Octree Decomposition Research Articles

Automatic generation of robot and manual assembly plans using octrees

PurposeThis paper aims to investigate automatic assembly planning for robot and manual assembly.Design/methodology/approachThe octree decomposition technique is applied to approximate a computer‐aided design model with an octree representation which is then used to generate robot and manual assembly plans. An assembly planning system able to generate assembly plans was developed to build these prototype models.FindingsOctree decomposition is an effective assembly planning tool. Assembly plans can automatically be generated for robot and manual assembly using octree models.Research limitations/implicationsOne disadvantage of the octree decomposition technique is that it approximates a part model with cubes instead of using the actual model. This limits its use and applications when complex assemblies must be planned, but in the context of prototyping can allow a rough component to be formed which can later be finished by hand.Practical implicationsAssembly plans can be generated using octree decomposition, however, new algorithms must be developed to overcome its limitations.Originality/valueThis paper has proved that the octree decomposition technique is an effective assembly planning tool. As a result, an assembly planning system has been developed. Assembly plans for automatic and manual assembly can be generated automatically by the proposed system, which is a novelty since there are no fully automatic assembly planning systems for manual assembly reported in the literature.

Manufacturability analysis to combine additive and subtractive processes

PurposeThe purpose of this paper is to propose a methodology to estimate manufacturing complexity for both machining and layered manufacturing. The goal is to take into account manufacturing constraints at design stage in order to realize tools (dies and molds) by a combination of a subtractive process (high‐speed machining) and an additive process (selective laser sintering).Design/methodology/approachManufacturability indexes are defined and calculated from the tool computer‐aided design (CAD) model, according to geometric, material and specification information. The indexes are divided into two categories: global and local. For local indexes, a decomposition of the tool CAD model is used, based on an octree decomposition algorithm and a map of manufacturing complexity is obtained.FindingsThe manufacturability indexes values provide a well‐detailed view of which areas of the tool may advantageously be machined or manufactured by an additive process.Originality/valueNowadays, layered manufacturing processes are coming to maturity, but there is still no way to compare these new processes with traditional ones (like machining) at the early design stage. In this paper, a new methodology is proposed to combine additive and subtractive processes, for tooling design and manufacturing. A manufacturability analysis is based on an octree decomposition, with calculation of manufacturing complexity indexes from the tool CAD model.

Octree-Based Production of Near Net Shape Components

Near net shape (NNS) manufacturing refers to the production of products that require a finishing operation of some kind. NNS manufacturing is important because it enables a significant reduction in: machining work, raw material usage, production time, and energy consumption. This paper presents an integrated system for the production of near net shape components based on the Octree decomposition of 3-D models. The Octree representation is used to automatically decompose and approximate the 3-D models, and to generate the robot instructions required to create assemblies of blocks secured by adhesive. Not only is the system capable of producing shapes of variable precision and complexity (including overhanging or reentrant shapes) from a variety of materials, but it also requires no production tooling (e.g., molds, dies, jigs, or fixtures). This paper details how a number of well-known Octree algorithms for subdivision, neighbor findings, and tree traversal have been modified to support this novel application. This paper ends by reporting the construction of two mechanical components in the prototype cell, and discussing the overall feasibility of the system.

Geometry-guided progressive lossless 3D mesh coding with octree (OT) decomposition

A new progressive lossless 3D triangular mesh encoder is proposed in this work, which can encode any 3D triangular mesh with an arbitrary topological structure. Given a mesh, the quantized 3D vertices are first partitioned into an octree (OT) structure, which is then traversed from the root and gradually to the leaves. During the traversal, each 3D cell in the tree front is subdivided into eight childcells. For each cell subdivision, both local geometry and connectivity changes are encoded, where the connectivity coding is guided by the geometry coding. Furthermore, prioritized cell subdivision is performed in the tree front to provide better rate-distortion (RD) performance. Experiments show that the proposed mesh coder outperforms the kd-tree algorithm in both geometry and connectivity coding efficiency. For the geometry coding part, the range of improvement is typically around 10%~20%, but may go up to 50%~60% for meshes with highly regular geometry data and/or tight clustering of vertices.

