Bounding Volume Research Articles

Variational 3D Shape Segmentation for Bounding Volume Computation

Abstract We propose a variational approach to computing an optimal segmentation of a 3D shape for computing a union of tight bounding volumes. Based on an affine invariant measure of e‐tightness, the resemblance to ellipsoid, a novel functional is formulated that governs an optimization process to obtain a partition with multiple components. Refinement of segmentation is driven by application‐specific error measures, so that the final bounding volume meets pre‐specified user requirement. We present examples to demonstrate the effectiveness of our method and show that it works well for computing ellipsoidal bounding volumes as well as oriented bounding boxes.

Hierarchical face cluster partitioning of polygonal surfaces and high‐speed rendering

AbstractA computer's rendering capacity cannot handle the increased amount of data when rendering high‐quality, three‐dimensional computer graphic images. This results in problems such as rendering not being possible depending on the subject image, or the rendering speed dropping too far. To resolve these problems, we propose a method for generating a new hierarchical three‐dimensional data structure based on recursive face cluster partitioning, and a high‐speed rendering data extraction algorithm using that data structure. In the proposed algorithm, local resolution control using the approximating polygon of a face cluster, and precise invisible surface culling using the bounding volume of the face cluster can be executed in parallel. High‐speed rendering can be performed with little deterioration in quality, even for a large amount of data. The effectiveness of this algorithm was confirmed with a local resolution control experiment and a large‐scale three‐dimensional model rendering experiment. © 2007 Wiley Periodicals, Inc. Syst Comp Jpn, 38(8): 32– 43, 2007; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/scj.20581

Interactive Continuous Collision Detection Using Swept Volume for Avatars

We present an interactive algorithm for continuous collision detection between a moving avatar and its surrounding virtual environment. Our algorithm is able to compute the first time of contact between the avatar and the environment interactively, and also guarantees within a user-provided error threshold that no collision ever happens before the first contact occurs.We model the avatar as an articulated body using line skeletons with constant offsets and the virtual environment as a collection of polygonized objects. Given the position and orientation of the avatar at discrete time steps, we use an arbitrary in-between motion to interpolate the path for each link between discrete instances. We bound the swept space of each link using interval arithmetic and dynamically compute a bounding volume hierarchy (BVH) to cull links that are not in close proximity to the objects in the virtual environment. The swept volumes (SVs) of the remaining links are used to check for possible interference and estimate the time of collision between the surface of the SV and the rest of the objects. Furthermore, we use graphics hardware to accelerate collision queries on the dynamically generated swept surfaces.Our approach requires no precomputation and is applicable to general articulated bodies that do not contain a loop. We have implemented the algorithm on a 2.8 GHz Pentium IV PC with an NVIDIA GeForce 6800 Ultra graphics card and applied it to an avatar with 16 links, moving in a virtual environment composed of hundreds of thousands of polygons. Our prototype system is able to detect all contacts between the moving avatar and the environment in 10–30 ms.

A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations

This paper presents a new contact searching algorithm for large deformation mortar-based contact formulations. In this algorithm, a bounding volume hierarchy, defined in the context of a binary tree, is built for each contact surface based on the geometry of the surface. A global contact searching procedure based on these bounding volume trees is first performed to find all candidate contact element pairs, and then a local searching procedure is done to find all the mortar segments having contributions to the mortar integrals that define the contact formulation. The searching algorithm is shown to be very efficient and readily applicable to a variety of large sliding contact problems.

