一种高效的建筑仿真模型的绘制算法方案

提出了一种有效的建筑实体建模和真实感绘制算法,其基本思路是以混合ＣＳＧ／Ｂ－Ｒｅｐ法为基础,通过参数化表面的解析重构和表面外法线的定义来构造复杂的建筑实体,同时记录各网格点的空间参数,进行真实感图形绘制。     

Bezier曲面的适应性细分和三角形化的四叉树方法

计算机生成具有浓淡的参数曲面的方法之一是先对曲面进行适应性细分,并对所得到的曲面细分三角形化,得到曲面的三角形网表示,从而可以对每个三角形施行通常的浓淡处理算法。本文介绍了适应性细分双三次Bezier曲面的方法及曲面细分的四叉树表示,在此基础上给出了一个将曲面细分三角形化的算法。该算法防止了由于适应性细分而可能产生的曲面上的裂缝。     

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.     

机械产品的特征信息处理

本文讨论了单纯采用CSG模型和单纯采用B-Rep模型来表达机械产品的特征信息时所遇到的一些实际困难,根据机械产品设计与制造一体化的特殊要求,提出了基于CSG+B-Rep数据结构的特征信息表达方案。其主要特点是以面为特征定义的基本单位,利用FSMTS中CSG与B-ReP的一致对应关系,将产品的特征信息PIT链入CSG和B-Rep组成的循环链中,其优点在于既可通过CSG摸型建立参数化的产品模型,又可通过交互方式定义和修改产品的特征信息。     

大规模地形真实感渲染技术研究

针对快速增长的数据规模和计算机图形硬件处理能力之间的矛盾,对大规模地形真实感渲染技术进行研究。采用基于四叉树的层次细节算法渲染大规模地形,设计四叉树地形的存储结构,以视距和地形粗糙度的双重标准确定地形节点的细节程度,给出利用裙边修补裂缝的方法。实验结果表明,该技术能快速实时地完成大规模地形数据的调度和场景的真实感渲染。     

Approximating CSG trees of moving objects

A discussion of the relationship between two solid representation schemes is presented: CSG trees and recursive spatial subdivision exemplified by the bintree, a generalization of the quadtree and octree. Detailed algorithms are developed and analyzed for evaluating CSG trees by bintree conversion. These techniques are shown to enable the addition of the time dimension and motion to the approximate analysis of CSG trees. This facilitates the solution of problems such as static and dynamic interference detection. A technique for projecting across any dimension is also shown. For “well-behaved” CSG trees the execution time of the conversion algorithm is directly related to the spatial complexity of the object represented by the CSG tree (i.e., as the resolution increases, it is asymptotically proportional to the number of bintree nodes and does not depend on the size or form of the CSG tree representation). The set of well-behaved CSG trees include all trees that define multidimensional polyhedra in a manner that does not give rise to tangential intersections at CSG tree nodes. This is an expanded version of a paper titled “Bintrees, CSG Trees, and Time” which appeared inProceedings of the SIGGRAPH '85 Conference, San Francisco (July 1985), pp. 121–130. This work was supported in part by the National Science Foundation under Grants DCR-83-02118 and IRI-88-02457 and in part by the Finnish Academy Deceased on August 5, 1989     

Solving CSG equations for checking equivalency between two different geometric models

For two given parametric constructive solid geometry (CSG) models, the problem of determining their parameter domains in which the two models are equivalent is addressed. Here, two CSG models are equivalent if they represent the exact same region in R³, although their constituent features and feature attributes may differ. In this paper, an approach for solving the problem in a limited scope is proposed, in which a CSG model is polyhedral, its parametric form is explicit and its feature orientations are fixed. The solution includes the equivalent parameter domain for each model and parameter mapping that associates these two models on their equivalent parameter domains. One application of this research is to identify the equivalent parameter domains of two parametric part models, respectively, in the design option space and in the capability envelope set of a parametric machining process in order to facilitate the interoperation between part design and process planning through the generated parameter mapping between these two different kinds of models.     

Direct rendering of Boolean combinations of self-trimmed surfaces

We explore different semantics for the solid defined by a self-crossing surface (immersed sub-manifold). Specifically, we introduce rules for the interior/exterior classification of the connected components of the complement of a self-crossing surface produced through a continuous deformation process of an initial embedded manifold. We propose efficient GPU algorithms for rendering the boundary of the regularized union of the interior components, which is a subset of the initial surface and is called the trimmed boundary or simply the trim. This classification and rendering process is accomplished in real time through a rasterization process without computing any self-intersection curve, and hence is suited to support animations of self-crossing surfaces. The solid bounded by the trim can be combined with other solids and with half-spaces using Boolean operations and hence may be capped (trimmed by a half-space) or used as a primitive in direct CSG rendering. Being able to render the trim in real time makes it possible to adapt the tessellation of the trim in real time by using view-dependent levels-of-detail or adaptive subdivision.     

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.     

