以复形为基础的非流型造型与基于物理的造型相结合的物 …

提出了一个新的表示物体的框架，通过非流形造型与基于物理的造型相结合，从拓扑结构和几何信息两个方面扩大了模型的表示范围，以代数拓扑中的复形为基础的非流形造型的作用是生成物体的拓扑框架，既可以表示ＣＡＤ的物体，更适合表示具有复杂拓扑的自然物体，基于物理的造型的作用是在拓扑框架上生成最终的几可信息，二者的给提供了一种新的几何造型手段。     

多分辨率几何造型系统设计与实现

将小波分析、细分造型、网格化简等多分辨率造型技术与基于NURBS的造型技术相结合,独立开发了多分辨率几何造型系统.给出了改进的辐射边拓扑数据结构,统一表示线性网格曲面和参数曲面以及流形和非流形形体.依据STEP标准定义了几何元素类型,基于UML描述了类结构定义.最后介绍了系统功能模块并给出了运行实例.     

非流形几何造型的布尔运算

非流形的几何造型用统一的结构来表示线框、表面和实体,是目前几何造型系统研究的热点。而模型的构造需要一个有效的布尔算法。论文提出一种由布尔运算定义的能够快速和任意重塑几何模型的新方法。这种方法利用非流形几何造型的性能,使得人们可以反复进行交互设计,并可用于特征造型。     

建立在数据库上的实体造型,曲面造型系统—HYBRID

HYBRID是一个建立在数据库上的实体造型及曲面造型系统,该系统是在北京航天航空大学的PANDA实体造型系统的基础上开发的。HYBRID以集合运算(交、并、差)为工具,由简单物体——基本体素及二维图形,形成复杂物体。系统采用了CSG、B-rep数据结构充分地表示了体的几何信息及拓扑信息。数据库的使用使系统存储量增大,管理统一、方便,图形及非图形信息容易统一处理。曲面造型采用了非均匀有理B样条曲面插值,通过路径、截面的定义形成曲面。HYBRID适用于作为机械、建筑计算机辅助设计的支撑工具及管道的曲面设计。     

非流形几何造型技术与应用

从非流形形体的表示方法和操作两个方面，对非流形几何造型技术进行了分析，探讨了其可能的应用领域。     

非流形几何建模拓扑数据结构的研究

当前ＣＡＤ技术的发展趋势是特征造型、行为建模、信息集成。几何建模作为ＣＡＤ系统的核心,是影响ＣＡＤ系统功能的重要因素。非流形几何建模可以用统一的数据结构来表示线框、曲面、实体模型,从而为在底层实现特征造型、变量化设计、行为建模提供了可能。本文概括了非流形几何建模的基础理论知识,提出了一种基于非流形几何建模的新型拓扑数据结构,应用ＯＯＰ及开放式软件开发思想探讨了开发具有自主知识产权的三维实体ＣＡＤ平     

新一代几何造型系统—GEMS4.0

ＧＥＭＳ４．０是清华大学ＣＡＤ中心在工作站上用Ｃ语言开发的新一代几何造型系统。和９０年代初问世的第三代几何造型系统相比，它具有如下特点：基于线框，表面，实体和特征表示的非流形造型；具有参数化设计，变量几何，尺寸驱动；扫描面，自由曲面和雕塑面用非均匀有理Ｂ样条（ＮＵＲＢＳ）表示，几何数据及属性的文件传送和数据库存取基于国际标准ＳＴＥＰ；基于窗口环境，面向对象的事件驱动和数据表格驱动的系统结构有利于开     

支持特征的非流形造型数据结构的研究

文章提出了一种新的数据结构,统一的表示了线框、表面和实体三种模型,及非几何特征信息,扩大传统实体造型的覆盖域,并可表示非流形模型。     

非流形模型的几何造型与应用

本文以代数拓扑中的复形理论作为非流形模型的数学基础，确定了非流形模型的表示域，给出了以单纯复形为基础的拓扑算子，提出了以非流形模型为基础的支持从概念设计到加工、分析的集成系统框架结构。     

非流形模型的几何造型与应用

本文以代数拓扑中的复形理论作为非流形模型的数学基础，确定了非流形模型的表示域，给出了以单纯复形为基础的拓扑算子，提出了以非流形模型为基础的支持从概念设计到加工、分析的集成系统框架结构。     

Physically based modeling and simulation with dynamic spherical volumetric simplex splines

In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object’s geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as the brain shifting during surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique.     

Octree-based automatic mesh generation for non-manifold domains

Automatic mesh generation within the context of non-manifold geometric models is far from a commercial reality. While manifold objects are the most commonly encountered domains in many applications, other applications such as those requiring multiple material models and mixedmodel representations (combination of 1-D, 2-D and 3-D domains) fall beyond the realm of the existing automatic meshing procedures as they require a non-conventional modeling enviroment, namely the non-manifold topology (NMT) based environment. This paper focuses on automatic mesh generation issues in the context of two such applications: (i) finite element modeling for multiple material models and (ii) geometric abstractions requiring a mixed-model representation. Specifically, the paper describes a geometry utility system, built around an NMT data structure and geometry-based meshing algorithms that ensure the validity of the mesh for non-manifold domains.GE Consulting Services.     

