Depth-Buffering Display Techniques for Constructive Solid Geometry

Solid modelers based on constructive solid geometry (CSG) typically generate shaded displays directly from CSG by using ray-casting techniques, which do not require informatin on the faces, edges, and vertices that bound a solid. This article describes an alternative-a simple new algorithm based on a depth-buffering or z-buffering approach. The z-buffer display algorithm operates directly on CSG, does not require explicit boundary data, and is easier to implement than ray casting. Ray-casting and z-beffering algorithms have comparable performances, but z-buffering is often faster for objects with complex surfaces, because it avoids expensive curve/surface intersection calculations. Because of their simplicity, depth-buffering algorithms for CSG are well-suited to hardware implementations, and may lead to machines simpler than those now being built for ray casting.     

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.     

Screen-Area Coherence for Interactive Scanline Display Algorithms

This article proposes and demonstrates a technique enabling polygon-based scanline hidden-surface algorithms to be used in applications that require a moderate degree of user interaction. Interactive speeds have been achieved through the use of screen-area coherence,a derivative of frame-to-frame coherence and object coherence. This coherence takes advantage of the face that most of the area of the screen does not change from one frame to the next in applications that have constant viewing positions for a number of frames and in which a majority of the image remains the same. One such application, the user interface of constructive solid geometry (CSG) based modelers, allows a user to modify a model by adding, deleting, repositioning, and performing volumetric Boolean operations on solid geometric primitives. Other possible applications include robot simulation, NC verification, facility layout, surface modeling, and some types of animation. In this article, screen-area coherence is used as the rationale for recalculating only those portions of an image that correspond to a geometric change. More specifically, this article describes a scanline hidden-surface removal procedure that uses screen-area coherence to achieve interactive speeds. A display algorithm using screen-area coherence within a CSG-based scanline hidden-surface algorithm was implemented and tested. Screen-area coherence reduced the average frame update time to about one quarter of the original time for three test sequences of CSG modeling operations.     

Accurate GPU-accelerated surface integrals for moment computation

We present algorithms for computing accurate moments of solid models that are represented using multiple trimmed NURBS surfaces and triangles. Our algorithms make use of programmable Graphics Processing Units (GPUs) to accelerate the moment computations. For NURBS surfaces, we evaluate the surface coordinates and normals accurately, with theoretical bounds, using our GPU NURBS evaluator. We have developed a framework that makes use of this data to evaluate surface integrals of trimmed NURBS surfaces in real time. Since typical solid models also contain flat planes that are usually tessellated into triangles, our framework also includes GPU acceleration of the moment contributions of such flat faces. Using our framework, we can compute volume and moments of solid models with theoretical guarantees. Our algorithms support local geometry changes, which is useful for providing interactive feedback to the designer while the solid model is being designed. We can compute the center of mass and check for stability of the solid model interactively. Other applications of such real-time moment computation include deformation modeling, animation, and physically based simulations.     

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.     

复杂疾病模型快速参数求解算法

全基因组关联研究（GWAS）是在探究人类复杂疾病相关基因的重要方法,实用有效的算法是GWAS成功的关键,因此根据疾病模型生成模拟数据对GWAS算法进行比较测试具有重要的意义。模拟测试要求根据各种输入的控制量计算出疾病模型的相关参数,但是目前缺乏相关公开的算法。提出了一个求解这些参数的分支限界算法。大量实验测试表明该算法能快速精确地计算出疾病模型的相关参数,可用于搭建GWAS算法测试平台。     

基于独立环路组合的多面体视图三维重建

提出了一种基于平面独立环路组合的多面体视图三维重建完整算法，即先把三视图中的每个视图分解成一个个独立的不可再分的平面独立环路，然后从三面视图的三个环路组中逐个取出可能的环路组合按构造实心体几何方法（CSG）构成局部实心体模型，最后将局部实心体模型组合成整体实心体模型。已按上述算法编制出了能在Auto CAD图形系统中使用的实用软件。     

