Efficient representation and extraction of 2-manifold isosurfaces using kd-trees

Greß, Alexander; Klein, Reinhard

doi:10.1016/j.gmod.2004.06.010

Cited by 20 publications

(10 citation statements)

References 27 publications

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“…In this representation, the separation of space is a reflexion of the topology of the existing objects resulting in a tree that precisely matches it. The PCL library offers one implementation integrating the FLANN library, where the kd-tree is used [8].…”

Section: Efficient Data Structures For World Representationmentioning

confidence: 99%

Applying Frontier Cells Based Exploration and Lazy Theta* Path Planning over Single Grid-Based World Representation for Autonomous Inspection of Large 3D Structures with an UAS

Faria

Maza

Viguria

2018

J Intell Robot Syst

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Aerial robots are a promising platform to perform autonomous inspection of infrastructures. For this application, the world is a large and unknown space, requiring light data structures to store its representation while performing autonomous exploration and path planning for obstacle avoidance. In this paper, we combine frontier cells based exploration with the Lazy Theta* path planning algorithm over the same light sparse grid-the octree implementation of octomap. Test-driven development has been adopted for the software implementation and the subsequent automated testing process. These tests provided insight into the amount of iterations needed to generate a path with different voxel configurations. The results for synthetic and real datasets are analyzed having as baseline a regular grid with the same resolution as the maximum resolution of the octree. The number of iterations needed to find frontier cells for exploration was smaller in all cases by, at least, one order of magnitude. For the Lazy Theta* algorithm there was a reduction in the number of iterations needed to find the solution in 75% of the cases. These reductions can be explained both by the existent grouping of regions with the same status and by the ability to confine inspection to the known voxels of the octree.

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Section: Efficient Data Structures For World Representationmentioning

confidence: 99%

Applying Frontier Cells Based Exploration and Lazy Theta* Path Planning over Single Grid-Based World Representation for Autonomous Inspection of Large 3D Structures with an UAS

Faria

Maza

Viguria

2018

J Intell Robot Syst

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“…Model simplification has been extensively applied to triangular meshes [5] and extended to tetrahedral meshes evaluating the approximation error and the quality of the obtained mesh [4]. Methods for LOD sequences of triangular and tetrahedral meshes can also be found extensively in the literature [16] as well as methods to simplify quadrilateral meshes [11,21]. In contrast to these methods, that rely on geometric operations as edge-collapse or clustering, simplification can follow other strategies.…”

Section: Related Workmentioning

confidence: 99%

Merging Faces: A New Orthogonal Simplification of Solid Models

Cruz-Matías

Ayala

2013

Discrete Geometry for Computer Imagery

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A new approach to simplify orthogonal pseudo-polyhedra (OPP) and binary volumes is presented. The method is incremental and produces a level-of-detail (LOD) sequence of OPP. Any object of this sequence contains the previous objects and, therefore, it is a bounding orthogonal approximation of them. The sequence finishes with the minimum axis-aligned bounding box (AABB). OPP are represented by the Extreme Vertices Model, a complete model that stores a subset of their vertices and performs fast Boolean operations. Simplification is achieved using a new approach called merging faces, which relies on the application of 2D Boolean operations. We also present a technique, based on the model continuity, for a better shape preservation. The method has been tested with several datasets and compared with two similar methods.

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“…This method enables a bottom-up simplification process, but does not guarantee that the extracted meshes are conforming. Later approaches [31], [32] ensure that the extracted surface is manifold, but do not guarantee that is is free of self-intersections. Conversely, the approach of Ju and Udeshi [33] ensures that the surface does not intersect, but does not guarantee that it is manifold.…”

Section: Related Workmentioning

confidence: 99%

Isodiamond Hierarchies: An Efficient Multiresolution Representation for Isosurfaces and Interval Volumes

Weiss

Floriani

2010

IEEE Trans. Visual. Comput. Graphics

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Abstract-Efficient multiresolution representations for isosurfaces and interval volumes are becoming increasingly important as the gap between volume data sizes and processing speed continues to widen. Our multiresolution scalar field model is a hierarchy of tetrahedral clusters generated by longest edge bisection, that we call a hierarchy of diamonds. We propose two multiresolution models for representing isosurfaces, or interval volumes, extracted from a hierarchy of diamonds which exploit its regular structure. These models are defined by subsets of diamonds in the hierarchy, that we call isodiamonds, which are enhanced with geometric and topological information for encoding the relation between the isosurface, or interval volume, and the diamond itself. The first multiresolution model, called a relevant isodiamond hierarchy, encodes the isodiamonds intersected by the isosurface, or interval volume, as well as their non-intersected ancestors, while the second model, called a minimal isodiamond hierarchy, encodes only the intersected isodiamonds. Since both models operate directly on the extracted isosurface or interval volume, they require significantly less memory and support faster selective refinement queries than the original multiresolution scalar field, but do not support dynamic isovalue modifications. Moreover, since a minimal isodiamond hierarchy only encodes intersected isodiamonds, its extracted meshes require significantly less memory than those extracted from a relevant isodiamond hierarchy. We demonstrate the compactness of isodiamond hierarchies by comparing them to an indexed representation of the mesh at full resolution.

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Efficient representation and extraction of 2-manifold isosurfaces using kd-trees

Cited by 20 publications

References 27 publications

Applying Frontier Cells Based Exploration and Lazy Theta* Path Planning over Single Grid-Based World Representation for Autonomous Inspection of Large 3D Structures with an UAS

Applying Frontier Cells Based Exploration and Lazy Theta* Path Planning over Single Grid-Based World Representation for Autonomous Inspection of Large 3D Structures with an UAS

Merging Faces: A New Orthogonal Simplification of Solid Models

Isodiamond Hierarchies: An Efficient Multiresolution Representation for Isosurfaces and Interval Volumes

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