Computing on rays: A parallel approach for surface mesh modeling from multi-material volumetric data

Ray representation (Ray-rep) of a solid has been studied and used in the solid modeling community for many years because of its compactness and simplicity. This paper presents a parallel approach for mesh surface modeling from multi-material volume data using an extended Ray-rep as an intermediate, where every homogeneous region is enclosed by a set of two-manifold surface meshes on the resultant model. The approach consists of three major algorithms: firstly, an algorithm is developed to convert the given multi-material volumetric data into a Ray-rep for heterogeneous solid; secondly, filtering algorithm is exploited to process the rays of heterogeneous solid in parallel; and lastly, the adaptive mesh surfaces are generated from the Ray-rep through a dual-contouring like algorithm. Here the intermediate surfaces between two constituent materials can be directly extracted without building the volumetric mesh, and the manifold topology is preserved on each surface patch. Furthermore, general offset surface can be easily computed in this paradigm by designing a special parallel operator for the rays.     

Lazy Solid Texture Synthesis

Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre‐computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre‐process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates high resolution solid textures on surfaces within seconds. Memory usage and synthesis time only depend on the output textured surface area. The GPU implementation of our method rapidly synthesizes new textures for the surfaces appearing when interactively breaking or cutting objects.     

Fast generation of spherical slicing surfaces for irregular volume rendering

An efficient algorithm for generating a set of concentric spherical slicing surfaces for volume rendering of irregular volume datasets is presented. Our original algorithm, which approximates volume rendering by accumulating concentric spherical slicing surfaces from back to front, generates these surfaces by means of a conventional isosurface generation algorithm. However, this causes a performance bottleneck. To solve the problem, we propose a proliferous generation of slicing surfaces from seed cells, which are automatically determined according to the extremum points of the values of distances from a viewing point. A benchmark test shows that this approach can improve the performance significantly. In addition, we compare this algorithm with a raycasting algorithm that we proposed previously, and discuss a criterion for selecting which one to use for maximizing the performance     

Equidistant Smoothing of Polyhedra with Arbitrary Topologies

Smoothing of polyhedron with arbitrary topology is an important issue in CAGD and CAD/CAM, but so far it is deemed to be difficult to smooth the complex corners of a polyhedron. In this paper, the concept of distance surfaces of a surface and a solid is introduced, and the incisive properties of such surfaces are addressed which provide a theoretical foundation for modifying a general corner. The method is based on making constricted volume and the maximum distance the volume can be constricted is given too. It is shown that by the proposed method in this paper any polyhedron can be G¹ smoothed with quadraic and, sometimes toroidal surfaces. The new approach is suitable for engineering design and NC machining. The associated algorithm based on the classification theorem of corners is simple, fast and robust.     

Boundary of the volume swept by a free-form solid in screw motion

The swept volume of a moving solid is a powerful computational and visualization concept. It provides an excellent aid for path and accessibility planning in robotics and for simulating various manufacturing operations. It has proven difficult to evaluate the boundary of the volume swept by a solid bounded by trimmed parametric surfaces undergoing an arbitrary analytic motion. Hence, prior solutions use one or several of the following simplifications: (1) approximate the volume by the union of a finite set of solid instances sampled along the motion; (2) approximate the curved solid by a polyhedron; and (3) approximate the motion by a sequence of simpler motions. The approach proposed here is based on the third type of simplification: it uses a polyscrew (continuous, piecewise-helical) approximation of the motion. This approach leads to a simple algorithm that generates candidate faces, computes the two-cells of their arrangement, and uses a new point-in-sweep test to select the correct cells whose union forms the boundary of the swept volume.     

基于任意骨架的隐式曲面造型技术

给出了一个新的基于任意多面体网格骨架的构造性自由曲面造型算法.算法首先由每个给定骨架构造出一个距离场,然后利用隐函数光滑过渡技术和CSG(constructive solid geometry)表示技术将所构造的隐式曲面自由地两两粘合成一张光滑曲面.隐式曲面的多边形化算法则用来生成最终曲面网格.以任意骨架作为基本体素,突破了传统隐式曲面以点为基本骨架的限制.而且,距离曲面很好地逼近了原骨架形状,使用户可直观地对复杂曲面进行交互设计.而形变函数的引入,则极大地丰富了此方法的造型能力.实验结果表明,基于该算法的原型系统能够方便、直观地构造复杂的自由曲面.     

