G3连续过渡曲面的构造

过渡曲面在CAD／CAM中具有十分重要的作用，其构造与风荷连续性，几何不变量密切相关。本文通过对几何不变量法曲率，测地挠率和几何连续关系的推导，得到构造G^3几何连续过渡曲面的充分条件，结合连接线定理，用超限插值法解决了两个参数面间G3几何连续时渡问题。     

曲面积分的参数矢量表示式及其应用

曲面积分的参数矢量表示式及其应用郭洪芝，陈荣胜（天津大学）曲面积分的参数矢量表示式不仅在场论中有着比较广泛地应用，而且它对简化曲面积分的计算，特别是当曲面积分的积分域为圆柱面或球面时。掌握并运用参数矢量表示式去计算曲面积分，往往比通常所采用的基本计算...     

广义Bézier曲线与曲面在连接中的应用

通常的贝齐尔（Ｂｅｚｉｅｒ）曲线、曲面，在其端点或边界只具有ＧＣ１阶插值性．本文在保持通常贝齐尔曲线、曲面性质的基础上，定义了一种广义的贝齐尔曲线、曲面，使其在曲线段的端点和曲面片的边界具有高阶光滑插值性，它可方便地光滑连接两条参数型的曲线段和两张以上参数型曲面片，并且连接方式是ＧＣｒ（ｒ≥１）的．所以广义贝齐尔曲线、曲面在计算机辅助设计应用中更具有独特的意义．     

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．     

一类具有任意次数的参数多项式极小曲面

极小曲面是在几何造型设计中有着重要应用的一类特殊曲面.本文从几何造型的视角提出一类次数任意的参数多项式极小曲面.所提出的极小曲面具有显式的参数表示,并具有一些重要的几何性质,如对称性、包含直线和自交性.根据几何性质,本文将该参数多项式极小曲面划分为4类:n=4k+1,n=4k+2,n=4k+3,n=4+4,其中n是极小曲面的次数,k是正整数.本文给出与之相对应的共轭极小曲面的显式参数形式,并实现其等距变形.     

高亏格曲面上地图的计数

本文给出了可定向曲面(亏格2,3)和不可定向曲面(亏格5)上根瓣丛以边数为参数时相应的计数显式.与此同时,考虑一类与瓣从拓扑等价的地图类: (无环,简单)近2-正则地图,通过一种组合方法,给出了多参数下平面近2一正则地图的计数显式,亦得到了任意亏格曲面上该类地图的具体个数.     

关于隐式代数曲面的一种几何连续性定义

本利用函数的幂级数给出了隐式代数曲面的一种几何连续性定义，证明了在此定义下的k阶几何连续即为k阶变尺度(rescaling)连续，并举例说明了其应用的方便性。     

关于隐式代数曲面的一种几何连续性定义

本文利用函数的幂级数给出了隐式代数曲面的一种几何连续性定义．证明了在此定义下的ｋ阶几何连续即为ｋ阶变尺度（ｒｅｓｃａｌｉｎｇ）连续，并举例说明了其应用的方便性．     

曲面的三阶局部切触在5坐标曲面加工中应用

运用微分几何中的切触原理，研究了在多轴数控机床中刀具切削圆与零件曲面的切触条件和局部坐标系下的局部三阶切触条件，并用截形对刀具切削圆与曲面的贴近程度进行了分析。相对于现有献本理论更严密，深入到曲面三阶参数而不仅是二阶参数曲率，既适合初等解析曲面又适合计算几何的拟合曲面，计算过程准确(曲率的导数很难求)，求解方便(只要解一阶非线性方程)。     

正交变换在曲线,曲面积分计算中的应用

正交变换在曲线、曲面积分计算中的应用林元重（江西萍乡高等专科学校３３７０５５）对于三维空间的曲线积分与曲面积分，如果知道其积分曲线或积分曲面的参数形式，一般可按数学分析教材所介绍的公式计算．但是，对于某些曲线、曲面积分，要把积分曲线或曲面用适当的参数...     

Blending implicit interval curves and surfaces

This paper is concerned with blending algebraic implicit curve and surface representation where the functional representations have inaccuracies. Algebraic implicit interval curves and surfaces are first defined as interval algebraic objects. The interval Buchberger algorithm, relying on polynomial interval division, is then outlined. General blending problems for algebraic implicit curves and surfaces are considered and various continuity conditions are applied. Computational cases are developed for specific problems.     

