共查询到19条相似文献,搜索用时 437 毫秒
1.
一类非端点插值B样条曲线降阶的方法 总被引:1,自引:0,他引:1
降阶算法是B样条曲线和曲面设计的一个基本算法,它广泛应用于组合曲线,蒙皮或扫描曲面等设计中.Piegl与Tiller曾给出B样条曲线的降阶方法.本文给出了解决更一般的非端点插值B样条曲线降阶的方法.新的方法主要是通过对现有的节点插入方法进行分析,给出了一种端点插值递推公式,并利用此公式对Piegl与Tiller降阶方法加以改进,使之能够解决非端点插值均匀及非均匀B样条曲线的降阶问题. 相似文献
2.
双三次B样条插值曲面 总被引:2,自引:0,他引:2
本文研究三次B样条插值曲面。对于给定的拓扑网格点阵Pi,j。导出了其插值三次B样条曲面的控制顶点,每四个顶点Pi,j,Pi l,j,Pi,j 1,Pi 1,j 1由九个三次B样条曲面片构成,整个曲面是C^2连续的,最后,给出了一个数值实例。 相似文献
3.
一类双k次B样条曲面的G1连续性条件 总被引:2,自引:0,他引:2
本文针对两个k×k次B样条曲面的节点向量为端点插值、内部是单节点的情形 ,给出它们之间的G1光滑拼接条件 ,同时得到它们的公共边界曲线的控制顶点所要满足的本征方程 .其中本征方程是B样条曲面片所独有的现象 . 相似文献
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B样条基的转换矩阵及其应用 总被引:2,自引:2,他引:0
本文研究任意两个B样条基可转换的条件及转换矩阵,给出了关于转换矩阵元素的表示及性质等理论结果,并推导出了两个递推公式,为实际计算转换矩阵的元素提供了易于实现的数学方法。本文还讨论了B样条基转换矩阵在CAGD中的应用,特别讨论了B样条曲线的节点插入、升阶和分解问题。本文的结果为B样条曲线的节点插入、升阶、分解等运算提供了一个统一的数学模型和实现方法。 相似文献
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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
8.
二次带形状参数双曲B样条曲线 总被引:1,自引:0,他引:1
在空间Ω_5=span{1,sinh t,cosh t,sinh 2t,cosh 2t}上给出了二次带形状参数双曲B样条的基函数.由这组基组成的二次双曲B样条曲线是C~1连续的,同时具有很多与二次B样条曲线类似的性质和几何结构,并且可以精确表示双曲线.在控制多边形固定的情况下,可以通过调节形状参数的大小来进一步调整曲线的形状. 相似文献
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将B样条曲线转换为Bézier曲线,基于Bézier曲线间的光滑拼接的理论,研究了带多形状参数的Bézier曲线(CE-Bézier曲线)与均匀B样条曲线的拼接问题,得出均匀B样条曲线与CE-Bézier曲线的G0,G1,G2光滑拼接条件.在达到拼接条件的前提下,通过改变CE-Bézier曲线的形状参数的数值大小,可以灵活调整拼接曲线的形状. 相似文献
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1 引言在CAD曲面造型中,对于复杂的模型,通常无法用一张曲面将其表示出来.当采用多张曲面表示的时候,就涉及到曲面的裁剪、过渡、拼接等问题(见[1],[2],[3]).在本文中, 我们对于基曲面是裁剪B样条曲面,裁剪线是B样条曲线的情况,提出两种构造光滑过渡曲面的方法.其中第一种方法能够较快的生成近似G1连续的过渡曲面,而第二种方法是对Filip在[2]中的工作的发展,所生成的过渡曲面不但是G1连续的,而且可以灵活地调整形状. 相似文献
11.
G~1 Continuity Conditions of B-spline Surfaces 总被引:2,自引:0,他引:2
According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N > 2) patch B-spline surfaces meeting at a common corner are given at the end. 相似文献
12.
Ma Jitao 《数学年刊B辑(英文版)》1992,13(2):251-256
Some necessary and sufficient conditions of the oontinuity of A_x~+ are given in [1] In this paper, some advances on the base and the condition of the oontinuity of A_~+ for Semi-Fredholm operators A_x are presented. 相似文献
13.
Evan M. BullockChristopher William Davis 《Topology and its Applications》2012,159(1):133-143
A polynomial f(t) with rational coefficients is strongly irreducible if f(tk) is irreducible for all positive integers k. Likewise, two polynomials f and g are strongly coprime if f(tk) and g(tl) are relatively prime for all positive integers k and l. We provide some sufficient conditions for strong irreducibility and prove that the Alexander polynomials of twist knots are pairwise strongly coprime and that most of them are strongly irreducible. We apply these results to describe the structure of the subgroup of the rational knot concordance group generated by the twist knots and to provide an explicit set of knots which represent linearly independent elements deep in the solvable filtration of the knot concordance group. 相似文献
14.
This paper is concerned with continuity and differentiability of NEMYTSKIJ operators acting between spaces of summable abstract functions. In a first part, necessary and sufficient conditions for continuity are collected. Then main emphasis is given to sufficient conditions for differentiability in the sense of FRÉCHET and GÂTEAUX . Finally, second order differentiability is briefly discussed. 相似文献
15.
Geometric continuity is a very important issue in CAGD and has gained more attention. In this paper we present the new concept of polynomial preserving Gn continuity (PPGn) between rectangular and triangular Bézier surfaces. Necessary and sufficient conditions of PPGn are established explicitly. A simple and useful sufficient condition is also presented. The results can be used more effectively in connecting surfaces and composing rectangular and triangular patches. 相似文献
16.
The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition. 相似文献
17.
V. Šeda 《Annali di Matematica Pura ed Applicata》1970,86(1):357-365
Summary In the paper sufficient conditions for H?lder continuity of the solution of the first initial-bouudary value problem for the
heat equation are established. These results complete the statements proved in the paper[1].
Entrata in Redazione il 5 gennaio 1970. 相似文献
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In this paper, a key assumption is introduced by virtue of a parametric gap function. Then, by using the key assumption, sufficient conditions of the continuity and Hausdorff continuity of a solution set map for a parametric weak vector variational inequality are obtained in Banach spaces with the objective space being finite-dimensional. 相似文献
19.
Yu. K. Demjanovich 《Mathematische Nachrichten》1996,177(1):57-79
S. G. Mikhlin was the first to construct systematically coordinate functions on an equidistant grid solving a system of approximate equations (called “fundamental relations”, see [5]; Goel discussed some special cases earlier in 1969; see also [1, 4, 6]). Further, the idea was developed in the case of irregular grids (which may have finite accumulation points, see [1] ). This paper is devoted to the investigation of A-minimal splines, introduced by the author; they include polynomial minimal splines which have been discussed earlier. Using the idea mentioned above, we give necessary and sufficient conditions for existence, uniqueness and g-continuity of these splines. The application of these results to polynomial splines of m-th degree on an equidistant grid leads us, in particular, to necessary and sufficient conditions for the continuity of their i-th derivative (i = 1, ?, m). These conditions do not exclude discontinuities of other derivatives (e.g. of order less than i). This allows us to give a certain classification of minimal spline spaces. It turns out that the spline classes are in one-to-one-correspondence with certain planes contained in a hyperplane. 相似文献