Interactive continuous collision detection for non-convex polyhedra

We present a highly interactive, continuous collision detection algorithm for rigid, general polyhedra. Given initial and final configurations of a moving polyhedral model, our algorithm creates a continuous motion with constant translational and angular velocities, thereby interpolating the initial and final configurations of the model. Then, our algorithm reports whether the model under the interpolated motion collides with other rigid polyhedral models in environments, and if it does, the algorithm reports its first time of contact (TOC) with the environment as well as its associated contact features at TOC.Our algorithm is a generalization of conservative advancement [19] to general polyhedra. In this approach, we calculate the motion bound of a moving polyhedral model and estimate the TOC based on this bound, and advance the model by the current TOC estimate. We iterate this process until the inter-distance between the moving model and the other objects in the environments is below a user-defined distance threshold.We pose the problem of calculating the motion bound as a linear programming problem and provide an efficient, novel solution based on the simplex method. Moreover, we also provide a hierarchical advancement technique based on a bounding volume traversal tree to generalize the conservative advancement for non-convex models.Our algorithm is relatively simple to implement and has very small computational overhead of merely performing discrete collision detection multiple times. We extensively benchmarked our algorithm in different scenarios, and in comparison to other known continuous collision detection algorithms, the performance improvement ranges by a factor of 1.4∼45.5 depending on benchmarking scenarios. Moreover, our algorithm can perform CCD at 120∼15460 frames per second on a 3.6 GHz Pentium 4 PC for complex models consisting of 10K∼70K triangles.

A novel data hiding scheme for color images using a BSP tree

In this paper, we propose a novel data hiding technique for color images using a BSP (Binary Space Partitioning) tree. First, we treat the RGB values at each pixel as a three-dimensional (3D) virtual point in the XYZ coordinates and a bounding volume is employed to enclose them. Using predefined termination criteria, we construct a BSP tree by recursively decomposing the bounding volume into voxels containing one or several 3D virtual points. The voxels are then further categorized into eight subspaces, each of which is numbered and represented as three-digit binary characters. In the embedding process, we first traverse the BSP tree, locating a leaf voxel; then we embed every three bits of the secret message into the points inside the leaf voxel. This is realized by translating a point’s current position to the corresponding numbered subspace. Finally, we transform the data-embedded 3D points to the stego color image. Our technique is a blind extraction scheme, where embedded messages can be extracted without the aid of the original cover image. It achieves high data capacity, equivalent to at least three times the number of pixels in the cover image. The stego image causes insignificant visual distortion under this high data capacity embedding scheme. In addition, we can take advantage of the properties of tree data structure to improve the security of the embedding process, making it difficult to extract the secret message without the secret key provided. Finally, when we adaptively modify the thresholds used to construct the BSP tree, our technique can be robust against attacks including image cropping, pixel value perturbation, and pixel reordering. But, the scheme is not robust against image compression, blurring, scaling, sharpening, and rotation attacks.

Memory‐Conserving Bounding Volume Hierarchies with Coherent Raytracing

Abstract Bounding volume hierarchies (BVHs) are a popular method for speeding up raytracing, but they can consume a large amount of memory for complex scenes. We investigate a hierarchical scheme for encoding BVHs that reduces the BVH storage requirements by 63%–75%. The computational overhead of the scheme can be reduced to negligible levels by shooting bundles of rays through the BVH (coherent raytracing). This gives the speed of a coherency‐based raytracer combined with substantial memory savings.

Approximate collision response using closest feature maps

In this paper we consider the novel idea of closest feature maps (CFMs) applied to refinable collision response in order to address the potential issues and problems associated with over approximation of contact information for time-critical collision detection schemes that utilise sphere-tree bounding volume hierarchies. Existing solutions to time-critical collision handling can at times suffer from over-approximation of required contacting data, which may lead to undesirable or implausible physical response. Our CFM solution essentially utilises information for contact data approximation based on the underlying geometry of the colliding objects rather than potentially problematic properties of the contacting bounding volumes. The merits of the scheme lie in its simplicity and effectiveness to handle refinable collision data in an efficient manner and could quite easily be extended to incorporate other types of bounding volume hierarchies for interruptible collision handling.

A dynamic bounding volume hierarchy for generalized collision detection

In this paper, we propose a new dynamic and efficient bounding volume hierarchy for breakable objects undergoing structured and/or unstructured motion. Our object–space method is based on different ways to incrementally update the hierarchy during simulation by exploiting temporal coherence and lazy evaluation techniques. This leads to significant advantages in terms of execution speed. Furthermore, we also show how our method lends itself naturally for an adaptive low memory cost implementation, which may be of critical importance in some applications. Finally, we propose two different techniques for detecting self-intersections, one using our hierarchical data structure, and the other is an improved sorting-based method.

