Holes In Meshes Research Articles

A new spatial data structure for triangular mesh with toroidal patches

We introduce a novel spatial data structure for a triangular mesh consisting of osculating toroidal patches. A toroidal patch is generated using the differential geometry of a vertex by approximating a local surface to estimate the principal curvatures and directions. Within a given tolerance, the adjacent faces of a vertex can effectively be approximated by the toroidal patch. For efficient usage, toroidal patches are constructed in a hierarchical manner using various tolerance values ϵ=10−3,10−4, and 10−5 and combined with the conventional Bounding Volume Hierarchy (BVH). To demonstrate the effectiveness of our approach, we employ our spatial data structure for filling holes in triangular meshes. After generating a hole-filled patch, we update the hole-filled patch’s vertices using the normals and positions of the toroidal patches. To the best of our knowledge, this is the first application of toroidal patches to triangular mesh.

FILLING GAPS BETWEEN MESHES OF TREE CROWN AND TREE TRUNK BASED ON BOUNDARY CONSTRAINTS AND COORDINATE PROJECTION FOR 3D TREE MODELLING

Abstract. In order to reconstruct high-quality 3D tree models, trunks and crowns could be reconstructed using appropriate methods separately and merged together. During this process, gaps will appear after tree models are spliced, which will affect the models' topological connectivity and visual effects. In this paper, a gap-repair algorithm for tree mesh models based on boundary restriction and coordinates projection is proposed. The algorithm first extracts all the holes in the tree trunk meshes and crown meshes and matched them according to their relative positions. Then, the gaps in the tree meshes are identified. After that, based on the projection of the hole vertices from 3D space to 2D space, the relative positions of the hole vertices were determined, and vertex connection and surface addition were carried out to generate a 2-manifold patch. Finally, the patch was refined to keep its density of vertices similar to the surrounding meshes. Real 3D Tree meshes of different species were used to conduct experiments, and the quality of the repaired tree models are evaluated qualitatively and quantitatively. Experimental results revealed that the proposed algorithm could fill gaps in tree meshes quickly and effectively, so as to achieve the topology connection and smooth transition between the trunk and crown meshes.

Adapting geometry of complex geological structures to finite-element stress–strain modeling of impregnated ore bodies in Komsomolsky Mine

Continuously rising standards of the FEM-based stress–strain modeling of complex geological structures implacably overlaborate a model framework geometry. Different defects may arise as a consequence, such as holes in polygonal meshes, intersections of planes, degenerated polygons, or triangular polygons with one angle greatly exceeding the other two angles. This complicates operation, disables generation of a quality mesh of finite elements and sometimes makes the use of the initial geometry impossible. This article offers algorithms to remove defective sites from the skeletons of geological structures in numerical modeling. Furthermore, the method to optimize topology of initial skeletons is described; this method uses an outside software (Autodesk 3ds Max) and ensures a maximally beneficial ratio of the polygonal mesh topology quality and the initial geometry preservation. This algorithm helps eliminate local crowding points in the finite element mesh and possible stress raisers which take no considerable part in geometrical amplification. This article describes the application results of the algorithms as the case-studies of skeletons of complex geological structures. The comparison of the finite element mesh quality and number of finite elements for the skeletons with and without optimization reveals the improving quality of the finite element meshes with the decreasing number of finite elements in case of the skeletons after topology optimization and removal of defects. The algorithms are especially effective in large-scale modeling when the number and quality of finite elements in each part of a model essentially influence the time and accuracy of computation.

LIMOFilling: Local Information Guide Hole-Filling and Sharp Feature Recovery for Manifold Meshes

Manifold mesh, a triangular network for representing 3D objects, is widely used to reconstruct accurate 3D models of objects structure. The complexity of these objects and self-occlusion, however, can cause cameras to miss some areas, creating holes in the model. The existing hole-filling methods do not have the ability to detect holes at the model boundaries, leaving overlaps between the newly generated triangles, and also lack the ability to recover missing sharp features in the hole-region. To solve these problems, LIMOFilling, a new method for filling holes in 3D manifold meshes was proposed, and recovering the sharp features. The proposed method, detects the boundary holes robustly by constructing local overlap judgments, and provides the possibility for sharp features recovery using local structure information, as well as reduces the cost of maintaining manifold meshes thus enhancing their utility. The novel method against the existing methods have been tested on different types of holes in four scenes. Experimental results demonstrate the visual effect of the proposed method and the quality of the generated meshes, relative to the existing methods. The proposed hole-detection algorithm found almost all of the holes in different scenes and qualitatively, the subsequent repairs are difficult to see with the naked eye.

Automatic voxel-based 3D indoor reconstruction and room partitioning from triangle meshes

With the gaining popularity and proliferation of building information modeling (BIM) techniques, a growing demand emerges for accurate, up-to-date and semantically-enriched digital representations of built environments. In this regard, current mobile indoor mapping systems like the Microsoft HoloLens or Matterport allow to efficiently acquire triangle meshes of indoor building environments. However, manually reconstructing digital models of building interiors on the basis of these triangle meshes is a cumbersome and time-consuming task. Consequently, in this work, we propose a fully automatic, voxel-based indoor reconstruction approach to derive semantically-enriched and geometrically completed indoor models in voxel representation from unstructured triangle meshes. The presented approach does not require room surfaces such as walls, ceilings or floors to be planar or aligned with the coordinate axes. Furthermore, it does not rely on a clear vertical subdivision in distinct floor levels and even allows for slanted floors such as ramps or stair flights. It thus can also be applied to challenging indoor environments featuring curved room surfaces and complex vertical room layouts. The proposed approach labels voxels as ‘Ceiling’, ‘Floor’, ‘Wall’, ‘Wall Opening’, ‘Interior Object’ and ‘Empty Interior’. Room surfaces are geometrically completed in case of holes in the input triangle meshes caused by occlusion or incomplete mapping. Furthermore, the derived interior space is partitioned into rooms and connecting transition spaces. To demonstrate the performance of our approach, we conduct a thorough quantitative evaluation on four labeled benchmark datasets. To this aim, we present a novel and adequate, automatic evaluation method. The four datasets have been acquired with the Microsoft HoloLens and are available along with the manually modeled ground truth. We also release the code of our implementation of the voxel-based indoor reconstruction approach presented in this paper as well as the code for the automated evaluation against the ground truth data at https://github.com/huepat/voxir.