Graphical model construction based on evolutionary algorithms

1 Introduction Evolutionary algorithms(EAs) [1～5] are stochastic search and optimization techniques, which were inspired by the analogy of evolution and population genetics. They have been demonstrated to be effective and robust in searching very large, varied, spaces in a wide range of applications, including classification, machine learning, ecological, so- cial systems and so on. However, most of the common evo- lutionary algorithms using simple operators are incapable of learning the reg…     

CSG-EESI: a new solid representation scheme and a conversion expertsystem

A representation scheme is proposed for describing 3-D mechanical parts and structural bodies which are formed from planes and quadratic faces. Since the method combines features of the constructive solid geometry (CSG) representation and an extension of the enhanced (EESI) spherical image representation (ESI), it is designated the CSG-EESI. In this scheme, the body model is roughly divided into two levels: the higher level corresponds to a restricted CSG tree that contains the structural information describing how the various subparts form the body; the lower level contains the geometric information for those simple subparts and represents them by an extension of enhanced spherical images. The scheme can be used both as the medium between pictorial models and relational models and as an internal model to facilitate the recognition of bodies. An expert system written in C-PROLOG on a VAX 11/750 is presented that converts BR-like models into the CSG-EESI representation is presented     

基于LMI方法的保性能迭代学习算法设计

研究基于性能的迭代学习算法设计与优化问题.首先定义了迭代域二次型性能函数,然后针对线性离散系统给出了迭代域最优迭代学习算法;基于线性矩阵不等式(LMI)方法,针对不确定线性离散系统给出了保性能迭代学习算法及其优化方法.对于这两类迭代学习算法,只要调整性能函数中的权系数矩阵,便可很好地调整迭代学习收敛速度.另外,保性能迭代学习算法设计及优化过程,可利用MATLAB工具箱很方便地求解.     

一维布尔运算算法研究

在探索集成化方法的过程中,人们逐步认识到从实体模型中提取加工特征,以实现CAD与CAM的集成是CIMS的一个重要环节.本文根据各种CSG模型面向加工特征的开放程度,提出了二层结构CSG模型最利于特征识别的观点;在总结二叉树CSG模型的各种一维布尔运算算法基础上,探讨了二层结构CSG模型一维布尔运算的快速算法。并给出了它在图形显示中的应用实例.     

Efficient editing of solid models by exploiting structural and spatial locality

Computer aided design systems based on solid modellers must provide fast visual feedback to users when objects are edited. This implies that boundary representations must be updated rapidly, because displays typically are generated in current-generation modellers from face, edge and vertex data.This paper describes algorithms for updating a boundary representation when an object's constructive solid geometry (CSG) representation is edited. The algorithms exploit the structural (representational) locality inherent in most object modifications by taking advantage of previously computed boundary representations for (sub-) objects that are not affected by the editing operations. They also exploit spatial locality by re-computing boundaries only within the spatial region where changes can occur. The algorithms are efficient, and are guaranteed to produce valid solids because they are based on CSG.     

Designing and Implementing a Grid-Distortion Mapping Based on Variational Principles

A grid-distortion mapping based on variational principles is described. The mapping is first defined between any two equivalent regular grids with minor geometric restrictions, and is then optimally extended to the interior of the source grid in a sense to be defined. The result is independent of the particular representation of the curves, and depends only on geometric properties of the grids. We then proceed to construct an approximation to the mapping defined and demonstrate its implementation. Finally, this algorithm is compared to several competing ones, in particular separable (scanline) algorithms.     

