Parallel display of objects represented by linear octrees

The storage, display, and manipulation of three dimensional volumetric information requires large amounts of computing resources, both in terms of memory, and processing power. Most existing serial algorithms that display 3-D objects on a 2-D screen are found to be too slow to process the large amounts of volume data in a reasonable time. Hence, one way to increase the performance of the display algorithm is to process individual volume elements (voxels) in parallel. The first part of this paper presents a brief over view of the linear octree data structure which represents 3-D objects by an eight-way branching tree, while the second part focusses on the parallel display of such objects. We have shown that, for an object represented by a linear octree and enclosed in a 2ⁿ×2ⁿ×2ⁿ universe, the maximum number of voxels that can be processed in parallel is 3ⁿ, and the maximum number of time steps required to display such an object is 4ⁿ. This paper presents a set of formulae which identify the processing element (PE) as well as the time step in which a given linear octree node is processed. Similarly, a procedure which determines the locational code of a linear octree node which must be processed by a given PE, at some specific time step, is presented, along with a strategy for determining whether a PE is active or idle     

An algorithm for converting the boundary representation of a CAD model to its octree representation

Present CAD systems store the solid model of an object using a convenient representation. Boundary models and CSG (Constructive Solid Geometry) models are the most frequently used representations. Based on recent research findings, octree representation of an object presents a promising approach in solving problems in the areas of Computer Graphics, Manufacturing and Robotics. The most notable use of octree representations is in CAD-based robotic path planning problems. Octree models have also been used in fast rendering of 3-D solid models using ray tracing methods. This paper presents an algorithm for converting the boundary representation of polyhedral models to its octree representation. Such an algorithm would provide the link between an object generated using a solid modelling system and the application involving an octree representation of an object. The algorithm is demonstrated by converting a polyhedral boundary model of a sample object to its octree representation.     

Node Partitioning in an Octree Display Pipeline

The node partitioning stage of a graphics pipeline to transform and display octree encoded objects is described. Its function is to accept a sequence of octree node codes, from which the hidden nodes have been removed, and to partition it into sets of nodes which are suitable for a multiprocessor rendering stage. Each set is capable of being processed and displayed independently.     

Global,Dense Multiscale Reconstruction for a Billion Points

We present a variational approach for surface reconstruction from a set of oriented points with scale information. We focus particularly on scenarios with nonuniform point densities due to images taken from different distances. In contrast to previous methods, we integrate the scale information in the objective and globally optimize the signed distance function of the surface on a balanced octree grid. We use a finite element discretization on the dual structure of the octree minimizing the number of variables. The tetrahedral mesh is generated efficiently with a lookup table which allows to map octree cells to the nodes of the finite elements. We optimize memory efficiency by data aggregation, such that robust data terms can be used even on very large scenes. The surface normals are explicitly optimized and used for surface extraction to improve the reconstruction at edges and corners.     

Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws

Conservation laws are solved by a local Galerkin finite element procedure with adaptive space-time mesh refinement and explicit time integration. The Courant stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. Processor load imbalances, introduced at adaptive enrichment steps, are corrected by using traversals of an octree representing a spatial decomposition of the domain. To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size. Partition boundary smoothing reduces the communications volume of partitioning procedures for a modest cost. Computational results comparing parallel octree and inertial partitioning procedures are presented for the three-dimensional Euler equations of compressible flow solved on an IBM SP2 computer.     

改进的八叉树模型在3D刀轨显示系统中的应用

在传统的八叉树模型的基础上增加了扩展八叉树结点,同时引入了混合式的八叉树教据结构,并将它们应用到数控加工的三维刀轨显示系统中;叙述了实体从B-rep表示法转换为相应的改进型八叉树模型的方法,并在这种改进的八叉树模型的基础上完成对零件加工过程的实时性仿真;最后通过运行实际的数控加工程序证明该算法的可行性和有效性.     

三维激光点云数据的可视化研究

大量的点云数据是通过三维激光扫描得到的,而点云数据的显示快慢受到了数据索引的直接影响,这是一个基础性问题。经过研究,八叉树与叶节点KD树相结合的混合空间索引结构以及LOD构建的层次细节模型是用来解决点云数据管理与可视化效率不高的问题的有效方法。在局部,通过在叶子节点中构建的KD树实现高效的查询和显示;在全局,为了实现快速检索与调度使用了八叉树模型。采用这种混合数据模型进行点云组织,建立空间索引,并对点云数据进行LOD构建,实现了点云数据的高效检索以及可视化。     

Hidden Octree Node Removal as a Pipeline Process

A processing pipeline solution to the generation and display of octree encoded 3-D objects is described. Particular emphasis is given to an algorithm which removes that part a of linear octree code which describes parts of the object which are invisible from a prescribed viewing position. The scope of the algorithm is restricted to viewing directions which are parallel to the Cartesian axes and to orthogonal projections. The algorithm is specifically designed to operate as a single stage within a pipeline of processes.     

