Octree Division Research Articles

Rapid Reconstruction of a Three-Dimensional Mesh Model Based on Oblique Images in the Internet of Things

One of the main targets of the Internet of Things (IoT) is the construction of smart cities, and many industries based on the IoT serve popular applications in a smart city. However, 3-D reconstruction constitutes a major difficulty in the construction of a smart city. In recent years, oblique photography technology has been widely applied in the rapid 3-D modeling and other aspects of smart cities. However, in the automatic construction of a 3-D mesh model for oblique photogrammetry, complex building geometries make it very difficult to construct a triangular mesh model. Therefore, a network construction method is needed that can not only effectively construct a 3-D mesh model but also address the results of auto-modeling for an oblique image. The representative network construction method is a huge triangulation network in which the constructed surface of the object does not satisfy the manifold features and it is inconvenient to optimize and edit the model, yielding a low network construction efficiency. To solve these problems, a new method for constructing a high-quality manifold mesh model is proposed in this paper. First, an adaptive octree division algorithm is used to divide the point cloud data into sub domains that cover each other. Then, a mesh reconstruction is performed in each sub domain, and an efficient mesh construction algorithm based on relabeling the vertices of the directed graph is proposed to construct the manifold mesh. Finally, a triangular facet orientation method is used to homogenize the normal vectors of the mesh. The experimental results proof that the proposed method greatly improves the mesh reconstruction, effectively reflects the model details, and possesses a strong anti-noise ability. Also, it has a good robustness and is particularly suitable for the 3-D reconstruction of large scenes and complex surfaces.

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

In asteroid rendezvous missions, the dynamical environment near an asteroid’s surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes, which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped near-Earth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.

A Study on the Interference Detection and Correction in 5-Axis CNC Incremental Forming

A kind of high efficient and accurate method for the interference detection and correction of 5-axis CNC incremental forming tool and sheet part on the basis of STL(Sterolithography) model is proposed considering the detection efficiency, accuracy and correction. STL model of sheet part is discretizated along the edges after the triangular facets have been subdivised according to the minimum edge of the cube obtained by octree division algorithm so that the octree segmentation for the discrete point cloud model are more regularly. And in order to directly detect the interference area without recursive search, the discrete point cloud model is expand to an octree division model with index sequence. Meanwhile the forming tool is surrounded by axis-aligned bounding boxes and the interference location is detected through the octree division model roughly. The interference location is detected in detail through the discrete points in cubes of the octree division model and the forming tool of the cylinder shape. The interference correction is conducted on the section cutting plane which is along the axis direction of forming tool at interference points. The case study shows that the proposed method can quickly find the interference as well as give the correction, and the whole operation process is stable and reliable.

An automatic method of measuring foot girths for custom footwear using local RBF implicit surfaces

Three-dimensional point cloud data of a foot are used to determine the critical dimensions for making custom footwear. However, automatic and accurate measurement of dimensions, especially girths, is an issue of concern to many designers and footwear developers. Existing methods for measuring girths are primarily based on points or generated triangles, but their accuracy is heavily dependent on the density of the point cloud data. In this paper we present the use of the Radial Basis Function (RBF) surface modelling technique for measuring girths as it has the advantage of being able to operate on unorganised three-dimensional points, so that the generated surface passes through every scanned point, while repairing incomplete meshes. To overcome the high computational expense of the RBF method, local surface recovery, octree division and combination, inverse power method and improved Cholesky factorisation are used. The girth measurements obtained from adopting these approaches are compared against the existing measurement methods. Experimental results demonstrate that the local RBF implicit surface can provide more stable and accurate measurements using relatively less time, proving its value in custom footwear manufacture.

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR (‘Earth’ in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q 1 – p 0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q 1 – p 0 ) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh–Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.