Parametric curve with an implicit domain

In this paper we present a new representation of curve, named parametric curve with an implicit domain (PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.     

基于参数连续HC Bézier-like曲线的过渡曲线的构造

在形状调配过程中,过渡曲线的连续性往往是很难保证的.给出HC Bézier-like曲线的定义,然后从过渡曲线满足一定连续性的角度出发,利用HC Bézier-like曲线的端点性质,研究形状参数曲线的参数连续特征保持问题.给出线性混合过程中,一阶和二阶参数连续保持条件,从而得出一般的HC Bézier-like曲线在...     

BOUNDARY PENALTY FINITE ELEMENT METHODS FOR BLENDING SURFACES,I BASIC THEORY

1.IntroductionBlendingsurfacesissaidifwhentwoframesurfaces(orbodies)arelocatedalreadyjasmoothlytransferringsurfaceissoughttoconnectthetwoframesurfacesalongcertainboundary.Usually,theterminology"smoothness"meansthattheblendingsurfacebelongstogeometriccontinuityCI(Foleyetal.(90)[14),i.e.,theblendingsurfaceanditstangentplanearecontinuousuntilthejointboundary.Manyliteraturesarereportedonthissubject.Wemerelymentionafewofthemrelevanttothispaper.Uniforml)Thi.workwassupportedbytheresearchgrantsfromt…     

Correspondence and (2,1)-Bézier Surfaces

Tom Sederberg's method of moving curves (surfaces) is a new and effective tool for implicitizing curves (surfaces). From our point of view, the curve (surface) can be defined by using moving curves (surfaces) which in algebraic geometry are called correspondences. It turns out that from this definition we can easily derive both parametric and implicit representations of the curve (surface). In this paper, we investigate the geometry of the bi-degree (2,1)-Bézier surface and study the relationship between singularities and correspondences. We also characterize all the possible singular curves in terms of the control points of the surface.     

Intersection of a ruled surface with a free-form surface

This paper presents a simple method for computing the intersection curve of a ruled surface and a free-form surface. The basic idea is to reduce the problem of surface intersection to the one of projecting an appropriate curve such as a directrix of the ruled surface, along its indicatrix curve (direction vector field of its generating lines), onto the free-form surface; the projection curve is just the intersection curve. With techniques in classical differential geometry, we derive the differential equations of the intersection curve in the cases of parametrically and implicitly defined free-form surfaces. The intersection curve naturally inherits the parameter of the chosen directrix. Moreover, it is independent of the base surface geometry and its parameterization, and is obtained by numerically solving the initial-value problem for a system of first-order ordinary differential equations in the parametric domain associated to the surface representation for parametric case or in 3D space for implicit case. Some experimental examples are also given to demonstrate that the presented method is effective and potentially useful in computer aided design and computer graphics. An erratum to this article can be found at     

CONVEXITY THEOREM OF PARAMETRIC TRIANGULAR BEZIER SURFACES

The author introduces twist vectors of control nets of parametric triangular Bezier surfaces, With twist vectors and other geomtric magnitudes a sufficient condition for parametric triangular Bezier surfaces to be convex is offered. Incidently a necessary and sufficient condition for triangular Bezier surfaces of parametric form to degenerate to that of functional form is given. A less stringent sufficient condition is proposed for quadratic.Bezier surfaces to be convex.     

一类有理插值曲面模型及其可视化约束控制

本文构造一类新的基于函数值和偏导数值的双变量加权混合有理插值样条.与已有的有理插值样条相比,这类新的有理插值样条具有以下四方面的特性,其一,插值函数可以由简单的对称基函数来表示;其二,对任何正参数,插值函数满足C1连续,而且,在不限制参数取值的条件之下,插值曲面保持光滑;其三,插值函数不但含有参数,而且带有加权系数,增加了插值函数的自由度;其四,插值曲面的形状随着参数与加权系数的变化而变化.同时,本文讨论此类插值曲面的性质,包括基函数的性质、积分加权系数的性质和插值函数的边界性质.此类插值函数的优势在于,不改变给定插值数据的前提下,通过选择合适的参数和不同的加权系数,对插值区域内的任意点的函数值进行修改.因此可将其应用于曲面设计,根据实际设计需要,自由地修改曲面形状.数值实验表明,此类新的有理样条插值具有良好的约束控制性质.