八元树三维表示法的磁盘存储与恢复

八元树是一种优秀的三维空间表示方法。从序列断层图像或者三维数据场建立八元树的三维表示是一个比较费时的复杂过程。为了省略每次从原始数据重新构造八元树的过程,将内存中已经建立好的八元树结构以文件的方式保存到磁盘上。当再次做八元树的三维处理应用时,再直接从保存的磁盘文件恢复出八元树。文中提出了一种快速有效的八元树三维表示法的磁盘存储与恢复算法,并实验验证了其可行性。     

一种有效的序列断层图象的八元树构造算法

利用八元树进行物体的三维重是一种十分有效的方法。本文针对医国学图象处理中的实体三维重建顺分析了序断层图象的空间布局和八元树结构的荐,提出了一种通过断层序列图象直接建立八元树的快速算法,并易于在微机上编程实现该算法。     

一种基于松散八叉树的复杂场景可见性裁剪算法

针对传统八叉树方法的不足,在采用松散八叉树组织场景、利用八叉树空间划分优点的同时弥补其局限性.为提高遮挡查询效率,将子节点依视点排序,针对复杂场景采用双层裁剪技术以进一步提高性能.实验结果表明,文中算法对深度复杂度高、面片数量大的复杂场景具有较好的裁剪效率,能够很好地满足实时绘制的要求.     

一种基于八叉树的三维实体内部可视化技术

鉴于传统的图形学-面图形学只能表达三维实体的表面的形状和属性，不能表达实体内部的属性，如纹理、密度场以及温度场等，因而在计算机图形学、CAD以及有限元分析等许多领域都需要一种新的可视化技术-三维实体的可视化技术，以表达实体内部的属性；三维实体的可视化技术是新兴的图形学-体图形学的一个重要组成部分，为了实现三维实体的可视化，针对CAD造型系统中的实际要求，根据体图形学的理论和八叉树的特点，提出了一种基于八叉树的实体内部可视化技术，该技术采用八叉树算法对边界数据结构表达的实体进行体元化。由于实体内部属性变化的不均匀，算法采用了不规则体元，以充分表达实体内部的细节，实际应用效果表明，该算法不但能充分表达实体内部属性，而且也具有一定的造型功能。     

场景分割算法及其在实时漫游系统中的应用

实时漫游中对实时性的要求很高,但通常情况下场景绘制速度很难满足实际需求,基于包络球检索和八叉树分割的思想,提出一种基于场景分割的加速绘制算法,并对绘制过程中探照灯的处理进行了探讨。     

面向体数据的虚拟八叉树模型研究

针对常规八叉树和线性八叉树的不足,提出了一种基于多级Z-Order曲线、无指针/无位置码的虚拟八叉树模型。在时间方面,由于采用了规则划分的节点数据块及其简单高效的索引结构,新模型具有很高的内存访问效率;在空间方面,由于节点中无指针和位置码信息,而且采用了新的基于规则节点块的合并和压缩原则,新模型具有很好的存储效率。测试结果表明,虚拟八叉树模型同时具有指针八叉树在时间效率、线性八叉树在空间效率两方面的优势,是一种高效的三维体数据组织模型,在体图形学相关的领域中具有重要的研究意义和应用价值。     

Incremental Polygonization of Implicit Surfaces

This paper describes an incremental polygonization technique for implicit surfaces built from skeletal elements. Our method is dedicated to fast previewing in an interactive modeling system environment. We rely on an octree decomposition of space combined with Lipschitz conditions to recursively subdivide cells until a given level of precision is reached and converge to the implicit surface. We use a trilinear interpolation approximation of the field function to create a topologically consistent tessellation characterized by an adjacency graph. Our algorithm aims at updating the mesh locally in regions of space where changes in the potential field occurred. Therefore, we propose an octree inflating and deflating strategy to preserve the octree structure as much as possible and to avoid useless or redundant computations. Timings show that our incremental algorithm dramatically speeds up the overall polygonization process for complex objects.     

