基于自适应延迟切割的三角网格布尔运算优化

规则化的布尔运算被广泛应用在三维建模系统中.近年来,随着图形硬件的发展,基于三角网格的规则化布尔算法由于输出结果能直接被图形硬件处理,表现出了明显的优势.但是传统的算法由于采用CSG树局部评估策略,使得面片在相交测试中反复被切割,并且由于面片分类在切割后的模型之间直接进行,导致算法无法在保证鲁棒性的同时实现高性能.为了避免这些问题,本文呈现了一种CSG树全局评估算法来统一执行单次和连续布尔运算.算法由两部分组成：自适应的延迟切割和全局化面片分类.在自适应的延迟切割阶段,算法通过仔细处理多个三角面片相交导致的各种情况使得延迟切割被扩展到整个CSG树来避免由于面片的反复切割带来的数值误差累积并利用自适应的八叉树使得相交测试能在线性时间内完成.在全局化面片分类阶段,算法通过分治法使得分类始终在切割后的面片和原始输入模型之间进行来保证分类的精度;通过结合组分类策略和自适应的八叉树来进一步优化了分类性能。实验结果表明,本文提出的算法无论是在执行单次或连续布尔运算时都能在保证鲁棒性同时性能优于其他的算法,因此本文算法可广泛应用于交互式建模系统中,如数字雕刻、计算机辅助设计和制造（CAD/CAM）等.     

Interactive vizualization of constructive solid geometry scenes on graphic processors

A ray-tracing algorithm for interactive visualization of very large and structurally complicated scenes presented in the constructive solid geometry (CSG) form is suggested. The algorithm is capable of visualizing such scenes in real time by using a graphic processor. As primitives, classical shapes and objects represented in an analytical form (in particular, second-order surfaces and implicit functions) are used. Unlike other similar algorithms, our algorithm produces the final image in a single pass and has no constraints on the maximum number of primitives and on the CSG tree depth. The key feature of the algorithm is a method for optimizing CSG models, which converts the input tree to an equivalent spatially coherent and well-balanced form (a completely balanced equivalent tree may not exist). The performance of visualization after applying the optimization technique is shown to depend on only the computational resource of the GPU (in contrast to multi-pass algorithms whose performance is restricted by memory capacity). It has been shown experimentally that our algorithm is capable of rendering CSG models consisting of more than a million CSG primitives with the tree depth up to 24.     

Boolean operations with implicit and parametric representation of primitives using R-functions

We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a constructive solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.     

Octree creation via C.S.G. definition

The common method for generating the octrees of complex objects, is based upon generating the octrees of several pre-defined primitives and applying Boolean operations on them. Regardless how the octrees representing the primitives are generated (top-down or bottom-up) the octree of a desired object is obtained by performing Boolean operations among the primitives comprising the object according to the object's CSG (constructive solid Geometry) representation. When carrying out this procedure, most of the computing and memory resources are used for generating and storing the octants comprising the primitives. However, the majority of those octants are not required for the representation of the final object. In this paper the extention of the top-down approach to the CSG level (i.e., generating the octree of an object directly from its CSG representation) is proposed. With this method there is no need to generate the octrees of the primitives comprising the object nor to perform Boolean operations on them. Moreover, only these octants which belong to the final object are generated.     

An algorithm for visible-line and visible-surface display of CSG models

An algorithm is presented for display of Constructive Solid Geometry (CSG) models, in which Boolean evaluation of a model is done during image generation only for the visible parts of the model.The algorithm is based on Atherton's CSG scan-line algorithm. It involves, however, dividing the image plane into strips of varying width, inside which areas are determined where only one face is visible. This may involve subdivision of an area into smaller areas.Two versions of the algorithm are presented: an efficient visible-line version for a raster display, and a visible-surface version, which turns out to be an improved variant for simple models of Atherton's algorithm.Sample images and CPU times for some models are given to show the efficiency of the algorithm.     