Determining interference between pairs of solids defined constructively in computer animation

This paper presents theory and implementation of a method for detecting interference between a pair of solid objects. Often at times, when performing simulations, two solids may unwittingly interpenetrate each other. The two components of the system presented in this paper are: (1) a surface representation method to model solid objects; and (2) a method for detecting interference. Body representation of a solid in this system is based upon enveloping each solid with surfaces (called positive entities). Most computer aided design (CAD) systems use solid modeling techniques to represent solid objects. Since most solid models use Boolean operations to model complex objects, a method is presented to envelop complex objects with parametric surfaces. A method for tracing intersection curves between two surfaces is also presented. Discontinuities on surfaces are defined as negative entitics in order to extend the method to complex solids. Determining interference is based upon a numerical algorithm for computing points of intersection between boundary curves and parametrized entities. The existence of segments of these curves inside the boundary of positive and negative entities is established by computing the circulation of a function around the boundary curve. Interference between two solids is then detected. No limitations are imposed on the convexity or simplicity of the boundary curves treated.     

Automatic decomposition of 3D solids into contractible pieces using Reeb graphs

This work is motivated by the need to generate volumetric spline models for isogeometric analysis. There exist numerous constructions of volumetric spline models that represent contractible solids. We present a novel decomposition algorithm that splits general solids into pieces that can be dealt with by these existing methods. More precisely, we present a method to automatically decompose solid objects in boundary representation into pieces with fewer or no tunnels by cutting them with auxiliary surfaces. The segmentation is guided by a reduced form of the object’s boundary and volume Reeb graphs with respect to several Morse functions, the level sets of which define the cutting surfaces. Special attention is paid to the selection of suitable cutting surfaces, where we employ a quality criterion to avoid the creation of badly shaped pieces.     

针对全空子数据体的GPU体绘制

目的 体绘制是3维数据可视化的主要方法之一。用于体绘制的数据体中包含有大量的空体素,导致光线投射算法进行没有意义的重采样计算,必然降低绘制算法效率。针对全空子数据体体绘制低效问题,提出基于GPU体高效绘制方法。方法 利用八叉树数据结构组织数据,有效管理包含许多空体素的子数据体。通过绘制八叉树非全空叶子节点子数据体表面,使光线投射算法中起始和终止重采样位置更接近数据体中的可视部分,同时根据八叉树全空节点子数据体判定纹理查询结果,计算合适的跳跃步长,快速跳过八叉树中全空节点子数据体。结果 当数据体中空体素较多时,确定合适的八叉树深度,有效地跳过数据体中的空体素,减少体绘制运算量,实现对原基于体包围盒表面绘制的GPU光线投射算法的加速。结论 设计不透明度函数,凸显数据体中层位面,并将算法成功应用于地震数据可视化,取得很好应用效果。     

A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint

In this paper, we present an accurate and efficient algorithm to generate constant mean curvature surfaces with volume constraint using a phase-field model. We implement our proposed algorithm using an unconditionally gradient stable nonlinear splitting scheme. Starting from the periodic nodal surface approximation to minimal surfaces, we can generate various constant mean curvature surfaces with given volume fractions. We generate and study the Schwarz primitive (P), Schwarz diamond (D), and Schoen gyroid (G) surfaces with various volume fractions. This technique for generating constant mean curvature surfaces can be used to design biomedical scaffolds with optimal mechanical and biomorphic properties.     

基于黎曼度量参数曲面四边形网格生成方法及UG 实现

论文给出了基于黎曼度量的参数曲面网格生成的改进铺砖算法。阐述了曲 面自身的黎曼度量,并且运用黎曼度量计算二维参数域上单元节点的位置,从而使映射到三 维物理空间的四边形网格形状良好。文中对原有铺砖法相交处理进行了改进,在运用铺砖法 的同时调用UG-NX 强大的二次开发库函数获取相应的信息,直接在UG-NX 模型的表面生 成四边形网格。算例表明,该法能在曲面上生成质量好的网格。     

Automatic mesh generation scheme for a two- or three-dimensional triangular curved surface

Two different methods of automatic mesh generation—the area system and the isoparametric coordinate system—both using quadratic shape function, have been introduced to generate meshes for curved triangular surfaces. Depending on geometrical and material variations, part of the region to be discretized is manually divided into a number of triangular zones. An algorithm is given to generate meshes of triangular elements with three or six nodes automatically using quadratic shape function and area-coordinate system for these zones. Any node number can be assigned to the vertices of a triangular zone. Different zones will be tied together automatically by using a merge algorithm. The application of the volume-coordinate system and quadratic shape function in generating solid elements for triangular prisms will also be discussed.     

