Bounding Volume Hierarchy Research Articles

Precise convex hull computation for freeform models using a hierarchical Gauss map and a Coons bounding volume hierarchy

We present an interactive-speed algorithm for computing the precise convex hull of freeform geometric models. The algorithm is based on two pre-built data structures: (i) a Gauss map organized in a hierarchy of normal pyramids and (ii) a Coons bounding volume hierarchy (CBVH) which effectively approximates freeform surfaces with a hierarchy of bilinear surfaces. For the axis direction of each normal pyramid, we sample a point on the convex hull boundary using the CBVH. The sampled points together with the hierarchy of normal pyramids serve as a hierarchical approximation of the convex hull, with which we can eliminate the majority of redundant surface patches. We compute the precise trimmed surface patches on the convex hull boundary using a numerical tracing technique and then stitch them together in a correct topology while filling the gaps with tritangent planes and bitangent developable scrolls. We demonstrate the effectiveness of our algorithm using experimental results.

Fast Collision Detection and Deformation of Soft Tissue in Virtual Surgery

In the virtual scene of robot assisted virtual surgery simulation system, the surgical instruments achieve complex motion following the haptic devices and the soft tissue deforms continuously under interaction forces. In order to meet the rapidity of collision detection, an algorithm based on changeable direction hull bounding volume hierarchy is proposed. Strategy of combining surface model with body model is developed for soft tissue deformation. Skeleton sphere model of soft tissue is built. Deformation can be achieved based on mass-spring theory after matching collision information with the skeleton sphere model. The experiments show that the proposed collision detection method implements faster speed compared with fixed direction hull algorithm and soft tissue deforms through combination of collision information with sphere model.

Radial view based culling for continuous self-collision detection of skeletal models

We present a novel radial-view-based culling method for continuous self-collision detection (CSCD) of skeletal models. Our method targets closed triangular meshes used to represent the surface of a model. It can be easily integrated with bounding volume hierarchies (BVHs) and used as the first stage for culling non-colliding triangle pairs. A mesh is decomposed into clusters with respect to a set of observer primitives (i.e., observer points and line segments) on the skeleton of the mesh so that each cluster is associated with an observer primitive. One BVH is then built for each cluster. At the runtime stage, a radial view test is performed from the observer primitive of each cluster to check its collision state. Every pair of clusters is also checked for collisions. We evaluated our method on various models and compared its performance with prior methods. Experimental results show that our method reduces the number of the bounding volume overlapping tests and the number of potentially colliding triangle pairs, thereby improving the overall process of CSCD.

Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes

Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaus-sian kernel functions is employed to generate implicit models for biomolecules. The coefficients in the summation are designed as functions of the structure indices, which specify the structures at a certain level and enable a local resolution control on the biomolecular surface. A method called neighboring search is adopted to locate the grid points close to the expected biomolecular surface, and reduce the number of grids to be analyzed. For a specific grid point, a KD-tree or bounding volume hierarchy is applied to search for the atoms contributing to its density computation, and faraway atoms are ignored due to the decay of Gaussian kernel functions. In addition to density map construction, three modes are also employed and compared during mesh generation and quality improvement to generate high quality tetrahedral meshes: CPU sequential, multi-core CPU parallel and GPU parallel. We have applied our algorithm to several large proteins and obtained good results.

Quad Separation Algorithm for Bounding-Volume Hierarchies Construction in Virtual Environment Application

In order to perform fast collision detection technique in Virtual Environment Application, researchers need to maintain the behaviour of the object itself before the objects come into contact. By enhancing the speed of intersection using Bounding-Volume Hierarchies technique, it helps to reduce the complexity and speed up the intersection process. Thus, in this paper we presented our novel algorithm for constructing Bounding-Volume Hierarchies using Quad Splitting method. Together with the Quad Splitting method is the implementation of Spatial Object Median Splitting technique (SOMS) in order to create a well-balanced tree for the object. We believed the key of performing fast intersection between two or more objects in Virtual Environment Application required a well-balanced and proper tree technique for Bounding-Volume hierarchies.

