Catmull-Clark细分曲面能量精确分析方法

提出了一种新的精确计算包含奇异顶点的Catmull-Clark细分曲面能量的方法.通过把Catmull-Clark细分曲面片转化成双3次B样条曲面片,导出了任意拓扑结构的细分曲面完整的能量计算公式.该方法不需要对细分曲面进行递归细分,就能计算出细分曲面的膜能量和薄板能量,与现有方法相比,该方法能快速准确地计算出细分曲面的能量.曲面光顺实例表明,用该方法计算细分曲面能量高效可行.     

A new algorithm for designing developable Bézier surfaces

A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper. Project supported by the National Basic Research Program (973) of China (No. 2004CB719400), the National Natural Science Foundation of China (Nos. 60373033 and 60333010) and the National Natural Science Foundation for Innovative Research Groups (No. 60021201), China     

二次曲面作为网格插值曲面的不可能性

研究了二次曲面即低次隐式曲面在各种网格条件下的情况，并得出结论：二次曲面作为C″连续的网格插值曲面一般是不可能的，并指出隐式曲面不适合作为网格插值曲面、而高阶的NURBS曲面可作为网格插值曲面。     

汉语短语研究的新视界--读熊文华新著《短语别裁》

熊文华先生近著《短语别裁》(民族出版社,2003年,下称《别裁》)是近年来学界短语研究的一部力作,熊著通过对大量语料细致的观察分析,不但比较成功的解决了汉语短语研究中的一系列问题,更重要的是,用“三个平面”的语法理论为短语研究开启了一扇新的视窗,使我们看到了一个新的多维度的视界。     

Wang-Ball曲线的细分变换

本文首先介绍Wang-Ball曲线细分的快速算法;然后利用与Bezier曲线的转换矩阵,推导出Wang-Ball曲线的细分变换为相似变换;同时,并给出了具体的数值实例.     

Designing Bézier surfaces minimizing the L2-norm of the Gaussian curvature

In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.     

Two-order Hermite vector-interpolating subdivision schemes

INTRODUCTION Along with the great progress in 3D data meas- urement device and the popularization of complex solid modelling, recursive subdivision has been a research focus in CAGD and CG (Wang et al., 2001). However, most interpolating subdivision schemes are Lagrange-type schemes whose smoothness is not easily verified. The geometric features of this kind of subdivided curves and surfaces are difficult to be generated, which restricts the application of subdivi- sion methods. From a…     

Designing Bézier surfaces minimizing the L2-norm of the Gaussian curvature

In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.     

Similarity-based denoising of point-sampled surfaces

A non-local denoising （NLD） algorithm for point-sampled surfaces （PSSs） is presented based on similarities, including geometry intensity and features of sample points. By using the trilateral filtering operator, the differential signal of each sample point is determined and called ＂geometry intensity＂. Based on covariance analysis, a regular grid of geometry intensity of a sample point is constructed, and the geometry-intensity similarity of two points is measured according to their grids. Based on mean shift clustering, the PSSs are clustered in terms of the local geometry-features similarity. The smoothed geometry intensity, i.e., offset distance, of the sample point is estimated according to the two similarities. Using the resulting intensity, the noise component from PSSs is finally removed by adjusting the position of each sample point along its own normal direction. Experimental results demonstrate that the algorithm is robust and can produce a more accurate denoising result while having better feature preservation.     

一种细分格式生成极限曲面的法向量的求法

本文在Levin给出的三角域上生成极限曲面的法向量求法基础上 ,给出拟蝴蝶形细分在矩形域上生成极限曲面的情况 ,并得到了两个自由度 ,可以对法向量进行优化选取 ,这对讨论曲面的等距面有广泛的实际意义