隐式曲面与参数曲面的G3过渡

通过几何过渡方法，结合重新标度连续概念，利用隐式曲面与参数曲面的各自等距曲面的交线，构成隐式曲面与参数曲面问的过渡面．用曲面的隐式与隐式、参数与参数形式，证明了所作的过渡面与给出的隐式曲面与参数曲面在连接线处是G^3连接的。     

矩形域与三角域Bezier曲面间的PPG~n变换

1．引言曲线,曲面间的几何连续性问题近几年来引起人们的广泛注意和兴趣［1－10］．在1984年国际CAGD会议上R．E．Barnhill和G．Farm将它列为计算几何尚待解决的重大问题之一．一方面是由于在CAGD中总希望所构造的曲线和曲面有更多的自由度或者有更多的几何控制参数以便使设计人员能自由地控制所要设计的对象的几何形状;另一方面是由于需要研究自由曲线曲面间的基于几何连续的拼接和各种形式的连续过渡曲面来构造更为复杂而灵活的曲线,曲面和几何体山．几何连续性的定义在不同的论文中不尽相同,但其本质是非奇异参数变换下的不变…     

曲面上一种等距不变量的构造

提出一种基于曲面内蕴度量的等距变换不变量构造方法.通过不变几何基元构造不变核,再对不变核进行多重积分,得到曲面上的等距不变量.这种不变量完全基于曲面的内在属性,有直观的几何解释,并且不受数量约束.实验表明,它对于描述曲面的等距变换,如不同表情的同一人脸、不同姿态的同一人体运动等具有潜在应用意义.     

De Sitter空间中类空曲线的对偶曲面的不变量

主要从切触几何的视角考察3维de Sitter空间中类空曲线的第一光锥对偶曲面和双曲对偶曲面的不变量的几何性质.     

裁剪B样条曲面间过渡曲面的构造

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．     

Bezier曲面间几何连续拼接与拼接曲面构造

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。     

曲线、曲面几何连续性问题

曲面间几何连续性及其拼接问题是计算机辅助几何设计与图形学中重要而又困难的问题,本文从图形内在的接触不变的观点出发来研究几何连续性问题。指出接触不变向量是曲面几何连续性的本质,给出两曲面间几何连续性的充要条件和简单的判别方法,通过解线性方程组给出连续性方程的通解并由此构造出与已知曲面为n阶几何连续的曲面的全体。     

分片代数超曲面的构造与参系数分片多项式系统的研究进展

多元样条是具有一定光滑度的分片多项式,具有一定光滑度的分片代数(超)曲面(即多元样条的零点集)是表示或逼近曲面的重要工具.研究一种有效方法用于构造具有一定光滑度和预先给定拓扑的实分片代数超曲面是解决如何表示或逼近具有一定拓扑结构(特别是复杂拓扑结构)的几何物体问题的重要途径之一,也是计算几何与代数几何研究中一个新的重要主题.参系数分片多项式系统不仅与曲面相交、拼接和过渡曲面生成等一系列研究密切相关,而且是参系数半代数系统的本质推广.本文介绍分片代数超曲面的构造与参系数分片多项式系统的一些最近的研究进展.     

关于Finsler曲面的几何和拓扑

本文在Ｆｉｎｓｌｅｒ曲面上定义了一个新的不变量Ｈ。该不变量等于零刻画了Ｒｉｅｍａｎｎ流形。文章给出了Ｈ的一个上界并且构造了Ｈ为常值的非Ｒｉｅｍａｎｎ的Ｆｉｎｓｌｅｒ曲面。此外，本文还推广了Ｌａｎｄｓｂｅｒｇ曲面的Ｇａｕｓ－Ｂｏｎｎｅｔ－Ｃｈｅｒｎ定理并分类了非正曲率的Ｆｉｎｓｌｅｒ曲面。     

二次超曲面在切点的几何连续性

二次超曲面在切点的几何连续性姜献峰，梁友栋（浙江大学，杭州３１００２７）１９９０年５月１７日收到．１９９２年７月１１日收到修改、压缩稿．在计算机辅助几何设计（ＣＡＧＤ）中，复杂曲面通常是用一系列较为简单的曲面片．经一定的几何连续拼接而成．参数曲面几何...     

A Transference Result of the L p Continuity from Jacobi Riesz Transform to the Gaussian and Laguerre Riesz Transforms

In this paper we develop a transference method to obtain the Gaussian-Riesz transform’s L ^p -continuity and the Laguerre-Riesz transform’s L ^p -continuity from the L ^p -continuity of the Jacobi-Riesz transform, in dimension one, using the well known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials.     

与给定多边形相切的一类含参数三角样条曲线

基于一类与给定多边形相切的三角样条曲线,通过在基函数中引入形状参数λ,在保持原曲线的光滑性及其他基本性质不变的条件下,构造出一类能自由调控曲线形态的含参数三角样条曲线,并结合图例讨论了其相关性质.     

Weak continuity on generalized topological spaces

We introduce the notions of weak (g, g′)-continuity and weak (ψ, ψ′)-continuity on GTS’s and GNS’s, respectively, and investigate characterizations for such functions and relationships between weak (g, g′)-continuity and weak (ψ, ψ′)-continuity.     

Stability of penalty finite-element methods for nonconforming problems

Penalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth-order problems in which C¹-continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce the C¹-continuity constraint appears promising. In this study we demonstrate equivalence of the finite-element penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is not met.     

Sets of points of discontinuity and differentiability of certain operators

An investigation of the structure of the set of points off-continuity of an operator A (f-continuity is an analog of the Lipschitz condition).Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 323–331, March, 1971.     

Remarks on enlargements of generalized topologies

The concept of enlargement of a generalized topology was introduced by á. Császár [4]. He also introduced the concepts of (κ,λ)-continuity and (κ _μ ,λ _ν)-continuity on enlargements. In this paper, we characterize the (κ,λ)-continuity and introduce the concept of strong (κ,λ)-continuity on enlargements. In particular, we study characterizations for the strong (κ,λ)-continuity and the relationships among (μ,ν)-continuity, (κ,λ)-continuity, strong (κ,λ)-continuity and (κ _μ ,λ _ν)-continuity.     

On weak neighborhood systems and spaces

We introduce and study the concepts of weak neighborhood systems, weak neighborhood spaces, ω(ψ, ψ′)-continuity, ω-continuity and ω*-continuity on WNS’s. This work was supported by a grant from Research Institute for Basic Science at Kangwon National University.     

On moduli of p-continuity

Moduli of p-continuity provide a measure of fractional smoothness of functions via p-variation. We prove a sharp estimate of the modulus of p-continuity in terms of the modulus of q-continuity (1<p<q<??).     

On weakly (τ, m)-continuous functions

In this paper we introduce a new notion of weakly (τ, m)-continuous functions as functions from a topological space into a set satisfying some minimal conditions. We obtain some characterizations and several properties of such functions. This function leads to the formulation of a unified theory of weak continuity [20], almosts-continuity [33],p(θ)-continuity [10] andp-continuity [41].