Massively Parallel Hierarchical Scene Processing with Applications in Rendering

AbstractWe present a novel method for massively parallel hierarchical scene processing on the GPU, which is based on sequential decomposition of the given hierarchical algorithm into small functional blocks. The computation is fully managed by the GPU using a specialized task pool which facilitates synchronization and communication of processing units. We present two applications of the proposed approach: construction of the bounding volume hierarchies and collision detection based on divide‐and‐conquer ray tracing. The results indicate that using our approach we achieve high utilization of the GPU even for complex hierarchical problems which pose a challenge for massive parallelization. The results indicate that using our approach we achieve high utilization of the GPU even for complex hierarchical problems which pose a challenge for massive parallelization.

Fast BVH construction and refit for ray tracing of dynamic scenes

As the complexity of virtual environments increases, it becomes a critical issue to ray tracing of dynamic scenes interactively. In this paper, we propose an effective method to address this issue. Firstly, we improve the Surface Area Heuristics (SAH) based bounding volume hierarchies (BVHs) construction algorithm and present a sub-interval search criterion for predicting the optimal split plane position. Compared with the standard SAH approach, our algorithm is much faster but has a little quality degradation. Secondly, we present two new BVH refitting operations, which could run fast and obtain considerable quality of BVHs. The two operations are general and applicable to complex and dynamic scenes including a wide range of deformation. Lastly we use multithread to handle the dynamic scenes during animation, one thread for BVHs rebuilding asynchronously, the others for BVHs refitting and ray tracing. The results of this experiment show that our method is effective. Compared with the previous works, it obtains higher and smoother frame rate.

Realistic deformation of 3D human blood vessels

ABSTRACTWe present a real‐time algorithm for realistically deforming 3D human blood vessels, while automatically detecting and avoiding interference among a large number of blood vessels under deformation. Sweep surfaces are employed for this purpose. Using a dynamic bounding volume hierarchy, specially designed for sweep surfaces, we support collision detection and other related geometric computations in real time. Copyright © 2013 John Wiley & Sons, Ltd.

Fast Insertion‐Based Optimization of Bounding Volume Hierarchies

AbstractWe present an algorithm for fast optimization of bounding volume hierarchies (BVH) for efficient ray tracing. We perform selective updates of the hierarchy driven by the cost model derived from the surface area heuristic. In each step, the algorithm updates a fraction of the hierarchy nodes to minimize the overall hierarchy cost. The updates are realized by simple operations on the tree nodes: removal, search and insertion. Our method can quickly reduce the cost of the hierarchy constructed by the traditional techniques, such as the surface area heuristic. We evaluate the properties of the proposed method on fourteen test scenes of different complexity including individual objects and architectural scenes. The results show that our method can improve a BVH initially constructed with the surface area heuristic by up to 27% and a BVH constructed with the spatial median split by up to 88%.

PDQ: Parallel Distance Queries for deformable meshes

This paper presents a new algorithm to efficiently maintain Bounding-Volume Hierarchies (BVHs) for fast distance queries with deformable polygon meshes using multi-core architectures. The method involves inflating the bounding volumes in an efficient manner to guarantee the enclosure of the deformable model within the BVH at all times. This is done at low additional computation and memory cost without significantly degrading the quality of the BVH and also in a fashion that allows a simple parallel implementation. Additionally, to facilitate fast queries specifically for deforming meshes, we propose a novel algorithm for the bottom-up construction of BVHs that results in much faster distance queries.

Efficient Hausdorff Distance computation for freeform geometric models in close proximity

We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results.

Real‐time cutting simulation of meshless deformable object using dynamic bounding volume hierarchy

ABSTRACTThis paper proposes a novel method for a real‐time cutting simulation of deformable objects using meshless method. The method utilizes a rapid refinement of topological relations among the simulation nodes of meshless deformable objects. Topological relations are defined as an undirected graph based on a visibility criterion. The graph connects the adjacent nodes that lie within a support of each node. The topological relations are refined by removing the edges of the graph that is intersected by the cut surface during the cutting simulation. Our approach utilizes a bounding volume hierarchy (BVH) to accelerate the computation of the intersection test. The BVH reconstruction algorithm is proposed to account for the cases where pieces of the object are completely cut out from the object. Algorithms to examine the connectivity among simulation nodes and accordingly reconstructing the BVH using two‐level BVH are presented. The proposed approach achieves real‐time cutting simulation of deformable objects through the rapid refinement of the topological relation. In addition, the computational performance of the cutting procedure is preserved during the entire simulation, thanks to the real‐time reconstruction of the BVH. Copyright © 2012 John Wiley & Sons, Ltd.