Relleno de huecos en mallas 3D completas mediante algoritmos de restauración de imagen

In this work a method for filling holes in 3D meshes based on a 2D image restoration algorithm is expounded. To do that, data must be converted to a suitable input format, a 3D to 2D transformation is executed by projecting the 3D surface onto a grid. Therefore, the proposed algorithm starts by a first stage of holes identification. Then, a meaningful mesh portiéon is choosen for each hole. Afterward, the suitable plane of projection must be computed to get the range image of the mesh portion. Later, it is applied the restauration image algorithm to the range image. Finally, an inverse transformation 2D to 3D is performed and the new produced data are integrated with the initial mesh. The result is a robust algorithm which works correctly with several kind of holes and for di_erent sizes of them.

Filling Holes in Triangular Meshes in Engineering

In this paper, a novel hole-filling algorithm for triangular meshes is proposed. Firstly, the hole is triangulated into a set of new triangles using modified principle of minimum angle. Then the initial patching mesh is refined according to the density of vertices on boundary edges. Finally, the patching mesh is optimized via the bilateral filter to recover missed features. Experimental results demonstrate that the proposed algorithm fills complex holes robustly, and preserves geometric features to a certain extent as well. The resulted meshes are of good quality for engineering.

Filling Holes in Triangular Meshes with Feature Preserved

In this paper, a novel hole-filling algorithm for triangular meshes is proposed. Firstly, the hole is triangulated into a set of new triangles using modified principle of minimum angle. Then the initial patching mesh is refined according to the density of vertices on boundary edges. Finally, the patching mesh is optimized via the bilateral filter to recover missed features. Experimental results demonstrate that the proposed algorithm fills complex holes robustly, and preserves geometric features to a certain extent as well.

An algorithm for filling complex holes in reverse engineering

The existence of holes in meshes makes it difficult for mesh operations, especially when comes to model rebuilding, rapid prototyping and finite element analysis. Existing hole-filling algorithms are capable of filling holes on small and smooth regions of a model. For large holes with complex boundaries or in curved region, they may not result in satisfactory results. This paper proposes an algorithm which first split the holes into flatter ones and then split the complex holes based the concept of edge expansion. It incrementally splits a complex hole into simple ones by respecting the 3D shape of its boundary and the neighboring meshes, and then fills each resulting simple hole with planar triangulation. The proposed algorithm works well for a variety of complex holes and can better preserve the detailed features of the original mesh.

Filling holes in meshes using a mechanical model to simulate the curvature variation minimization

The presence of holes in a triangle mesh is classically ascribed to the deficiencies of the point cloud acquired from a physical object to be reverse engineered. This lack of information results from both the scanning process and the object complexity. The consequences are simply not acceptable in many application domains (e.g. visualization, finite element analysis or STL prototyping). This paper addresses the way these holes can be filled in while minimizing the curvature variation between the surrounding and inserted meshes. The curvature variation is simulated by the variation between external forces applied to the nodes of a linear mechanical model coupled to the meshes. The functional to be minimized is quadratic and a set of geometric constraints can be added to further shape the inserted mesh. In addition, a complete cleaning toolbox is proposed to remove degenerated and badly oriented triangles resulting from the scanning process.

Geometry completion and detail generation by texture synthesis

We present a novel method for patching holes in polygonal meshes and synthesizing surfaces with details based on existing geometry. The most novel feature of our proposed method is that we transform the 3D geometry synthesis problem into a 2D domain by parameterizing surfaces and solve this problem in that domain. We then derive local geometry gradient images that encode intrinsic local geometry properties, which are invariant to object translation and rotation. The 3D geometry of holes is then reconstructed from synthesized local gradient images. This method can be extended to execute other mesh editing operations such as geometry detail transfer or synthesis. The resulting major benefits of performing geometry synthesis in 2D are more flexible and robust control, better leveraging of the wealth of current 2D image completion methods, and greater efficiency.

Evaluation of the dispersive nature of meshes used for the spherical aberration correction of electrostatic lenses

Although spherical aberration of electrostatic lenses can be corrected in principle by employing meshes, the holes in meshes give rise to local disturbances in the electric field and the performance of mesh lenses deteriorates somewhat due to this effect. The disturbed electric field around mesh holes has a lens action, so a mesh can be regarded as a set of single-aperture lenses. It is shown that the optical properties of single-aperture lenses can be approximated to high precision by means of a transfer matrix. Using this formulation, the lens effect added by the presence of holes is extracted without ambiguity from the action of the total lens field. Moreover, the condition where a single-aperture lens can be regarded as a thin lens with a certain focal length is clarified. An image of a point source is blurred by mesh holes, and the amount of blurring is explained to high precision by their first-order defocusing action as single-aperture lenses; calculations using ray tracing have confirmed this. It is shown that the blurring can be suppressed to an acceptable level in applications such as transfer optics for electron spectrometers.