Rapid pairwise intersection tests using programmable GPUs

Detecting self-intersections within a triangular mesh model is fundamentally a quadratic problem in terms of its computational complexity, since in principle all triangles must be compared with all others. We reflect the 2D nature of this process by storing the triangles as multiple 1D textures in texture memory, and then exploit the massive parallelism of graphics processing units (GPUs) to perform pairwise comparisons, using a pixel shader. This approach avoids the creation and maintenance of auxiliary geometric structures, such as a bounding volume hierarchy (BVH); but nevertheless we can plug in auxiliary culling schemes, and use stencils to indicate triangle pairs that do not need to be compared. To overcome the readback bottleneck between GPU and CPU, we use a hierarchical encoding scheme. We have applied our technique to detecting self-intersections in extensively deformed models, and we achieve an order of magnitude increase in performance over CPU-based techniques such as [17].

Lightweight Bounding Volumes for Ray Tracing

This paper presents a memory-efficient auxiliary data structure for ray tracing called a lightweight bounding volume hierarchy, or LBVH. The new data structure reduces memory requirements in three ways: using implicit indexing, limited precision numbers, and a high branching factor. We show that LBVHs can be nearly as effective as standard bounding volumes in terms of speed while using significantly less memory. C++ source code for a ray tracer that implements LBVHs is provided online.

Dosimetric consequences of the application of off-line setup error correction protocols and a hull-volume definition strategy for intensity modulated radiotherapy of prostate cancer

PurposeTo evaluate the consequences of a planning volume definition based on multiple CTs and the application of off-line setup error correction for the treatment of prostate cancer with intensity-modulated radiotherapy (IMRT). Further, to compare various setup correction protocols (SCP) by their influence on the average dose distributions. Materials and methodsA planning target volume (PTV) consisting of the bounding volume of prostate contours of five CTs (CTV_hull) plus an additional margin of 5mm and a virtual Rectum_hull volume (the solid bounding volume of the five corresponding rectum contours) are used for treatment planning. Simulations of treatment courses with the non-parametric bootstrap method allow to estimate the distribution of the expected equivalent uniform dose (EUD). The impact of off-line setup error correction protocols is evaluated based on estimated EUD distributions. ResultsOff-line SCP allow to achieve the intended prostate and rectum EUD and a reliable coverage of the CTV despite the reduced margins. The EUD of the virtual hull volumes is a good estimate for the EUD of prostate and rectal wall. ConclusionTreatment planning based on Rectum_hull and CTV_hull plus setup margin as PTV in combination with SCP results in a robust and safe IMRT planning concept.

Efficient Collision Detection among Moving Spheres with Unknown Trajectories

Collision detection is critical for applications that demand a great deal of spatial interaction among objects. In such applications the trajectory of an object is often not known in advance either since a user is allowed to move an object at his/her will, or since an object moves under the rules that are hard to describe by exact mathematical formulas. In this paper we present a new algorithm that efficiently detects the collisions among moving spheres with unknown trajectories. We assume that the current position and velocity of every sphere can be probed at any time although its trajectory is unknown. We also assume that the magnitude of the acceleration of each sphere is bounded. Under these assumptions, we represent the bounding volume of the sphere as a moving sphere of variable radius, called a time-varying bound. Whenever the time-varying bounds of two spheres collide with each other, they are checked for actual collision. Exploiting these bounds, the previous event-driven approach for detecting the collisions among multiple moving spheres with ballistic trajectories is generalized for those with unknown trajectories. The proposed algorithm shows an interactive performance for thousands of moving spheres with unknown trajectories without any hardware help.

An efficient solid angle sampling technique using bounding volume approach

Solid angle sampling is an important variance‐reduced technique when solving global illumination problems by Monte Carlo methods. In this paper, we present an efficient solid angle sampling technique where a paraboloidal luminaire is taken as a case study. The efficiency of our technique is due to the fact that we employ a tight bounding volume to approximate the solid angle. Our technique includes three processes. The construction process builds a bounding volume. It is a convex, frustum‐like polyhedron with a compromise between the tightness and the vertex numbers. The projection process approximates the solid angle as a convex spherical polygon on a unit hemisphere. Finally, the triangulation process triangulates the convex spherical polygon into spherical triangles for stratified sampling. We analyzed our technique in Monte Carlo direct lighting and Monte Carlo path tracing rendering algorithms. The results show that our technique provides up to 90% sampling efficiency. The significance of the proposed technique is that solid angle sampling, from being not possible for the paraboloidal luminaire, is now feasible. In addition, this technique is efficient for sampling, and it is also applicable to other types of luminaires, such as cylindrical and conic luminaires.

