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.     

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.     

Adaptive sampling for mesh spectrum editing

INTRODUCTION Free-form surface editing plays an importan part in geometric modeling, such as Free-Form De- formation (FFD), level of detail editing. Users need to be careful to avoid artifacts in the result surface. In this paper, we present a new mesh editing technique based on geometry signal wavelet analysis. It indi- rectly modifies vertex positions in spatial domain by the simple geometry proxy that is simplified from the original mesh, and performs filtering and enhance- ment in f…     

Automatic recognition of intersecting features of freeform sheet metal parts

This paper presents an approach for recognizing both isolated and intersecting geometric features of freeform surface models of parts, for the purpose of automating the process planning of sheet metal forming. The developed methodology has three major steps： subdivision of B-spline surfaces, detection of protrusions and depressions, and recognition of geometric features for sheet metal forming domain. The input geometry data format of the part is based on an IGES CAD surface model represented in the form of trimmed B-spline surfaces. Each surface is classified or subdivided into different curvature regions with the aid of curvature property surfaces obtained by using symbolic computation of B-spline surfaces. Those regions satisfying a particular geometry and topology relation are recognized as protrusion and depression （DP） shapes. The DP shapes are then classified into different geometric features using a rule-based approach. A verified feasibility study of the developed method is also presented.     

局部对称黎曼流形中的常平均曲率紧致超曲面

研究局部对称黎曼流形中具有常平均曲率的紧致超曲面,得到了这类超曲面关于第二基本形式模长平方的一个拼挤定理,推广了由候中华给出的常曲率流形中具有常中曲率的紧致超曲面的相应结论.     

A level set based segmentation approach for point-sampled surfaces

Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces is proposed, which is based on the level set evolution scheme. To segment the model so as to align the patch boundaries with high curvature zones, the driven speed function for the zero level set inside narrow band is defined by the extended curvature field, which approaches zero speed as the propagating front approaches high curvature zone. The effectiveness of the proposed approach is demonstrated by our ex- perimental results. Furthermore, two applications of model segmentation are illustrated, such as piecewise parameterization and local editing for point-sampled geometry.     

高中学生运用FDI认知方式解决数学应用问题的表征及策略关系研究

国内外关于问题解决中表征和策略的研究成果不少，但涉及高中数学应用题解决中的问题表征及其与解题策略关系的研究不多。高中学生运用FDI认知方式解决数学应用问题有5个表征层次--文字表征、具体表征、抽象表征、形象表征和数学表征，4种解决策略--盲目搜索策略、情景推理策略、原理统率策略和数学模型策略。高中解决数学应用问题时的表征程度决定了其问题解决策略的选取，表征程度的学生倾向于选择相对优化的策略。     

Curvatures estimation on triangular mesh

Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmitt (1992) and Taubin (1995)presented two simple methods to estimate principal curvatures. They used circular arcs to approximate the normal curvature. We find this may cause large error in some cases. In this paper, we describe a more accurate method to estimate the normal curvature,and present a novel algorithm to estimate principal curvatures by simplifying the Chen and Schmitt's method. Some comparison results are also shown in this paper.     

张恨水报刊编辑思想中的现代性精神初探

张恨水是中国现代报刊发展史上的重要开拓者,他的报刊编辑思想为今人提供了重要的启示。在三十年的报刊编辑生涯中,他形成了自己独特的报刊编辑实践经验和编辑思想,在诸多方面表现出了鲜明的现代性追求。他立足于文化传统积极进行报业的现代化改良,在当时的报业界闯出了一条新路。他的报刊编辑思想显露出了鲜明的时代精神、自觉的商业意识和可贵的个性觉醒。     

Finsler流形中旗曲率几何性质的探讨

该文得到了Finsler流形中某点的一个领域内距离函数的表示,由此给出旗曲率的几何解释。     

A fast direct point-by-point generating algorithm for B Spline curves and surfaces

INTRODUCTION Curve generating algorithms are important incomputer graphics and CAD/CAM. For some simplecurves such as line, circle, ellipse, etc., we have somerendering algorithms such as DDA algorithm for line,Bresenham algorithm and midpoint algorithm forcircle, Pitteway’s algorithm for ellipse, etc. (Bresen-ham, 1977; Pitteway, 1985; Ammeraal, 1987; Foleyet al., 1990; 1993). For rendering parametric curves and surfaces, apopular method is to compute a set of points along thecurv…     