An Accurate Distance Algorithm for Octree‐Encoded Objects

AbstractDistance algorithms are most frequently used in robotics to determine the distance between two obstacles in the environment of a robot or between a sensor point and an object. Bounding volumes are a common technique; this technique relies on a hierarchical model representation of the two surfaces using axis‐aligned bounding boxes. Formoving objects it is interesting to use unaligned octrees to avoid the wrapping effect that occurs when performing octree decomposition in a common coordinate system after several rotations. We discuss the algorithm for computing accurate enclosures for the distance between objects represented by axis‐aligned or unaligned octrees. This algorithm is based on a new, recently published distance algorithm between two objects represented by axis‐aligned octrees. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An automated system for the assembly of octree models

This paper presents a novel approach for rapid prototyping based on the octree decomposition of 3D geometric models. The proposed method, referred as OcBlox, integrates an octree modeller, an assembly planning system, and a robotic assembly cell into an integrated system that builds approximate prototypes directly from 3D model data. Given an exact 3D model this system generates an octree decomposition of it, which approximates the shape cubic units referred as “Blox”. These cuboid units are automatically assembled to obtain an approximate physical prototype. This paper details the algorithms used to generate the octree's assembly sequence and demonstrates the feasibility of the OcBlox approach by describing a single resolution example of a prototype built with this automated system. An analysis of the potential of the approach to decrease the manufacturing time of physical components is detailed. Finally, the potential of OcBlox to support complex overhanging geometry is discussed.

Geometric techniques for efficient waste removal in LOM

A new CAPP system is proposed for the layered manufacturing technology of LOM (laminated object manufacturing). The traditional technique wastes much effort and time in the generation of rectangular grid patterns onto the exterior of the model to facilitate waste removal. In the proposed approach, several geometric properties of the model are exploited to dramatically reduce the waste removal grids. This, in turn, leads to redued build time with no effect on the build quality. The proposed method uses parting planes similar to those used in mold design in regions external to the part's convex hull, and an octree decomposition in the remaining regions. An integrated CAPP system incorporating these ideal has been developed, and several example parts demonstrate the efficiencies that the system delivers.

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.

Accurate High-Speed Spatial Normalization Using an Octree Method

The goal of regional spatial normalization is to remove anatomical differences between individual three-dimensional (3-D) brain images by warping them to match features of a standard brain atlas. Full-resolution volumetric spatial normalization methods use a high-degree-of-freedom coordinate transform, called a deformation field, for this task. Processing to fit features at the limiting resolution of a 3-D MR image volume is computationally intensive, limiting broad use of full-resolution regional spatial normalization. A highly efficient method, designed using an octree decomposition and analysis scheme, is presented to resolve the speed problem while targeting accuracy comparable to current volumetric methods. Translation and scaling capabilities of octree spatial normalization (OSN) were tested using computer models of solid objects (cubes and spheres). Boundary mismatch between transformed and target objects was zero for cubes and less than 1% for spheres. Regional independence of warping was tested using brain models consisting of a homogenous brain volume with one internal homogenous region (lateral ventricle). Boundary mismatch improved with successively smaller octant-level processing and approached levels of less than 1% for the brain and 5% for the lateral ventricle. Five 3-D MR brain images were transformed to a target 3-D brain image to assess boundary matching. Residual boundary mismatch was approximately 4% for the brain and 8% for the lateral ventricle, not as good as with homogeneous brain models, but similar to other results. Total processing time for OSN with a 2563 brain image (1-mm voxel spacing) was less than 10 min.

Machining of free-form solids using an octree volume decomposition approach

Objects with free-form shapes have typically been created as surface models. While the finishing tool path can be generated using the surface definition, there are still gaps between the final surface and the intermediate process planning steps. The common process planning information such as the sizes of rough cut tools, rough cut paths, intermediate shapes, and machined volumes cannot be determined based solely on the surface definition. To accomplish the link, one approach is to model the free-form shape as a solid model to obtain the volumetric process planning information. In this research, a free-form solid is defined as a solid with free-form surfaces as the boundary. To generate the information required for process planning, the free-form solid can be approximated with a set of cubic blocks in organized sizes using octree decomposition. The intersecting property between the free-form solid and the subdivided cubic blocks is used to determine further subdivisions. The subdivision proceeds until the cubic blocks are completely separated as full cubes and empty cubes within a specific accuracy. The set of full cubes represents the volume of the final part. The set of empty cubes represents the volume to be removed by machining. These cubic blocks ordered in various sizes can be used to select proper cutting tools and determine tool paths for rough cut and finish cut machining. The intermediate shapes and the machined volumes which are essential to automated process planning can also be obtained. Test software and example parts are presented and discussed.

