改进的基于欧氏距离测度网格模型体素化算法

在基于到网格多边形表面的法矢量函数作为距离标准的体素化算法的基础上，提出以多边形面的最小包围盒作为计算单元，以欧式距离作为测度实现网格模型的体素化，极大地提高了计算速度，使得只能在图形工作站上实现的算法在微机平台上得以实现．针对通常采用Flooding操作判断内外体素、但应用于存在封闭空腔的模型时将会产生错误的情况，设计了一种根据体素标志位序列判断内外体素的算法．     

基于体素可见度的高效直观传递函数设计算法

针对体绘制中传递函数设计问题,提出基于直观体素可见度设计传递函数的高效方法。用高斯混合模型（GMM）对体数据自动建模,提取体数据的聚类信息;根据高斯混合模型设计体素可见度模型。将传递函数设计转化为真实体素可见度与目标体素可见度距离最小化问题,使用最速下降法求解,得到最优传递函数。同时设计一套方便、灵活的交互工具,用来调节体素可见度模型。实验结果表明了该算法的高效性和直观性。     

三维带符号的欧氏距离变换及其应用

距离变换是图像处理中历史悠久的研究课题．该文将二维带符号的欧氏距离变换推广到三维，对其进行了优化，分析了它的计算复杂度，并应用于解决计算机图形学中的两个重要问题：第一，将图形对象的三角网格表示转换为它的距离场表示．即首先将三角网格模型离散为体素表示，利用三维带符号的距离变换，将求空间一点到图形对象的最短距离的全局搜索过程，转化为求这一点到离它最近的特征体素所包含的图形对象部分的局部搜索过程；第二，利用类似的思想，求两张空间曲面之间的最短距离．     

协作环境下的人机距离建模与最小距离迭代算法

为了使机器人适应更广泛、更复杂的任务需求,实现人与机器人的协作与共融,精确并实时地计算人与机器人之间的相对距离成为了不可避免的问题.针对该问题,提出了一种协作环境下的人机距离建模方法以及计算人机间最小距离的迭代算法.首先,利用机器人的3D模型构建机器人结构特征,并通过3D视觉传感器提取人体骨骼特征,将以上2组特征映射到同一坐标空间中建立协作环境下的人机距离模型.然后,在此模型的基础上迭代计算人与机器人间的最小距离并给出对应的空间位置点.最后以ABB公司的YuMi机器人为测试对象进行人机最小距离测量实验,实验结果表明该方法降低了建模难度、实现了计算的实时性,验证了该建模方法与迭代算法的有效性和实用性.     

基于八叉树结构的三维体素模型检索

随着VR/AR技术发展以及三维模型的广泛应用,实现三维检索具有越来越重要的现实意义.基于模型的检索较好地保留了模型的空间信息和几何特征,其不仅包含模型的表面信息而且还包含模型的内部属性.但是,基于模型的检索往往存在着高存储、高计算的问题.为了解决该问题,本文研究了三维模型预处理及三维模型表示的方法,提出了一种基于八叉树结构的三维体素模型检索方法,即将模型进行体素化处理后提取模型的粗粒度特征和细粒度特征,将两种特征进行融合用八叉树形式表达特征,输入到卷积神经网络中进行训练,最终通过特征的欧氏距离度量实现模型的检索.运用八叉树特征表示法,可以有效地节省体素化存储过程的空间占用量,而且也能保留原始三维网格模型的细节信息.同时考虑到计算性能,本文还在模型体素化的过程中做出一定的改进,通过仅对模型外表面进行体素化,实现了对体素化过程以及数据存储和卷积神经网络训练的优化,大大降低了时间开销.实验中将三维体素模型特征存储在八叉树结构中作为卷积神经网络的输入,结合SOFTMAX代价函数,通过大量的模型训练数据,对该卷积神经网络模型进行训练.与其他同类算法对比,证明了该算法在三维模型检索中的优越性.     

