible end point, implements the segmentation of the velocity curve. Because the criterion of segmentation can ensure that the next column of interpolation data will never conflict with the last column of interpolation data, it ensures the possibility of real-time machining in theory.5). Smooth deceleration at the end point. In this paper, A processing method of smooth deceleration at the end point is put forward, which can ensure when the parameter u arrives one, the velocity reduced to zero approximately.Theoretically, the improved feedrate adaptive algorithm guaranteed the velocity, acceleration and chord-error meet the demand of machining simultaneously, and the feedrate subsection and velocity look-ahead processing can ensure the real-time ability of this algorithm. The simulation results have shown that the velocity, acceleration and chord-error have all been well-satisfied the requirement after applying this algorithm, whilst the time consumption spent in interpolation calculation is far less (0.8%) than the time demanded in actual processing, this satisfied the real-time requirement.