A level-set based variational method for design and optimization of heterogeneous objects

A heterogeneous object is referred to as a solid object made of different constituent materials. The object is of a finite collection of regions of a set of prescribed material classes of continuously varying material properties. These properties have a discontinuous change across the interface of the material regions. In this paper, we propose a level-set based variational approach for the design of this class of heterogeneous objects. Central to the approach is a variational framework for a well-posed formulation of the design problem. In particular, we adapt the Mumford-Shah model which specifies that any point of the object belongs to either of two types: inside a material region of a well-defined gradient or on the boundary edges and surfaces of discontinuities. Furthermore, the set of discontinuities is represented implicitly, using a multi-phase level set model. This level-set based variational approach yields a computational system of coupled geometric evolution and diffusion partial differential equations. Promising features of the proposed method include strong regularity in the problem formulation and inherent capabilities of geometric and material modeling, yielding a common framework for optimization of the heterogeneous objects that incorporates dimension, shape, topology, and material properties. The proposed method is illustrated with several 2D examples of optimal design of multi-material structures and materials.     

A Survey on Data‐driven Dictionary‐based Methods for 3D Modeling

Dictionaries are very useful objects for data analysis, as they enable a compact representation of large sets of objects through the combination of atoms. Dictionary‐based techniques have also particularly benefited from the recent advances in machine learning, which has allowed for data‐driven algorithms to take advantage of the redundancy in the input dataset and discover relations between objects without human supervision or hard‐coded rules. Despite the success of dictionary‐based techniques on a wide range of tasks in geometric modeling and geometry processing, the literature is missing a principled state‐of‐the‐art of the current knowledge in this field. To fill this gap, we provide in this survey an overview of data‐driven dictionary‐based methods in geometric modeling. We structure our discussion by application domain: surface reconstruction, compression, and synthesis. Contrary to previous surveys, we place special emphasis on dictionary‐based methods suitable for 3D data synthesis, with applications in geometric modeling and design. Our ultimate goal is to enlight the fact that these techniques can be used to combine the data‐driven paradigm with design intent to synthesize new plausible objects with minimal human intervention. This is the main motivation to restrict the scope of the present survey to techniques handling point clouds and meshes, making use of dictionaries whose definition depends on the input data, and enabling shape reconstruction or synthesis through the combination of atoms.     

Geometry-aware domain decomposition for T-spline-based manifold modeling

This paper presents a new and effective method to construct manifold T-splines of complicated topology/geometry. The fundamental idea of our novel approach is the geometry-aware object segmentation, by which an arbitrarily complicated surface model can be decomposed into a group of disjoint components that comprise branches, handles, and base patches. Such a domain decomposition simplifies objects of arbitrary topological type into a family of genus-zero/one open surfaces, each of which can be conformally parameterized into a set of rectangles. In contrast to the conventional decomposition approaches, our method can guarantee that the cutting locus are consistent on the parametric domain. As a result, the resultant T-splines of decomposed components are automatically glued and have high-order continuity everywhere except at the extraordinary points. We show that the number of extraordinary points of the domain manifold is bounded by the number of segmented components. Furthermore, the entire mesh-to-spline data conversion pipeline can be implemented with full automation, and thus, has potential in shape modeling and reverse engineering applications of complicated real-world objects.     

Feature-based 3D non-manifold freeform object construction

This paper presents a novel technique for modeling a 3D non-manifold freeform model around a 3D reference model. To represent both the design abstractions and the incomplete topological information, a new non-manifold data structure is first defined. Our data structure embodies the functional vitalities of both the boundary representation data structure and the complex-based data structure. Along with our data structure, a set of topological operators is defined to manipulate the entities in the data structure. Based on the non-manifold data structure and the topological operators, we develop a technique to construct 3D freeform objects around a reference model. Intuitive 2D sketches are adopted to specify the detailed profile of the object constructed. The construction method is feature-based – every reference model has pre-defined features, and the feature template of the constructed object is related to the features of the reference model by feature node encoding. Therefore, the surfaces derived from one reference model can be regenerated automatically on another reference model with the same features. The geometry coverage of our geometric modeling approach includes both manifold and non-manifold 3D freeform objects.     

Modeling with blocks

This paper presents a simple and general modeling primitive, called a block, based on a generalized cuboid shape. Blocks are laid out and connected together to constitute the base shape of complex objects, from which is extracted a control mesh that can contain both smooth and sharp edges. The volumetric nature of the blocks allows for easy topology specification, as well as CSG operations between blocks. The surface parameterization inherited from the block faces provides support for texturing and displacement functions to apply surface details. A?variety of examples illustrate the generality of our blocks in both interactive and procedural modeling contexts.     

Internet网络拓扑建模

首先概述Internet网络拓扑建模的意义和分类;总结现阶段已发现的主要网络拓扑特性与度量指标;然后分析、讨论自治域级和路由器级的Internet网络拓扑建模与最新的研究成果;最后针对目前拓扑建模中存在的难点和问题给出总结,并展望未来的研究发展方向.     

真实感人脸模型的细分曲面重建

提出一种利用2张正交照片和细分曲面进行真实感三维人脸建模的方法,并实现了不同模型间的三维变形.为了构造个性化的人脸几何模型,将网格简化、自由曲面变形和细分结合起来,得到多个层次细节下的人脸模型;再经过纹理融合和映射,完成个性化的真实感三维人脸建模;同时利用线性插值实现了同拓扑真实感模型间的光滑变形.实验结果表明：该方法不仅可以进行有效的真实感三维人脸建模,而且变形简单流畅,具有广阔的应用前景.