Linear octree

Abstract: This article gives three viewing-transformation algorithms for displaying on a screen 3D pictures represented by linear octrees. All the procedures take advantage of the recursive labeling used to identify the successive decomposition of an object into octants. The first algorithm performs transformations directly on the linear octree, while the second and third algorithms determine the 3D border of the given object first and then project onto the screen the surface voxels thus found. All the algorithms perform the viewing transformations in O(RN) time, where R is the resolution of the picture and N is the number of elements in the linear octree. One of the algorithms provides views of the object at different layers of gray level, while another allows internal views.

Abstract: This paper presents the design, implementation, and evaluation of the etree, a database-oriented method for large out-of-core octree mesh generation. The main idea is to map an octree to a database structure and perform all octree operations by querying and updating the database. We apply two standard database techniques, the linear octree and the B-tree, to index and store the octants on disk. Then we introduce two new techniques, auto-navigation and local balancing, to address the special needs of mesh generation. Preliminary evaluation suggests that the etree method is an effective way of generating very large octree meshes on desktop machines.

Abstract: In this paper, a survey of octree representation and its applications in CAD is presented. The octree representation may be categorized as pure octree representation and polytree (or extended octree), and the latter is actually a boundary representation decomposed by octree. Linear octree which is a variant of regular octree representation has the advantage of saving memory space. The mapping between Cartesian coordinates and node addresses in linear octree is discussed. Then, algorithms for converting a boundary representation of 3D object into an octree are in vestigated and major approaches for transforming an octree encoded object are presented. After that, some of the applications of octree representation in CAD are listed, in particular, the applications in solid modeling, in accelerating ray tracing and in generating meshes for FEM.

Abstract: 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.