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238
Unstructured Forests of Octrees
"... Abstract—We present a parallel multigrid method for solving variable-coefficient elliptic partial differential equations on arbi-trary geometries using highly adapted meshes. Our method is designed for meshes that are built from an unstructured hexa-hedral macro mesh, in which each macro element is ..."
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is adaptively refined as an octree. This forest-of-octrees approach enables us to generate meshes for complex geometries with arbitrary levels of local refinement. We use geometric multigrid (GMG) for each of the octrees and algebraic multigrid (AMG) as the coarse grid solver. We designed our GMG sweeps
Generalization of Modified Octrees for Geometric Modeling
, 1997
"... . This paper discusses several aspects of modified octrees that can be generalized in order to obtain solid representations using less primitive elements than the traditional modified octree. The aspects under study include the use of elements of different type as internal nodes, a general refin ..."
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condition. Examples are given to compare a new implementation with previous approaches. 1 Introduction Since the last fifteen years, modified octrees have been used very often in geometric modeling and mesh generation[1, 2]. The modified octree approach works as follows: The 3-D domain is enclosed in a
Matching 3D Anatomical Surfaces with Non-Rigid Deformations using Octree-Splines.
- Geometric Methods in Computer Vision II,
"... Abstract This paper presents a new method for determining the minimal non-rigid deformation between two 3-D surfaces, such as those which describe anatomical structures in 3-D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method perform ..."
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Cited by 156 (2 self)
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performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute dislances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly
RECURSIVE ALGORITHMS FOR DISTRIBUTED FORESTS OF OCTREES
"... Abstract. The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based appli-cations. Efficient reference software has been made freely available to the public both in the form of the stand ..."
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Abstract. The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based appli-cations. Efficient reference software has been made freely available to the public both in the form
Unconstrained Isosurface Extraction on Arbitrary Octrees
, 2007
"... This paper presents a novel algorithm for generating a watertight level-set from an octree. We show that the levelset can be efficiently extracted regardless of the topology of the octree or the values assigned to the vertices. The key idea behind our approach is the definition of a set of binary ed ..."
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Cited by 26 (1 self)
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This paper presents a novel algorithm for generating a watertight level-set from an octree. We show that the levelset can be efficiently extracted regardless of the topology of the octree or the values assigned to the vertices. The key idea behind our approach is the definition of a set of binary
Adaptive Vertex Clustering Using Octrees
- SIAM Geometric Design and Computing
, 2003
"... We present an adaptive vertex clustering approach to out-of-core simpli cation of polygonal meshes using a dynamic octree. ..."
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Cited by 11 (0 self)
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We present an adaptive vertex clustering approach to out-of-core simpli cation of polygonal meshes using a dynamic octree.
SP-Octrees Visualization Using Impostors
"... SP-Octrees (Space-Partition Octrees) allow a multiresolution representation of polyhedral objects, and have been successfully used in progressive transmission. Nonetheless, the SP-Octree is a solid modeling structure, intended to solve problems as solid intersections and point inclusion tests. At in ..."
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. At intermediate levels of the SP-Octree, the visualization is a rough approximation of the object due to the fact that grey nodes are shown as the convex hull of the part of the solid included in that node. In this paper we present an approach to use SP-Octrees for adaptative visualization, that improves
used in Octree Ray Tracing Algorithms
"... Key words: ray tracing optimization, non-uniform spatial subdivision, octree, octtree, octree subdivision methods. The non-uniform spatial subdivision technique refined by Andrew Glassner [Glassner 1984] minimizes facet intersection tests (i) by automatically generating a density dependent spatial h ..."
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to further improve the overall approach by attempting to identify new octree construction methods that would decrease the number of traversals required to render the scene. This research focused on the subdivision technique used in constructing the octree. The conventional Glassner algorithm utilizes cubic
Multi-level Partition of Unity Implicits
- ACM TRANSACTIONS ON GRAPHICS
, 2003
"... We present a shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighti ..."
Abstract
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Cited by 218 (7 self)
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) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape. Our approach
Scalable parallel octree meshing for terascale applications
- in SC2005
, 2005
"... Abstract. This paper presents a new methodology for generating and adapting octree meshes for terascale applications. Our approach combines existing methods, such as parallel octree decomposition and space-filling curves, with a set of new methods that address the special needs of parallel octree me ..."
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Cited by 26 (10 self)
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Abstract. This paper presents a new methodology for generating and adapting octree meshes for terascale applications. Our approach combines existing methods, such as parallel octree decomposition and space-filling curves, with a set of new methods that address the special needs of parallel octree
Results 1 - 10
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238