实体模型的多分辨率中轴生成

针对模型降维的需要,提出一种实体模型的多分辨率中轴生成方法.首先根据模型的层次寻找模型中需要细化的部分,并据此对边界进行体素化;其次使用距离蔓延的方法计算多分辨率体素的距离;最后根据体素的距离计算出多分辨率的中轴体素.实验结果表明,该方法可以以低时间空间代价生成高质量的多分辨率中轴.     

自适应的基于点云的CAD模型重建方法

基本的随机抽样一致性(RANSAC)算法无法根据点云模型的噪声自适应地设定分割参数,并有效判断点云数据是否被合理分割。针对该问题,提出了一种自适应的基于点云模型的计算机辅助设计(CAD)模型重建方法。该方法采用RANSAC算法从点云数据中提取基本形状体素,使用直方图法分析点到相应形状体素表面的投影距离。对分割不合理的区域,按照该点云面片的高斯噪声设置新的分割参数,再次进行形状提取。经过一定轮数的迭代,该方法可以合理提取点云模型中的细小形状体素。然后通过校准形状体素的位置和方向、根据相邻形状体素之间的交线裁剪形状体素,实现CAD模型的重建。最后,以误差分布图和直方图分析了原始点云数据中点到CAD模型表面投影距离,有70.71%的点的投影距离不超过点云模型包围盒高度的1%。实验结果表明,以点云包围盒高度的1%为尺度向实验数据中加入噪声时,该方法仍能够通过自适应设置分割参数提取出合理的细小体素。     

基于数字距离变换的3D模型骨架提取算法

在获得三维模型体素表示的基础上 ,通过比较模型体素及其 2 6连通域体素到模型轮廓的最小欧式距离 ,提出了一种利用骨架体素 2 6连通域的对称性进行三维模型骨架体素提取的算法 整个算法只需遍历一次体数据集即可自动完成模型骨架的提取过程 .实验表明 ,该算法具有较高的效率和精度 .     

基于进化HMM 模型的动态Agent 系统建模方法

提出一种基于隐式Markov模型（HMM）的进化建模方法．使用进化算法随机搜索HMM的模型空间，自动选择HMM的结构和参数-完成对动态智能体系统行为的建模，学习智能体对周围环境的分割和反映方式．实验结果表明，该方法可以很好地搜索HMM的模型空间，并且避免了人工确定HMM模型结构的困难和手工设计模型所需的多次反复．     

基于非流形几何与特征树的异质材料实体可视化方法

提出一种异质材料实体可视化的方法．采用边界曲面细分技术减小材料分布的突变视觉效应;在不损失渲染质量的前提下,采用自适应曲面细分和冗余曲面滤除方法解决异质实体可视化效率差、难以实时显示的问题．给出了详细的异质实体边界网格生成算法,以显示异质实体的外部几何信息及其内部材料组分的三维分布．该算法采用基于特征树的曲面网格自适应细分策略,通过对异质实体特征树的拓扑结构分析来判定待渲染曲面的材料分布特性,仅对确实需要细分的曲面进行额外的网格细分,有效地减小了实体渲染中所需的计算量;利用非流形异质实体的表征方法,采用冗余曲面滤除方法直接滤除非相关的边界曲面,以满足实时可视化的要求．该方法已用于异质实体建模软件CAD4D中,实验结果表明,其可有效地实现异质实体的实时可视化显示．     

Constructive sculpting of heterogeneous volumetric objects using trivariate B-splines

This paper deals with modeling heterogeneous volumetric objects as point sets with attributes using trivariate B-splines. In contrast to homogeneous volumes with uniform distribution of material and other properties, a heterogeneous volumetric object has a number of variable attributes assigned at each point. An attribute is a mathematical model of an object property of an arbitrary nature (material, photometric, physical, statistical, etc.). In our approach, the function representation (FRep) is used as the basic model for both object geometry and attributes represented independently using real-valued scalar functions of point coordinates. While FRep directly defines object geometry, for an attribute it specifies a space partition used to define the attribute function. We propose a volume sculpting scheme with multiresolution capability based on trivariate B-spline functions to define both object geometry and its attributes. A new trivariate B-spline primitive is proposed that can be used as a leaf in an FRep constructive tree. An interactive volume modeler based on trivariate B-splines and other simple primitives is described, with a real-time repolygonization of the surface during modeling. We illustrate that the space partition obtained in the modeling process can be applied to define attributes for the objects with an arbitrary geometry model such as BRep or homogeneous volume models.     