Briefly Noted

Complete Copyright: An Everyday Guide for Librarians, ed. Carrie Russell. Chicago, IL: American Library Association, 2004. 262 p. $50 softcover (ISBN: 0-8389-3543-5) This spiral bound volume by one of ALA's copyright experts is at once strangely whimsical and hands-on helpful for librarians who are considering the practical implications of copyright law and policy. Organized into sections with a personal narrative (i.e., "Maggie Discovers Copyright"; "Professor Kahn Exercises Fair Use"; and "Ben's Interlibrary Loan Request is Denied") the rules, steps, regulations, and intentions of copyright are discussed in very accessible detail. The volume is oriented around these characters who show the way to understanding copyright, and it is filled with comic-book style illustrations and numerous sidebars and boxes that discuss prominent court cases, provide tips for various tasks, and list relevant "Q&As." The ALA Office of Information Technology Policy runs a companion Web site, http://www.ala.org/ala/washoff/WOissues/copyrightb/completecopyright. (T.J.) Dictionary for Library and Information Science, Joan M. Reitz. Westport, CT: Libraries Unlimited, 2004. 789 p. $50. (ISBN: 1-59158-075-7) From "abbreviation" to "Z39.50", this is a thorough dictionary of library terms and jargon. Initially compiled online as Hypertext Library Lingo, the collection of terms grew and now totals roughly 4,000. The full dictionary is also freely available online at http://lu.com/odlis/ (T.J.) From A to Zine: Building a Winning Zine Collection in Your Library, Julie Bartel. Chicago, IL: American Library Association, 2004. 168 p. $35. (ISBN: 0-8389-0886-1) Along with blogs and e-zines, zines—personal magazines, to oversimplify—are the ground floor for self-publishing output. The author argues that zine collections are valuable resources, especially for making a connection with high school and college-age students, and provides a primer on zines and zine culture as well as tips for building, maintaining, and publicizing a zine collection. (T.J.) [End Page 141] Libraries Without Walls 5: The Distributed Delivery of Library and Information Services, ed. Peter Brophy, Shelagh Fisher, and Jenny Craven. London: Facet Publishing, 2004. 320 p. $80 (ISBN: 1-85604-511-0) This fifth installment of the proceedings of the international "Libraries Without Walls" conference maintains the conference's focus on delivery of library services outside of the physical library. The contributions, most from U.K. librarians, are varied and address topics such as the integration of remote library services with distance learning services, systems and software, and the usability of digital libraries. While the jargon and acronyms of the primarily European contributions may be different, the issues addressed and, in some cases, the specific software and examples will be familiar to any academic librarian. (T.J.) Performance Management and Appraisal: A How-To-Do-It Manual for Librarians, G. Edward Evans. New York: Neal-Schuman, 2004. 293 p. $75 softcover (ISBN: 1-55570-498-0) This very practical volume is designed to illustrate the various types of performance appraisal and provide detailed guidance in conducting these appraisals in all types of libraries. With hopes that he might help move libraries to "reassess, redesign and restructure" their current assessment systems, the author outlines several broad approaches and methods that might be considered. Dozens of sample assessment forms are provided. (T.J.) Serials in the Park: NASIG 2003, ed. Patricia Sheldahl Frency and Richard L. Worthing. New York: Haworth Press, 2004. 356 p. $34.95 softcover (ISBN:0-7890-2565-5) Published simultaneously as The Serials Librarian, v. 46, nos. 1/2 and 3/4 This is the proceedings of the 18th annual North American Serials Interest Group conference in Portland, OR, and the papers in this volume leave hardly a single park metaphor unturned. The topics range widely but are primarily divided between personnel and management issues and issues specific to electronic journals. Many serials librarians swear by NASIG as their most valuable gathering, and the papers presented should be of interest to serialists anywhere. (T.J.)