Visualization algorithm for CSG polyhedral solids

An algorithm is presented here to visualize here to visualize CSG solids in wireframe with hidden faces eliminated. The approach taken is to construct the image of the CSG solid directly from the CSG tree. This algorithm takes into account the face coherence property and the depth of the faces to minimize the number of rays fired during the process. It mixes a two-dimensional polygonal clipping and a ray-casting algorithm.     

Efficient slicing procedure based on adaptive layer depth normal image

In layered modeling for rapid prototyping of products, compromising slicing accuracy and time is a critical issue. Based on adaptive Layer Depth Normal Image (LDNI), this paper proposes an efficient algorithm to achieve this compromise for complex Constructive Solid Geometry (CSG) models. First, each primitive at the tree leaf is converted into an adaptive LDNI solid whose Boolean operation can be performed efficiently. Then, a layered model is constructed directly from the Booleaned LDNI solid since it is actually a set of a layered and ordered point cloud. In addition to speed, efficient use of memory is also taken into account in design of the LDNI-based slicing algorithm. The capability and efficiency of this slicing algorithm are demonstrated by examples.     

Ray tracing CSG trees using the Sticks representation scheme

A fast ray tracing algorithm of CSG tree is presented. The algorithm uses an adaptive space subdivisions approach, based on the conversion of the objects of the scene into the volumetric Sticks representation scheme. This conversion scheme, which requires O(kn²) memory space to represent data in a n³ grid, makes it possible either to obtain very fast low-quality frontal orthographic projections, or to produce a high-quality rendering of the scene in time less than that needed by classical ray tracing and nearly independent of the number of objects in the scene. Furthermore, the characteristics of the Sticks scheme can be exploited to compute geometric or topological properties of the represented objects. Comparative analyses between the Sticks representation scheme and classical space subdivision schemes and between our Sticksbased ray tracing and classical algorithms are presented.     

A new space subdivision method for ray tracing CSG modelled scenes

A new algorithm for space tracing with CSG modelled scenes is presented. Space is divided in an irregular fashion to fit the objects as closely as possible. For this reason, primitive minimal bounding boxes are computed. Space subdivision is achieved in two steps: partitioning in projection plane and depth partitioning. A set of 3D regions named cells are then created. A Boolean CSG tree is distributed into the cell structure to form in each cell the minimal boolean CSG tree using the relevant primitives. The searching process for the next cell along the ray path is performed by using a local data structure associated with each cell. The goal of this structure is to link the cells together. An improvement, named mailbox, for all space tracing algorithms is detailed. Results are presented for two scenes to compare this new algorithm with Roth's algorithm.     

Grouping of objects in a space of heterogeneous variables with the use of taxonomic decision trees

A problem of classification of objects in the presence of heterogeneous (qualitative, ordinal, nominal, and Boolean) variables is considered. Taxonomic decision trees are used to solve the problem. A quality criterion for a tree is introduced that is based on the Bayesian estimate of the Kullback-Leibler distance between distributions. Statistical modeling is applied to show the efficiency of an algorithm for constructing a tree that uses this criterion.     

Interactive Rendering of CSG Models

We describe a CSG rendering algorithm that requires no evaluation of the CSG tree beyond normalization and pruning. It renders directly from the normalized CSG tree and primitives described (to the graphics system) by their facetted boundaries. It behaves correctly in the presence of user defined, “near” and “far” clipping planes. It has been implemented on standard graphics workstations using Iris GL¹ and Open GL² graphics libraries. Modestly sized models can be evaluated and rendered at interactive (less than a second per frame) speeds. We have combined the algorithm with an existing B-rep based modeller to provide interactive rendering of incremental updates to large models.     