Haptic rendering based on spatial run-length encoding

In this paper, an extendable volumetric representation based on run-lengths called spatial run-length encoding (S-RLE) is presented. The S-RLE representation is developed for a haptic shape modeling system that is based on simulated machining processes. In the system, shape modeling is simulated as virtual material removal processes similar to machining processes with volume-based haptic rendering. The object and the tools are represented by S-RLE. The data structure of S-RLE consists of two cross-referenced databases: one is a stack of lists in geometrical domain, recording the runs describing the space occupation of the object; the other is a table in physical domain, describing the physical properties of each element. The latter is extendable to include more diverse physical properties such as parts composed of heterogeneous materials. Algorithms for geometric operations and haptic rendering based on S-RLE are developed. The proposed S-RLE data structure has the features of efficient memory usage, quick collision detection, inherent representation for heterogeneous objects, and fast visual rendering.     

Modeling the material grading and structures of heterogeneous objects for layered manufacturing

The emphasis of this work is to discuss a scheme for modeling the material grading and structures of heterogeneous objects. To model the material grading of a heterogeneous object, a termed ‘grading source’ is defined. The grading sources are reference features, which specify the type and position of grading, and a material grading function for controlling the material variation within the geometric boundary of the objects. Within the proposed modeling scheme, a concept on representing objects, which are both heterogeneous in material and structure (e.g. composite laminates), will also be elaborated. For downstream layered manufacturing purposes, a contour sub-division algorithm on each layer arising from slicing a heterogeneous object is proposed. Within each slice, the material grading is decomposed into sub-contours according to the different grading variation. A parameter called ‘grading step-width’ is defined to control the number of sub-contours and resolution of the grading. With such discretization, it is, therefore, possible to build a heterogeneous object on layered manufacturing machines of different fabricating precision specification.     

A hierarchical representation for heterogeneous object modeling

A hierarchical representation for heterogeneous object modeling is presented in this paper. To model a heterogeneous object, Boundary representation is used for geometry representation, and a novel Heterogeneous Feature Tree (HFT) structure is proposed to represent the material distributions. HFT structure hierarchically organizes the material variation dependency relationships and is intuitive in modeling different types of material gradations. Based on the HFT structure, a recursive material evaluation algorithm is proposed to dynamically evaluate the material compositions at a specific location. Such a hierarchical representation guarantees complex material gradations and the user's design intent can be intuitively represented. Example heterogeneous objects modeled with this scheme are provided and potential applications are discussed.     

Constructive Hypervolume Modeling

This paper deals with modeling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real/abstract object or process under consideration. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical, etc.) defined at any point of the point set. We provide a brief survey of different modeling techniques related to point sets with attributes. It spans such different areas as solid modeling, heterogeneous objects modeling, scalar fields or “implicit surface” modeling and volume graphics. Then, on the basis of this survey we formulate requirements to a general model of hypervolumes (multidimensional point sets with multiple attributes). A general hypervolume model and its components such as objects, operations, and relations are introduced and discussed. A function representation (FRep) is used as the basic model for the point set geometry and attributes represented independently using real-valued scalar functions of several variables. Each function defining the geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This reflects the constructive nature of the symmetric approach to modeling geometry and associated attributes in multidimensional space. To demonstrate a particular application of the proposed general model, we consider in detail the problem of texturing, introduce a model of constructive hypervolume texture, and then discuss its implementation, as well as the special modeling language we used for modeling hypervolume objects.     