An Efficient and Robust Ray-Box Intersection Algorithm

The computational bottleneck in a ray tracer using bounding volume hierarchies is often the ray intersection routine with axis-aligned bounding boxes. We describe a version of this routine that uses IEEE numerical properties to ensure that those tests are both robust and efficient. Sample source code is available online.

Collision detection for deforming necklaces*1

In this paper, we propose to study deformable necklaces—flexible chains of balls, called beads, in which only adjacent balls may intersect. Such objects can be used to model macro-molecules, muscles, ropes, and other linear objects in the physical world. We exploit this linearity to develop geometric structures associated with necklaces that are useful for collision detection in physical simulations. We show how these structures can be implemented efficiently and maintained under necklace deformation. In particular, we study a bounding volume hierarchy based on spheres which can be used for collision and self-collision detection of deforming and moving necklaces. As our theoretical and experimental results show, such a hierarchy is easy to compute and, more importantly, is also easy to maintain when the necklace deforms. Using this hierarchy, we achieve a collision detection upper bound of O( n log n ) in two dimensions and O( n 2−2/ d ) in d -dimensions, d ⩾3. To our knowledge, this is the first subquadratic bound proved for a collision detection algorithm using predefined hierarchies. In addition, we show that the power diagram, with the help of some additional mechanisms, can be used to detect self-collisions of a necklace in a way that is complementary to the sphere hierarchy.

Collision detection for deforming necklaces

In this paper, we propose to study deformable necklaces—flexible chains of balls, called beads, in which only adjacent balls may intersect. Such objects can be used to model macro-molecules, muscles, ropes, and other linear objects in the physical world. We exploit this linearity to develop geometric structures associated with necklaces that are useful for collision detection in physical simulations. We show how these structures can be implemented efficiently and maintained under necklace deformation. In particular, we study a bounding volume hierarchy based on spheres which can be used for collision and self-collision detection of deforming and moving necklaces. As our theoretical and experimental results show, such a hierarchy is easy to compute and, more importantly, is also easy to maintain when the necklace deforms. Using this hierarchy, we achieve a collision detection upper bound of O( nlog n) in two dimensions and O( n 2−2/ d ) in d-dimensions, d⩾3. To our knowledge, this is the first subquadratic bound proved for a collision detection algorithm using predefined hierarchies. In addition, we show that the power diagram, with the help of some additional mechanisms, can be used to detect self-collisions of a necklace in a way that is complementary to the sphere hierarchy.

CYLINDRICAL HIERARCHY FOR DEFORMING NECKLACES

Recently, Guibas et al.10 studied deformable necklaces — flexible chains of balls, called beads, in which only adjacent balls can intersect. In this paper, we investigate the problem of covering a necklace by cylinders. We consider several problems under different optimization criteria. We show that optimal cylindrical cover of a necklace with n beads in ℝ3 by k cylinders can be computed in polynomial time. We also study a bounding volume hierarchy based on cylinders.

Adaptive Ray Tracing of Subdivision Surfaces

Abstract Subdivision Surfaces as well as (interactive) ray tracing have become an important issue in computer graphics.But ray tracing of subdivision surfaces has received only little attention. We present a new approach for raytracing of subdivision surfaces. The algorithm uses a projection of the ray onto the surface and works mainly intwo dimensions along this projection. While proceeding from patch to patch, we examine the bounding volume oftheir borders: the lower the distance between ray and subdivision surface, the more refinement steps are adaptivelyapplied to the surface but only along the projection of the ray. The adaptive refinement of a patch is controlled bycurvature, size, its membership to the silhouette, and its potential contribution to the light transport. The algorithmis simple and mainly consists of elementary geometric computations. Hence it is fast and easy to implementwithout the need for elaborate preprocessing. The algorithm is robust in the sense that it deals with all features ofsubdivision surfaces like creases and corners. Categories and Subject Descripters (according to ACM CCS): I.3.7 [Computer Graphics]: Raytracing