θ(1) time quadtree algorithm and its application for image geometric properties on a mesh connected computer (MCC)

Quadtree and octree decomposition of multicolored images is often used to solve problems of image processing. This paper describes a θ(1) time algorithm for the decomposition of the images into quadtree and octree on a mesh connected computer. Images will be stored in the MCC of the same size, at one pixel per processing element (PE). Certain applications of the algorithm are also described namely, the computation of such geometric properties as the area and perimeter. The complexity of these algorithms depends on the hierarchical data structure. They are carried out in O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> m + log m) times on an n × n MCC, where m = n/k, and k is the size of the smallest homogeneous quadrant in the image.

Load balancing for the parallel adaptive solution of partial differential equations

An adaptive technique for a partial differential system automatically adjusts a computational mesh or varies the order of a numerical procedure with a goal of obtaining a solution satisfying prescribed accuracy criteria in an optimal fashion. Processor load imbalances will, therefore, be introduced at adaptive enrichment steps during the course of a parallel computation. We develop and describe three procedures for retaining and restoring load balance that have low unit cost and are appropriate for use in an adaptive solution environment. Tiling balances load by using local optimality criteria within overlapping processor neighborhoods. Elemental data are migrated between processors within the same neighborhoods to restore balance. Tiling is restricted to uniform two-dimensional meshes and provides limited control of communications volume by priority-based element selection criteria. These shortcomings can potentially be overcome by creating a dynamic partition graph connecting processors and their neighboring regions. After coloring the edges of the graph, elemental data are iteratively transferred between processors by pairwise exchange to permit a more global migration. Octree decomposition of a spatial domain is a successful three-dimensional mesh generation strategy. The octree structure facilities a rapid load balancing procedure by performing tree traversals that (i) appraise subtree costs and (ii) partition spatial regions accordingly. Computational results are reported for two- and three-dimensional problems using nCUBE/2 hypercube, MasPar MP-2, and Thinking Machines CM-5 computers.

Tetrahedron-based octree encoding for automatic mesh generation

A simple octree-encoding algorithm based on a tetrahedron root has been developed for the fully automatic generation of 3D finite-element meshes. The algorithm starts octree decomposition from a regular tetrahedron root node instead of a hexahedron root node in order for the terminal node to have the same topology as the final tetrahedral mesh. As a result, the terminal octant can be used as a tetrahedral finite element without topology transformation. For this development, the following problems have been octree, and a sustematic prodedure that moves some neighbor-finding technique for the tetrahedron-based octree, and a systematic procedure that moves some vertices of the octants near the boundary onto the surface of the solid model.

An integrated approach for automated generation of two/three dimensional finite element grids using spatial occupancy enumeration and delaunay triangulation

AbstractThe paper describes the development of an automated triangulation algorithm for arbitrary domains. The method involves octree decomposition and subdomain meshing using Delaunay triangulation. Extension to three dimensional objects involving curved boundary surfaces is briefly described.

Applications of Quadtree, Octree, and Binary Tree Decomposition Techniques to Shape Analysis and Pattern Recognition

The binary tree, quadtree, and octree decomposition techniques are widely used in computer graphics and image processing problems. Here, the techniques are reexamined for pattern recognition and shape analysis applications. It has been shown that the quadtree and octree techniques can be used to find the shape hull of a set of points in space while their n-dimensional generalization can be used for divisive hierarchical clustering. Similarly, an n-dimensional binary tree decomposition of feature space can be used for efficient pattern classifier design. Illustrative examples are presented to show the usefulness and efficiency of these hierarchical decomposition techniques.