Firstly , based upon the technique of splitting the nurbs surfaces and bounding containers , a split algorithm is applied to calculate the minimum distance between two general nurbs surfaces 首先，根据曲面的分裂以及包围体的思想，介绍了一般nurbs曲面间最短距离的分裂算法，给出了算法的详细流程。
This thesis , from different analytical points of view , proposes three algorithms for the minimum distances between convex nurbs surfaces and general nurbs surfaces respectively 本文从不同的分析角度，分别就凸曲面和一般曲面展开研究，给出了nurbs曲面间距离求解的几种算法，解决了最为复杂的两参数曲面间的最短距离求解问题。
And a method of node optimization according to beeline is also put forward to decrease large amounts of short straight lines and ensure sameness of image profile to object prototype . it improves the precision of engraving and suffices the request of engrave machining 为减少边缘线上的大量结点和锯齿，保证优化后的图形轮廓与原图像逼近，提出了基于最短距离优化节点的解决方法，从而提高了精度，满足了雕刻加工的要求。
Firstly , based upon analyzing the geometric constraint condition of the nearest points , a method is given to refine the approximated distance between two surfaces through newton - raphson iteration . at the same times , the cases of boundaries are all considered in detail 首先，基于分析两张参数曲面间达最短距离所必须满足的几何约束条件及各种可能出现的边界情况处理，结合newton - raphson迭代法，提出了距离求解精化的一种方法。
All the results can be utilized by engineers , during the designing and construction . the main conclusions are listed as follows : ( 1 ) based on the shortest line between weak interbed and limit of excavation and the location of point of intersection between limit of excavation , classification of weak interbed distribution is set up , and the distance of distribution is defined ; ( 2 ) according to the strength and deformation equivalent principle , influence zone of weak interbed is introduced , and a new method to simulating the weak interbed with thickness is built ; ( 3 ) some quantificational results on influence of weak interbed respectively at crown , right shoulder and right wall are summarized ; ( 4 ) some quantificational results on influence of weak interbed with the distance between weak interbed and limit of excavation 0 . 2d , 0 . 5d , l . od are gained ; ( 5 ) some quantificational results on influence of weak interbed in the rock mass with confining coefficient 0 . 38 , 1 . 0 , 1 . 5 , 2 . 0 , 3 . 0 are summed up ; ( 6 ) some quantificational results are summarized on influence of the underground surrounding rock mass stability with weak interbed , in the representational surrounding rock mass graded ii , iii , iv ; ( 7 ) according to the studying results some advices are suggested on designing of underground engineering 主要结论如下： ( 1 )以软弱夹层到开挖轮廓线最短距离和最短距离线与开挖轮廓线的交点位置为指标对软弱夹层的分布部进行了分类，并确定了软弱夹层分布距离； ( 2 )根据强度等效和变形等效的原则，引入了软弱夹层影响带的概念，建立了模拟软弱夹层厚度的一种新方法； ( 3 )总结出了软弱夹层分布在拱顶、右拱肩、右边墙时对地下洞室稳定性影响的量化指标； ( 4 )分析出了软弱夹层距开挖轮廓线0 . 2d 、 0 . 5d 、 1 . 0d三种情况对地下洞室稳定性影响的量化指标； ( 5 )总结出了在不同的侧压力系数( 0 . 38 、 1 . 0 、 1 . 5 、 2 . 0 、 3 . 0 )地应力场中软弱夹层对稳定性影响的量化指标； ( 6 )得出了在、 、代表性围岩中软弱夹层对稳定性影响量化结果； ( 7 )根据数值试验成果提出了在有软弱夹层围岩中地下洞室设计原则的几点新内容。
Of the stipulation under the existing legislation on the shortest distance between such plants and residential premises ; whether it knows the relevant stipulations in the united states , united kingdom , japan and other advanced countries and the criteria for determining the permitted shortest distance ; if so , of the relevant details ; and 现行法例对这类厂房与住宅的最短距离有何规定；是否知悉美国、英国、日本及其他先进国家的相关规定以及厘定许可最短距离的准则；若然，有关的详情；及
On the background of selecting an optimal combination of elastic pads " height between the two adjacent cylinders , which carry out the design requirement of combinative cylinders assembled structure , in this dissertation , the optimal design model is established ground on geometrical and mechanical model of the combinative cylinders assembled structure . the algorithm that integrates multi - objective ' s decision - making method with minimal distance between two points in euclid ' s space into the modified genetic algorithm to solute the optimal model is presented 本文以选取层间弹性垫层厚度实现组合圆筒裱糊装配结构的设计要求为研究背景，依据组合圆筒裱糊装配结构的几何模型与力学模型，建立组合圆筒裱糊装配结构的优化模型，提出改进遗传算法与欧几里德空间最短距离准则的多目标决策方法相结合的优化算法。
Finally , a split algorithm is put forward to calculate the minimum distance between two general nurbs surfaces , in which the technique of splitting the nurbs surfaces and the convergence of control points are used , and spatial classification using the upper & lower bound and the convex hull property of the nurbs surfaces are applied to avoid unnecessary subdivisions 最后，探讨了nurbs曲面的分裂技术与控制网的收敛性问题，充分利用nurbs曲面的凸包性和距离值上下边界分类的思想，避免大量不必要的细分，提出了一般nurbs曲面间最短距离求解的分裂算法。