Practical nonlinear predictive control algorithms for neural Wiener models

This paper describes three nonlinear Model Predictive Control (MPC) algorithms for neural Wiener models. In all algorithms the model or the output trajectory is linearised on-line and used for prediction. In the first case model linearisation is performed in a simplified manner for the current operating of the process. In the second algorithm the predicted output trajectory is linearised along an assumed future input trajectory once at each sampling instant whereas in the third approach trajectory linearisation is carried out in an iterative way. As a result of linearisation, the future control policy is easily calculated from a quadratic programming problem or from a series of such problems. Good control accuracy and computational efficiency of described algorithms are demonstrated for two nonlinear processes: a polymerisation reactor and a neutralisation reactor are considered. Unlike many control structures for Wiener models, discussed algorithms do not need an inverse of the steady-state part of the model.     

基于反例确认的CPS不确定性模型校准

信息物理系统被广泛应用于众多关键领域,例如工业控制与智能制造.作为部署在这些关键领域中的系统,其系统质量尤为重要.然而,由于信息物理系统自身的复杂性以及系统中存在的不确定性（例如系统通过传感器感知环境时的偏差）,信息物理系统的质量保障面临巨大挑战.验证是保障系统质量的有效途径之一,基于系统模型与规约它可以证明系统是否满足要求的性质.现有一些信息物理系统的验证工作也取得了显著进展,例如模型检验技术就被已用工作用于验证系统在不确定性影响下的行为是否满足性质规约,并在性质违反的情况给出具体的反例.这些验证工作的一个重要输入就是不确定性模型,它描述了系统中不确定性的具体情况.而实际中要对系统中不确定性精确建模却并非易事,因此验证中使用的不确定性模型很可能与实际不完全相符,这将导致验证结果不准确并与现实偏离.针对这一问题,本文提出了一种基于反例确认的不确定性模型校准方法,来进一步精化验证结果以提高其准确度.首先通过确认反例在系统的执行中能否被触发来判断验证使用的不确定性模型是否精确.对于不精确的模型再利用遗传算法进行校准,并根据反例确认的结果来构造遗传算法的适应度函数以指导搜索,最后结合假设检验来帮助决定是否接受校准后的结果.在代表案例上的实验结果表明了我们提出的不确定性模型校准方法的有效性.     

Implementation, interpretation, and analysis of a suboptimal boundary finding algorithm

This paper presents a suboptimal boundary estimation algorithm for noisy images which is based upon an optimal maximum likelihood problem formulation. Both the maximum likelihood formulation and the resulting algorithm are described in detail, and computational results are given. In addition, the potential power of the likelihood formulation is demonstrated through the presentation of three simple but insightful analyses of algorithm performance. These analyses are based on a technique we have developed for comparing the accuracies of different boundary finding algorithms. This technique also helps in understanding the interplay of object shape and data models in the relative performances of boundary finders. Some of the algorithm design considerations resulting from the use of our analysis technique are new and, at first, surprising. Our technique appears to be the only one developed for comparing the accuracies of different boundary finding algorithms.     

CST: constructive solid trimming for rendering BReps and CSG

Abstract-To eliminate the need to evaluate the intersection curves in explicit representations of surface cutouts or of trimmed faces in BReps of CSG solids, we advocate using Constructive Solid Trimming (CST). A CST face is the intersection of a surface with a Blist representation of a trimming CSG volume. We propose a new GPU-based CSG rendering algorithm that trims the boundary of each primitive using a Blist of its active zone. This approach is faster than the previously reported Blister approach, eliminates occasional speckles of wrongly colored pixels, and provides additional capabilities: painting on surfaces, rendering semitransparent CSG models, and highlighting selected features in the BReps of CSG models.     

An efficient algorithm for finding the CSG representation of a simple polygon

Modeling two-dimensional and three-dimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary.We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedronP are based on the half-spaces supporting the faces ofP. For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our main contribution is an efficient and practicalO(n logn) algorithm for doing this boundary-to-CSG conversion for a simple polygon ofn sides. We also prove that such nice formulae do not always exist for general polyhedra in three dimensions.The first author would like to acknowledge the support of the National Science Foundation under Grants CCR87-00917 and CCR90-02352. The fourth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the first author was visiting the DEC Systems Research Center.