그래픽 하드웨어를 이용한 분자용 보로노이 다이어그램 계산

본 논문에서는 주어진 단백질 분자에 대해 3차원 보로노이 다이어그램을 계산하는 알고리즘을 제안한다. 분자는 반경이 서로 다른 구의 집합으로 표현되며, 각 구의 반경은 원자의 반데르바스 (van der Waals) 반경에 대응한다. 보로노이 다이어그램은 3차원 공간을 복셀(voxel)의 집합으로 분할한 뒤, 보로노이 다이어그램을 포함하는 복셀을 보수적으로 추출함으로써 구성된다. 분자의 계층적 성질을 이용하여 BVH(bounding volume hierarchy)를 구성하고, CUDA 프로그래밍을 통하여 그래픽 하드웨어 가속을 활용함으로써 계산 시간 효율성을 높인다. 공간이 최대 <TEX>$2^{24}$</TEX>개의 복셀로 분할될 경우, 단일 코어 CPU로 구현하는 알고리즘에 비해 계산 속도가 323배 가량 향상 되었다. We present an algorithm that computes a 3 dimensional Voronoi diagram for a protein molecule in this paper. The molecule is represented as a set of spheres with van der Waals radii. The Voronoi diagram is constructed in the 3D space by finding the voxels containing it. For the feasibility of the computation, we represent the molecule as a BVH (bounding volume hierarchy), and our system is accelerated by modern graphics hardware with CUDA programming support. Compared to single-core CPU implementations, experimental results show 323 times faster performance in the computation time, when the space is partitioned into <TEX>$2^{24}$</TEX> voxels.

Energy-based self-collision culling for arbitrary mesh deformations

In this paper, we accelerate self-collision detection (SCD) for a deforming triangle mesh by exploiting the idea that a mesh cannot self collide unless it deforms enough. Unlike prior work on subspace self-collision culling which is restricted to low-rank deformation subspaces, our energy-based approach supports arbitrary mesh deformations while still being fast. Given a bounding volume hierarchy (BVH) for a triangle mesh, we precompute Energy-based Self-Collision Culling (ESCC) certificates on bounding-volume-related sub-meshes which indicate the amount of deformation energy required for it to self collide. After updating energy values at runtime, many bounding-volume self-collision queries can be culled using the ESCC certificates. We propose an affine-frame Laplacian-based energy definition which sports a highly optimized certificate pre-process, and fast runtime energy evaluation. The latter is performed hierarchically to amortize Laplacian energy and affine-frame estimation computations. ESCC supports both discrete and continuous SCD with detailed and nonsmooth geometry. We observe significant culling on many examples, with SCD speed-ups up to 26X.

Energy-based self-collision culling for arbitrary mesh deformations

In this paper, we accelerate self-collision detection (SCD) for a deforming triangle mesh by exploiting the idea that a mesh cannot self collide unless it deforms enough. Unlike prior work on subspace self-collision culling which is restricted to low-rank deformation subspaces, our energy-based approach supports arbitrary mesh deformations while still being fast. Given a bounding volume hierarchy (BVH) for a triangle mesh, we precompute Energy-based Self-Collision Culling (ESCC) certificates on bounding-volume-related sub-meshes which indicate the amount of deformation energy required for it to self collide. After updating energy values at runtime, many bounding-volume self-collision queries can be culled using the ESCC certificates. We propose an affine-frame Laplacian-based energy definition which sports a highly optimized certificate pre-process, and fast runtime energy evaluation. The latter is performed hierarchically to amortize Laplacian energy and affine-frame estimation computations. ESCC supports both discrete and continuous SCD with detailed and nonsmooth geometry. We observe significant culling on many examples, with SCD speed-ups up to 26X.

