| 1. | An adaptive orthonormal collocation method based on quintic spline - wavelets of two defects for differential equations
五次二重样条小波的微分方程自适应正交配置 |
| 2. | ( 2 ) although spline curves are applied widely , but the research on the algorithms of quintic spline interpolation is little
( 2 )虽然样条曲线具有广泛的应用，但对五次样条插值算法的研究却很少。 |
| 3. | Compared with cubic splines , quintic splines have more advantages for surface machining . so the generation and processing of nc instructions have become one of the nucleal technologies of cam and cnc
由于与三次样条函数相比，五次样条函数具有更大的优越性，所以基于五次样条的nc指令生成与处理技术已成为cam技术和cnc技术的主要发展趋势之一。 |
| 4. | The systemic research on the algorithms and the correlative algorithms establish massive foundation for the application of quintic spline curves in nc machining . ( 3 ) until now , interpolation points have mostly been selected manually in an empirical way
五次样条插值算法及其配套算法的系统深入研究，为五次样条曲线在数控加工技术领域中的应用奠定了坚实的算法基础。 |
| 5. | In this dissertation , the algorithms of quintic spline interpolation and their applications in cnc , nc programming and re are researched in detailed , and the whole theory , methodology and technology of quintic splines are founded
论文重点对五次样条插值算法及其在re 、 nc编程和cnc技术等方面的应用进行了系统深入的研究，建立了一套完整的五次样条处理理论、方法及应用技术体系。 |
| 6. | It is necessary to explore methods to find out interpolation points for processing of substantive and dense digitized data in an automatic manner . this dissertation presents two algorithms called as " quintic - curve - method " and " sixtic - curve - method " which are applied to automatically select nodes for quintic spline interpolation
( 3 )针对大量稠密数字化数据五次样条插值的需要，开发了两种插值节点自动选择算法：五次曲线法和六次曲线法。 |
| 7. | Therefore , some algorithms of quintic spline interpolation are first developed or improved , tested and evaluated . the algorithm of local quintic spline interpolation ( qa3 ) and quintic b - spline interpolation ( qa4 ) therein are very propitious to curve fitting of discrete data points and to nc programming of freeform curves and surfaces
因此，完善、推导和开发了多种五次样条插值算法，并对其进行了测试和评价，认为：五次多项式样条局部插值算法qa3和五次b样条插值算法qa4非常适合于离散数据的曲线拟合和曲线曲面的nc编程。 |
| 8. | Based on the analysis of characteristics , quintic splines are considered as the best spline functions that can commendably satisfy the requirements of hsc of surfaces . so the generation and processing of quintic spline - based nc instructions , which includes the generating process of nc instructions , processing of geometrical data , feed control and real - time interpolation , are investigated , and the theory , method and technique are systemically founded
因此，对基于五次多项式样条的cnc系统通用的nc指令生成与处理技术进行了系统研究，包括基于五次样条的指令生成过程、几何数据处理、速度控制和实时插补技术等，系统地建立了一套比较完整的基于五次样条的cnc理论与方法体系。 |