Multi-volume CAD modeling for heterogeneous object design and fabrication

The current computer-aided technologies in disign and product development,the evolution of CAD modeling,and a framework of multi-volume CAD modeling system for heterogeneous object design and fabrication are presented in this paper.The multi-volume CAD modeling system is presented based on nonmanifold topological elements.Material identifications are defined as design attributes introduced along with geometric and topological information at the design stage.Extended Euler operation and reasoning Boolean operations for merging and extraction are executed according to the associated material identifications in the developed multi-volume modeling system for heterogeneous object.An application example and a pseudo-processing algorithm for prototyping of heterogeneous structure through solid free-form fabrication are also described.     

Feature-based design for heterogeneous objects

Heterogeneous objects are objects composed of different constituent materials. In these objects, multiple desirable properties from different constituent materials can be synthesized into one part. In order to obtain mass applications of such heterogeneous objects, efficient and effective design methodologies for heterogeneous objects are crucial.In this paper, we present a feature based design methodology to facilitate heterogeneous object design. Under this methodology, designers design heterogeneous objects using high-level design components that have engineering significance. These high level components are form features and material features. In this paper, we first examine the relationships between form features and material features in heterogeneous objects. We then propose three synthesized material features in accordance with our examination of these features. Based on these proposed features, we develop a feature based design methodology for heterogeneous objects. Two enabling methods for this design methodology, material heterogeneity specification within each feature and combination of these material features, are developed. A physics (diffusion) based B-spline method is developed to (1) allow design intent of material variation be explicitly captured by boundary conditions, (2) ensure smooth material variation across the feature volume. A novel method, direct face neighborhood alteration, is developed to increase the efficiency of combining heterogeneous material features.Examples of using this feature based design methodology for heterogeneous object design, such as a prosthesis design, are presented.     

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.     

Adaptive space decomposition for fast visualization of soft objects

We present a fast visualization scheme of soft objects by introducing an efficient evaluation method for a field function. The evaluation of a field function includes distance computation between a point in space and the defining primitives of the soft object. If the unnecessary distance computations between a point in space and the components that do not influence the point can be avoided, the evaluation can be accelerated. For this purpose, we decompose the space into adaptive‐sized cells according to the bounding volume of the components and build a data structure called an interval tree through which the influencing components for a point are sought. The bounding volume of a component is generated by considering the radius of a component and k‐DOPs. The proposed scheme can be used in many applications for soft objects such as modeling and rendering, especially in the interactive modeling process. Copyright © 2003 John Wiley & Sons, Ltd.     

Heterogeneous object modeling through direct face neighborhood alteration

Two recent advances—the use of functionally gradient materials in parts and layered manufacturing technology—have brought to the forefront the need for design and fabrication methodologies for heterogeneous objects. However, current solid modeling systems, a core component of computer-aided design and fabrication tools, are typically purely geometry based, and only after the modeling of product geometry, can a part's non-geometric attributes such as material composition be modeled. This sequential order of modeling leads to unnecessary operations and over-segmented 3D regions during heterogeneous object modeling processes.

To enable an efficient design of heterogeneous objects, we propose a novel method, direct face neighborhood operation. This approach combines the geometry and material decisions into a common computational framework as opposed to separate and sequential operations in existing modeling systems. We present theories and algorithms for direction face neighborhood alteration, which enables direct alteration of face neighborhood before 3D regions are formed. This alteration is based on set membership classification (SMC) and region material semantics. The SMC is computationally enhanced by the usage of topological characteristics of heterogeneous objects. After the SMC, boundary evaluation is performed according to the altered face neighborhood. In comparison with other solid modeling methods, the direct face neighborhood alteration method is computationally effective, allows direct B-Rep operations, and is efficient for persistent region naming. A prototype system has been implemented to validate the method and some examples are presented.