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1.
双三次Bezier曲面片的光滑拼接   总被引:5,自引:3,他引:2  
本文根据曲面的总曲率和平均曲率推导出双三次Bezier曲面片拼接的C^2连续条件。  相似文献   

2.
文章提出的5×5片双三次Bézier样条插值曲面的反算算法是受颅骨补缺仿生支架的三维数学建模的激发而产生的.针对于中间有一大片空缺而只有四个边角上可以给出插值条件的需要用很多双三次Bézier曲面片通过拼接来拟合的这样一类曲面,在解决曲面片的反算和连续光滑拼接的四个问题的基础上,本文设计出5×5片双三次Bézier曲面片的一种C~2光滑拼接的方案,并分析了控制顶点解的存在唯一性,还给出了应用实例.最后把方案进行拓展,在理论上设计分析了(5 4n_1)×(5 4n_2)片双三次Bézier曲面片的光滑拼接.  相似文献   

3.
本文根据曲面的总曲率和平均曲率推导出双三次Bézier曲面片拼接的C2连续条件.  相似文献   

4.
本文给出了由控制顶点网及拼接函数表示的两相邻Bezier曲面间任意阶几何连续的相容性条件并得到了所有与一给定Bezier曲面在边界上G~K连续的Bezier曲面的代数构造。同时研究了拼接函数不依赖于控制顶点网和相容性条件自动消失的两种重要的情形。  相似文献   

5.
区域插值     
在CAD,CAGD及工程技术中,曲面片之间的连接和光滑过渡是一个众所周知的重要问题,如二片Bezier曲面或Coons 曲面在交线处一般是不光滑的(如图1.1实线部分),因此要设计一张过渡曲面C(虚线部分)来光滑拼接这二张曲面,又如工程技术中,  相似文献   

6.
1.引言曲面造型是计算几何领域中一个重要的研究课题,在工程和制造中有着广泛的应用。Bezier曲面是当前曲面造型的重要方法之一,具有装配灵活,适应性强的优点。用矩形域和三角域Bezier曲面片混合造型,几乎可以构造任意形状的曲面。但Bezier曲面造型也  相似文献   

7.
关于函数Bezier三角片的研究已有了许多,就其包络性及其相伴曲面族之间的关系而言,已在[2]中得到了较彻底的讨论。对于张量积形式的Bezier曲面的研究目前还很少,原因之一在于其表示与计算的复杂性。本文利用它的一种新表示,引进移位算子,使其作图法和  相似文献   

8.
具有重结点的B-样条曲面G1的连续条件   总被引:1,自引:0,他引:1  
本文得到了关于两个双三次内部重结点B-样条曲面片G1连续的充分必要条件和在公共边界线上控制向量的本征条件.这些条件直接由两个B-样条曲面的控制向量表示.文[10]证明了使用内部单结点的双三次B-样条曲面来构造G1光滑曲面,局部格式不存在.使用本文的这些条件就可以构造出具有局部各式的G1光滑造型.  相似文献   

9.
在CAGD中,曲面片的光滑拼接是一个重要问题,而在多片(三片以上)曲面的光滑拼接过程中,将不可避免的要遇到光滑拼接条件的协调性(又称相容性)问题,[4]中系统地讨论了单形上超限多项式插值及相容性问题,本文主要讨论矩形域上多项式曲面片光滑拼接的协调性方程,并在此基础上讨论了矩形域上插值曲面的构造问题.  相似文献   

10.
本文得到了关于两个双三次内部重结点B-样条曲面片G1连续的充分必要条件和在公共边界线上控制向量的本征条件.这些条件直接由两个B-样条曲面的控制向量表示.文[10]证明了使用内部单结点的双三次B-样条曲面来构造G1光滑曲面,局部格式不存在.使用本文的这些条件就可以构造出具有局部各式的G1光滑造型.  相似文献   

11.
本文讨论两种Bézier曲面形式的转换关系和转换条件,并给出矩阵域Bézier曲面片和三角域Bézier曲面片拼接的几何连续条件。  相似文献   

12.
A Class of Multisided Surface PatchesLiuShuxin(刘树信);XingLiping(邢丽萍)(DepartmentofMathematics,JilinUniversity,Changchan,130023)...  相似文献   

13.
We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary (and quite restrictive) conditions for a patch to possess linear precision. A main focus is on linear precision for Krasauskas’ toric patches, which we show is equivalent to a certain rational map on \mathbb C\mathbb Pd{\mathbb C}{\mathbb P}^d being a birational isomorphism. Lastly, we establish the connection between linear precision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and show how iterative proportional fitting may be used to compute toric patches.  相似文献   

14.
严建明  张弘  罗桂烈 《数学研究》2007,40(2):152-158
本文利用Lyapunov-Razumikhin理论讨论了具有连续时滞和Ⅱ类功能性反应的非自治扩散竞争系统.此系统有两个种群n个斑块,其中一个种群可以在n个斑块中自由扩散,另一种群被限定在一斑块中不能扩散.当系数满足一定的条件时,证明了系统是持续生存的,此外,给出了该系统的一周期解全局吸引的充分条件.  相似文献   

15.
In this paper,a set of suffcient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.  相似文献   

16.
Necessary and sufficient conditions (n.a.s.c) are found for a subgroup of the automorphism group of a finite graph to be realizable as the restriction to an invariant spine of some group of homeomorphisms of a compact surface. Also, n.a.s.c. are found for the restricted case when the surface is required to be orientable. The conditions are formulated in terms of the action of stabilizers of vertices on their stars. In both cases, a parametrization of the possible representations is given. Several examples are treated, as well as an application to deciding whether a given finite group of outer automorphisms of a free group is realizable via a surface homeomorphism.  相似文献   

17.
We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and Bézier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. Furthermore, Bézier triangles and tensor product patches are special cases of trapezoidal patches.  相似文献   

18.
In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.  相似文献   

19.
Bernstein-BézierSurfacePatchesonArbitrarySpatialTriangulationZhouYunshi(周蕴时);ZhangXuemei(张雪梅)(InstituteofMathematics,Universi...  相似文献   

20.
In this paper, we study two species predator–prey Lotka–Volterra type dispersal system with periodic coefficients in two patches, in which both the prey and predator species can disperse between two patches. By utilizing analytic method, sufficient and realistic conditions on permanence and the existence of periodic solution are established. The theoretical results are confirmed by a special example and numerical simulations.  相似文献   

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