Volumetric data exploration using interval volume

A new type of geometric model called Interval volume for volumetric data exploration is presented. An interval volume represents a three dimensional subvolume for which the associate scalar values lie within a user specified interval, and provides one of the promising approaches to solid fitting, which is an extended concept of traditional surface fitting. A well known isosurfacing algorithm called Marching Cubes is extended to obtain a solid fitting algorithm, which extracts from a given volumetric data set a high resolution, polyhedral solid data structure of an interval volume. Branch-on-Need Octree is used as an auxiliary data structure to accelerate the extraction process. A variety of interval volume rendering methods and principal related operations, including measurements and focusing, are also presented. The effectiveness of measurement coupled visualization capabilities of the presented approach is demonstrated by application to visualizing a four dimensional simulated data from atomic collision research     

Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data

Scientific visualization has many effective methods for examining and exploring scalar and vector fields, but rather fewer for bivariate fields. We report the first general purpose approach for the interactive extraction of geometric separating surfaces in bivariate fields. This method is based on fiber surfaces: surfaces constructed from sets of fibers, the multivariate analogues of isolines. We show simple methods for fiber surface definition and extraction. In particular, we show a simple and efficient fiber surface extraction algorithm based on Marching Cubes. We also show how to construct fiber surfaces interactively with geometric primitives in the range of the function. We then extend this to build user interfaces that generate parameterized families of fiber surfaces with respect to arbitrary polygons. In the special case of isovalue‐gradient plots, fiber surfaces capture features geometrically for quantitative analysis that have previously only been analysed visually and qualitatively using multi‐dimensional transfer functions in volume rendering. We also demonstrate fiber surface extraction on a variety of bivariate data.     

基于GPU的交互式体数据切割

为实现实时高效的体数据切割操作,提出一种将人机交互和基于GPU的体绘制相结合的切割方法.先通过人机交互生成多个切割体的几何形状并三角化,将其作为基于GPU的光线投射算法的代理面,然后利用深度剥离算法获得光线在所有代理面上的出入射点坐标,并用多个通道完成体绘制.该方法在单个3D纹理上进行,可以实现多个任意形状的切割体切割,在节省GPU内存空间的同时,提高了切割后的绘制效率.     

Defining and rendering of textured objects through the use of exponential functions

We present a method for modeling and rendering various surface textures by actually defining them over the entire three-dimensional space. Once this is done any surface representable by an implicit function can be rendered. We do not do any volume rendering; instead the surfaces are ray traced directly. The implicit functions used to define various surfaces are taken to be exponential functions with exponents with large magnitudes. Use of such functions allows us to define even such surfaces as the surface (entire) of a rectangular solid or a truncated cone as precisely as we want. It also allows us to model complex surfaces through piecewise modeling and blending of different analytical surfaces. Even for simple surfaces, it allows us to calculate the ray-surface points of intersection and the normals at those points very precisely because of the large relative variation of the implicit functional density in the entire three-dimensional space. Both regular and stochastic textures can be modeled and rendered. A complete methodology together with several examples is presented.     

A high-speed integrated renderer for interpreting multiple 3D volume data

This paper proposes an integrated rendering algorithm for visualizing 3D volumetric and geometric data, such as surfaces, lines and points, simultaneously with depth information, and other algorithms for improving the performance of the rendering process of the first. The first algorithm extends a volume rendering algorithm based on ray-tracing so that it can handle both 3D volumetric and geometric data. It processes these data in accordance with their original representation formats to eliminate conversion artefacts such as spurious or missing surfaces, and also gives special treatment to volume segments so as to avoid errors in visibility at the intersections between volume segments and geometric data. The other algorithms employ adaptive termination of ray-tracing, elimination of rays that do not intersect the volume, and adaptive undersampling over an image plane. These improve the performance by three to seven times over the brute-force approach. The cost and versatility of the algorithm are evaluated by using data from the results of 3D computational fluid dynamics.     

An Interactive Deformation System for Granular Material

Computer Graphics (CG) animations of natural phenomena are currently widely used for movies and in video games. Granular materials occur widely in nature, and therefore it is necessary that CG animations represent ground surfaces composed of a granular material as well as model deformations when the granular material comes into contact with other physical rigid objects (called solid objects). In this paper, we propose a deformation algorithm for ground surfaces composed of granular material. The deformation algorithm is divided into three steps: (1) detection of the collision between a solid object and the ground surface, (2) displacement of the granular material and (3) erosion of the material at steep slopes. The proposed algorithm can handle solid objects of various shapes, including concave polyhedra by additionally using a layered data structure called the Height Span Map. Furthermore, a texture sliding technique is presented to render the motion of granular materials. In addition, our implementation of the deformation algorithm can be used at interactive frame rates.