体绘制的任意曲面切割方法

为了在体绘制的过程中,响应用户的实时交互以及对体数据进行切割。论文提出了一种预计算外部轮廓,基于ConstructiveSolidGeometry(CSG)的方法来进行切割的方法。预先计算的外部轮廓在整个体绘制过程中完成界定体元绘制的边界和进行切割交互的功能,因此提高了体元绘制和切割的效率。引入外部轮廓几何体之后,采用基于CSG的方法来进行交互式切割,保证了原有外部轮廓和切割体各自内部的拓扑关系。最后,通过对纹理坐标的实时计算,实现3D纹理的映射。论文借助于现有可编程图形流水线的功能实现该方法,完成了高效率的实时交互和绘制。     

Fast rendering of massive textured terrain data

This paper proposes a framework based on tile-pyramid model and linear quadtree tile-index, which enables the real-time rendering of out-of-core terrain data sets while guaranteeing geometric and texture accuracy. The Digital Elevation Model pyramid and the orthophoto pyramid are created in advance and the quadtree is used for constructing tile-index and managing data tiles. To achieve real-time loading of terrain dataset, the view frustum culling technology and the target-tiles searching algorithm based on resolution-testing and the tile-request prediction mechanism are used. While rendering the terrain tiles, the dynamic bintree triangulation is used. Experimental results show that based on the current personal computer, this framework can achieve good performance for real-time rendering of massive terrain dataset whose size is unlimited.     

Perception-motivated multiresolution rendering on sole-cube maps

This paper presents a novel GPU-based multiresolution rendering on sole-cube maps (SCMs), which is a variant of geometry images built upon spherical parameterization. Given spherical parametrization of a manifold mesh, the sphere domain is gnomonically projected to a closed cube, which constitutes the 6-chart sole-cube maps. A quadtree structure of SCMs and normal map atlas are then constructed by using the regular re-sampling. Then, by packing the quadtree nodes into the SCMs texture atlas, a new parallel multiresolution rendering is processed on the latest GPU in two rendering passes: the multiresolution node selection in fragment shader; the triangulation in vertex shader followed by the node culling operation in geometry shader. The proposed approach generates adaptive mesh surfaces dynamically, and can be fully implemented in GPU parallelization. The proposed scheme alleviates the computing load of multiresolution mesh refinement on CPU, and our GPU-based multiresolution rendering is demonstrated with a variety of examples. Our user study confirmed that the visual quality of the SCMs multiresolution rendering, in comparison with the meshes/geometry images rendering, is also highly efficient especially for complex models in large-scale virtual environment.     

Splat representation of parametric surfaces

Point and splat-based representations have become a suitable technique both for modeling and rendering complex 3D shapes. Converting other kinds of models as parametric surfaces to splat-based representations will allow to mix surface and splat-based models and to take advantage of the existing point-based rendering methods. In this work, we present an approach to convert a parametric surface into a splat-based representation. It works in parametric space, performs an adaptive sampling based on the surface curvature and a given error tolerance and uses power Voronoi diagrams. The goal is to approximate the surface with an optimized set of elliptical splats.     

Line art illustrations of parametric and implicit forms

A technique is presented for line art rendering of scenes composed of freeform surfaces. The line art that is created for parametric surfaces is practically intrinsic and is globally invariant to changes in the surface parameterization. This method is equally applicable for line art rendering of implicit forms, creating a unified line art rendering method for both parametric and implicit forms. This added flexibility exposes a new horizon of special, parameterization independent, line art effects. Moreover, the production of the line art illustrations can be combined with traditional rendering techniques such as transparency and texture mapping. Examples that demonstrate the capabilities of the proposed approach are presented for both the parametric and implicit forms     

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.     

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.     

On sampling regional data

The region quadtree is a very popular hierarchical data structure for the representation of binary images (regional data) and it is heavily used at the physical level of many spatial databases. Random sampling algorithms obtain approximate answers of aggregate queries on these databases efficiently. In the present report, we examine how four different sampling methods are applied to specific quadtree implementations (to the most widely used linear implementations). In addition, we examine how two probabilistic models (a parametric model of random images and a model of random trees) can be used for analysing the cost of these methods.     

虚拟战场环境中地形场景的实时简化技术

三维地形场景实时简化是构建虚拟战场环境中的基本问题,本文论述了一种基于限制四叉树的地形简化算法,实现对规则格网DEM的连续多分辨率表示,结合实时消隐技术,减少场景绘制的三角形数目,提高了大规模DEM地形场景的实时可视化和动态交互的速度。     

Manufacturing applications of octrees

It is well understood that effective and comprehensive CAD representation methods are necessary for modelling all the design and manufacturing functions in an automated environment. Recent research work has concentrated on using Constructive Solid Geometry (CSG) methods and Boundary Representation (B-Rep) schemes for representing design and manufacturing functions. This paper presents several novel ideas on the application of octree and quadtree based representation schemes in several manufacturing areas such as robotic task planning, tolerance representation and inspection, feature-based design, and assembly modelling and verification. Suggestions on the application of extended octrees for modelling metal forming operations are also presented.