运用改进的八叉树算法实现精确碰撞检测

提出一种精确碰撞检测算法,通过计算空间多面体之间距离实现碰撞检测功能.在计算2个多面体之间距离时,运用空间层次划分技术高效地寻找多面体中充分接近的三角面片,然后在这些三角面片中进行距离计算,以提高算法效率;同时运用改进的八叉树层次分割算法,与基本八叉树算法相比,减少了算法的空间复杂度.文中算法已经在超导Tokamak实验装置（EAST）虚拟装配仿真系统的碰撞检测模块中得到应用,通过实验比较,证明了该算法的可行性.     

CPU–GPU Parallel Framework for Real‐Time Interactive Cutting of Adaptive Octree‐Based Deformable Objects

A software framework taking advantage of parallel processing capabilities of CPUs and GPUs is designed for the real‐time interactive cutting simulation of deformable objects. Deformable objects are modelled as voxels connected by links. The voxels are embedded in an octree mesh used for deformation. Cutting is performed by disconnecting links swept by the cutting tool and then adaptively refining octree elements near the cutting tool trajectory. A surface mesh used for visual display is reconstructed from disconnected links using the dual contour method. Spatial hashing of the octree mesh and topology‐aware interpolation of distance field are used for collision. Our framework uses a novel GPU implementation for inter‐object collision and object self collision, while tool‐object collision, cutting and deformation are assigned to CPU, using multiple threads whenever possible. A novel method that splits cutting operations into four independent tasks running in parallel is designed. Our framework also performs data transfers between CPU and GPU simultaneously with other tasks to reduce their impact on performances. Simulation tests show that when compared to three‐threaded CPU implementations, our GPU accelerated collision is 53–160% faster; and the overall simulation frame rate is 47–98% faster.     

Stable Real-Time Surgical Cutting Simulation of Deformable Objects Embedded with Arbitrary Triangular Meshes

Surgical simulators need to simulate deformation and cutting of deformable objects. Adaptive octree mesh based cutting methods embed the deformable objects into octree meshes that are recursively refined near the cutting tool trajectory. Deformation is only applied to the octree meshes; thus the deformation instability problem caused by degenerated elements is avoided. Biological tissues and organs usually contain complex internal structures that are ignored by previous work. In this paper the deformable objects are modeled as voxels connected by links and embedded inside adaptive octree meshes. Links swept by the cutting tool are disconnected and object surface meshes are reconstructed from disconnected links. Two novel methods for embedding triangular meshes as internal structures are proposed. The surface mesh embedding method is applicable to arbitrary triangular meshes, but these meshes have no physical properties. The material sub-region embedding method associates the interiors enclosed by the triangular meshes with physical properties, but requires that these meshes are watertight, and have no self-intersections, and their smallest features are larger than a voxel. Some local features are constructed in a pre-calculation stage to increase simulation performance. Simulation tests show that our methods can cut embedded structures in a way consistent with the cutting of the deformable objects. Cut fragments can also deform correctly along with the deformable objects.     

Linear octrees by volume intersection

The paper describes a new algorithm for constructing a 3D approximation of an object from three orthogonal 2D silhouettes. The 2D views are represented as binary arrays and 3D approximation is obtained as a linear octree. The algorithm makes use of volume intersection of three cylinders obtained by sweeping three views in respective directions. The algorithm takes less time than an existing algorithm which makes use of three quadtrees and an octree for 2D and 3D image representation, respectively. Unlike the previous algorithm, the present algorithm does not require any preprocessing stage or condensation. It is Shown that the proposed algorithm is of o(T), where T is the total number of nodes in the resulting octree.     

Discrete Ray-Tracing of Huge Voxel Spaces

The quality of images produced by Discrete Ray-Tracing voxel spaces is highly dependent on 3d grid resolution. The huge amount of memory needed to store such grids often discards discrete Ray-Tracing as a practical visualization algorithm. The use of an octree can drastically change this when most of space is empty, as such is the case in most scenes. Although the memory problem can be bypassed using the octree, the performance problem still remains. A known fact is that the performance of discrete traversal is optimal for quite low resolutions. This problem can be easily solved by dividing the task in two steps, working in two low resolutions instead of just one high resolution, thus taking advantage of optimal times in both steps. This is possible thanks to the octree property of representing the same scene in several different resolutions. This article presents a two step Discrete Ray-Tracing method using an octree and shows, by comparing it with the single step version, that a substantial gain in performance is achieved.