A Variant Algorithm Of De Boor Derivation For NURBS Surface Direct Interpolation Algorithm And Its Simulation

Surface Interpolation Algorithm (SDI) has long been a main obstacle in developing a high-speed and high-accuracy CNC system; the difficulties facing the researchers and developers in the area of CNC system mainly lies in:1. The real-time requirement of surface interpolation algorithm. Its charater is that it should carry out tasks in the fixed time. It is that coordinates and velocity of all axes should be calculated in one interpolation period. The strong real-time requires that the calculation time is short enough. How to get a fast computing speed and strong real-time interpolation algorithm under limited hardware is one of the difficulties facing the surface interpolation.2. The precision requirement of surface interpolation algorithm. It is used to assess the interpolation result approach the fixed surface by interpolation errors. Interpolation errors include accumulated error and chord error. They are the significant measurements to assess the interpolation algorithm. How to get high accuracy interpolation algorithm for surface is another difficulty facing the surface interpolation.Targetting the above difficulties, a new approach which based on the de Boor algorithm was proposed, a novel interpolation algorithm was re-designed and re-derived. Then, program codes were wrote with VC/MFC and a new data structure named double cross-linked chain was applied. Finally a simulation was conducted to verify tiny steps and the quality performance of the interpolation algorithm with visualization. The results have shown the algorithm is valid.1. Concerned with the drawback of the existing algorithms which are based on matrix or B-spline for NURBS surface, that is, tremendous amount of calculations need in those algorithms, a novel approach based on de Boor algorithm for NURBS surface interpolation was derived. One of the main benefit lies that the partial derivative vectors of the surface can be easily derived and calculated. It avoided the great amount of calculations and thus saved a lot of time comparing with traditional algorithms;2. To verify the validation of interpolation algorithm on tiny steps and quality performance, a new data structure named double cross-linked chain was applied and designed. As a kind of List, the advantages of double cross-linked chain are helpful to the data monitored and stored.3. The u-and v-direction interpolation parameters were calculated in response to different angle of tool axis. A type of S shape controlled curve was proposed to ensure smooth actual interpolation velocity-acceleration curves, and the deceleration point was determined according to the symmetrical characteristic of S shape curve and NURBS theory.4. To verify the algorithm, an Algorithm Verification Simulation was conducted. The Simulation realized the Chord Error Verification, Velocity Verification and Acceleration Verification. The relational curves had been shown in the display area. The results have been shown that the interpolation algorithm of correcting velocity and acceleration first, and then, correcting the interpolation precision is valid.