H3(-1)中具有一个常主曲率的曲面

文章讨论H 3(-1)了中具有一个常主曲率的曲面,得到了另一主曲率与该常主曲率之间的关系。     

截面相似性零件的自适应测点规划研究

针对整个模型统一尺度规划和曲面间的衔接处理困难问题,提出“曲面模型-三角网格模型-截面线-点集-测点集”的规划策略,实现基于曲率特性的自适应测点规划。通过将数字化设计模型转换成统一粒度的密集三角网格模型,实现复杂型面的一致性描述;进而利用三角网格的拓扑信息,提取截面线;在截面线曲率估算的基础上,通过均分曲线质量进行测量点的自适应规划。结果表明,该研究能以较少的测点反映加工误差。     

Using relief texture for interactive and tangible virtual environments

This paper first introduces a way to improve interactivity with high polygon count virtual objects through the ＂mixed＂ use of image-based representation within one object. That is, both 3D polygonal and image-based representations are maintained for an object, and switched for rendering depending on the functional requirement of the object. Furthermore, in order to reduce the popping effect and provide smooth and gradual transition during the object representation switch, the object is subdivided with the subdivided parts possibly represented differently, i.e., using 3D models or images. As for the image-based representation, the relief texture （RT） method is used. In particular, through the use of the mixed representation, a new way called TangibleScreen is proposed to provide object tangibility by associating the image-based representation with a physical prop （projecting the RTs） in a selective and flexible way. Overall, the proposed method provides a way to maintain an interactive frame rate with selective perceptual details in a large-scale virtual environment, while allowing the user to interact with virtual objects in a tangible way.     

Seeing red: poetry and metaphor as responses to representational challenges in critical narrative research

Research with young people who ‘do not fit the mould’ requires innovative and unconventional methods, but what are the implications of such methods for scholarly representation? This paper reports on the development of such a method with students diagnosed Attention Deficit Hyperactivity Disorder and offers one view of the borderland spaces and tensions between critical theory and narrative inquiry. In particular, the paper defines the methodology that underpins the ‘critical cover narratives’ method, describes the application of this approach within a doctoral study, and identifies resultant issues of representation when combining narrative and critical approaches. The paper then details the use of a tapestry metaphor to reconcile these issues. The central premise of the paper is that differing methods produce different knowledge, which demands different forms of representation. In making this case, the paper discusses the importance of a balance between the epistemological and aesthetic within scholarly representations of narrative inquiry.     

GVF各向异性扩散和冲击滤波耦合的图像放大

提出了一种基于梯度向量流（Gradient Vector Flow,GVF）各向异性扩散和冲击滤波耦合的图像放大算法.该算法模型由边缘停止函数约束的平均曲率流在各向异性的扩散中平滑图像,能去除噪声等的干扰;GVF外力场将图像梯度边缘力场转变为有旋场进而去除图像放大中锯齿效应;数据保真项避免图像因扩散而过度失真,保留图像特征;耦合冲击滤波模型增强图像边缘和细节.实验结果表明,该算法在客观指标和主观效果上均是一种有效的图像放大算法.     

三维Minkowski空间中平均率为零的型如af(x) bg(y) h(z)=0类空曲面

讨论三维Minkowski空间L3={R3:dx2 dy2 -dz2 }中型如af(x) bg(y) h(z) =0极大类空曲面 ,得到该曲面的反函数形式     

矩形域上Bézier曲面片的凸性

根据Gauss曲率的符号,讨论了矩形域上B啨zier曲面片的凸性,得出用B啨zier点表示的凸性条件     

The Physics—Based Manifold Modeling Method for Free—form Surface Design

A new framework for free-surface design is proposed.Using Manifolds can generalize the spline scheme to surfaces of arbitrary topology,Physics-based modeling incorporate physical laws into shape representation to provide direct shape interaction.The combination presents a new method inherits the attractive properties of the manifold surface as well as that of the physcis-based models.     

量子力学中的物理实在

自在实体，指人类意识之外独立存在的客体，是康德的“自在之物”。现象实体，指自在实体作用于人的感官所引起的感觉表象，并强调有“形”有“体”的一面。人类的眼——脑系统无法从原子的发光现象直接建立电子的形象，但却可以通过电子波振幅中抽象出的曲率概念间接建构。量子力学描述的电子波是曲率波，是真实的物理实在。