特征编辑技术的研究

特征编辑已成为特征造型系统中提造型能力和造型效率的关键。为此文中提出重用ＣＳＧ和ＦＤＴ的特征线修改算法,且与模型构造的历史顺序无关。同时在特征编辑中满足面特征、体特征设计的前提假设条件下,提出特处非线性修改算法。     

Construction and optimization of CSG representations

Boundary representations (B-reps) and constructive solid geometry (CSG) are widely used representation schemes for solids. While the problem of computing a B-rep from a CSG representation is relatively well understood, the inverse problem of B-rep to CSG conversion has not been addressed in general. The ability to perform B-rep to CSG conversion has important implications for the architecture of solid modelling systems and, in addition, is of considerable theoretical interest.

The paper presents a general approach to B-rep to CSG conversion based on a partition of Euclidean space by surfaces induced from a B-rep, and on the well known fact that closed regular sets and regularized set operations form a Boolean algebra. It is shown that the conversion problem is well defined, and that the solution results in a CSG representation that is unique for a fixed set of halfspaces that serve as a ‘basis’ for the representation. The ‘basis’ set contains halfspaces induced from a B-rep plus additional non-unique separating halfspaces.

An important characteristic of B-rep to CSG conversion is the size of a resulting CSG representation. We consider minimization of CSG representations in some detail and suggest new minimization techniques.

While many important geometric and combinatorial issues remain open, a companion paper shows that the proposed approach to B-rep to CSG conversion and minimization is effective in E², In E³, an experimental system currently converts natural-quadric B-reps in PARASOLID to efficient CSG representations in PADL-2.     

基于SAT求解器的故障树最小割集求解算法

故障树分析广泛应用于核工业、航空航天和交通控制等安全攸关领域的安全性分析。求解故障树的最小割集是故障树分析的关键步骤。目前,对于大规模故障树的最小割集的求解方法主要是将故障树转化为二元决策图之后求解,其主要缺点在于算法在时间和空间上的消耗严重依赖良好的变量顺序。为了减少存储资源并加快求解速度,提出了一种基于可满足性问题的故障树最小割集求解算法。首先,将求解故障树最小割集问题转化为求解布尔可满足性问题。然后,利用可满足性问题求解器,通过迭代分析求得最小可满足解集合,即为对应故障树的最小割集。实验表明,本文算法求得的最小割集准确、有效并且在空间和时间上的消耗均要优于传统的基于二元决策图的故障树最小割集求解算法。     

基于知识的设计过程保存与重构

提出基于知识的广义特征信息模型和记录设计历史的广义特征CSG树的表示方法.通过对设计知识与广义特征的封装,构建了广义特征信息模型,在该模型基础上用CSG树的方法表示了设计过程.广义特征信息模型和广义特征CSG树存储于XML格式的广义特征信息表中,实现了设计过程的保存.通过对广义特征信息表的导入和解析,重构了设计过程,实现了设计过程和设计知识的重用.最后给出了在涡轮叶片设计中的实例.     

基于树形框架的随机分组反碰撞算法

现存反碰撞算法不能有效处理中小规模标签识别问题。为此,提出一种基于树形框架的随机分组反碰撞算法。在树形算法的基础上,改进标签分组方法,采用标签随机选择的方法对标签进行分组,由此形成标签识别树。实验结果表明,该算法相对帧时隙ALOHA算法,识别吞吐率上升约10%,相对树形算法实现更简单。     

A new space subdivision for ray tracing CSG solids

Ray tracing successfully creates realistic images of constructive solid geometry (CSG) solids. We describe a nonuniform space subdivision scheme that reduces both the number of ray-object intersection computations and point classifications. Our method uses the face planes of the primitives' S-bounds in a bottom-up fashion and produces a subdivision wherein the localized CSG tree in each leaf voxel is greatly minimized. The use of S-bounds in the space subdivision effectively reduces the number of intersection computations as well. The reduction of the localized CSG tree in turn further reduces the number of intersection computations and point classifications. We briefly review existing methods for ray tracing CSG solids, describe our proposed space subdivision method, discuss our implementation and compare it to Bouatouch's (1987) method, and summarize our test results