Geometry Presorting for Implicit Object Space Partitioning

AbstractWe present a new data structure for object space partitioning that can be represented completely implicitly. The bounds of each node in the tree structure are recreated at run‐time from the scene objects contained therein. By applying a presorting procedure to the geometry, only a known fraction of the geometry is needed to locate the bounding planes of any node. We evaluate the impact of the implicit bounding plane representation and compare our algorithm to a classic bounding volume hierarchy. Though the representation is completely implicit, we still achieve interactive frame rates on commodity hardware.

Rasterized Bounding Volume Hierarchies

AbstractWe present the rasterized bounding volume hierarchy (RBVH), a compact data structure that accelerates approximate ray casting of complex meshes and provides adjustable level of detail. During construction, we identify subtrees of BVHs containing surfaces that can be represented by height fields. For these subtrees the conventional ray‐surface intersection, which possibly involves a large number of triangles, is replaced by a simple ray marching procedure to find the intersection with the surface. We describe GPU algorithms for construction, ray casting, and data querying of the RBVH that achieve comparable or higher performance than state of the art acceleration structures for triangle meshes. Moreover, RBVHs provide an inherent surface parameterization for storing data on the surfaces and natively handle triangle and point‐based surface representations. We also show that RBVHs support adaptive level‐of‐detail and can be combined with traditional BVHs to handle complex scenes.

Visibility driven BVH build up algorithm for ray tracing

The minimization of traversal cost using surface area heuristic is extensively used to build high quality spatial subdivisions and bounding volume hierarchies for ray tracing. Despite the fair performance of trees built with the cost model, it is known that the underlying assumptions for surface area heuristics are not realistic. In this paper we show how the cost function of the surface area heuristic can be improved on using the assumed visibility of geometric primitives such as triangles. This way the build algorithm utilizes the exact or assumed visibility to construct more efficient BVHs by traversing smaller portion of the hierarchy. We show that by these inexpensive modifications to the cost function we can speed up the ray traversal by approximately 102% on average for path tracing of highly occluded scenes compared to standard surface area heuristics. Moreover, it is also possible to lower the construction time and memory usage by subdividing only those parts of the animated scene through which rays are expected to be traversed.

High accuracy NC milling simulation using composite adaptively sampled distance fields

We describe a new approach to shape representation called a composite adaptively sampled distance field (composite ADF) and describe its application to NC milling simulation. In a composite ADF each shape is represented by an analytic or procedural signed Euclidean distance field and the milled workpiece is given as the Boolean difference between distance fields representing the original workpiece volume and distance fields representing the volumes of the milling tool swept along the prescribed milling path. The computation of distance field of the swept volume of a milling tool is handled by an inverted trajectory approach where the problem is solved in tool coordinate frame instead of a world coordinate frame. An octree bounding volume hierarchy is used to sample the distance functions and provides spatial localization of geometric operations thereby dramatically increasing the speed of the system. The new method enables very fast simulation, especially of free-form surfaces, with accuracy better than 1 micron, and low memory requirements. We describe an implementation of 3 and 5-axis milling simulation.

Efficient Image‐Based Proximity Queries with Object‐Space Precision

AbstractWe present an efficient algorithm for object‐space proximity queries between multiple deformable triangular meshes. Our approach uses the rasterization capabilities of the GPU to produce an image‐space representation of the vertices. Using this image‐space representation, inter‐object vertex‐triangle distances and closest points lying under a user‐defined threshold are computed in parallel by conservative rasterization of bounding primitives and sorted using atomic operations. We additionally introduce a similar technique to detect penetrating vertices. We show how mechanisms of modern GPUs such as mipmapping, Early‐Z and Early‐Stencil culling can optimize the performance of our method. Our algorithm is able to compute dense proximity information for complex scenes made of more than a hundred thousand triangles in real time, outperforming a CPU implementation based on bounding volume hierarchies by more than an order of magnitude.