Geodesic Mesh Research Articles

The Application of Geodesic in Deployable Antenna Mesh Dividing

Space deployable antennna has the characteristics of Lightweight, large diameter, high precision etc, which can meet the requirements of the launch vehicle carrying and payload’s Electromagnetic performance. Antenna’s mesh dividing have the direct bearing on payload’s Electromagnetic performance, geodesic mesh dividing has the advantage of shortest length of mseh line. but the equation solving of geodesic is complicated,which Impeding the geodesic’s application In academic and engineering fields. in this paper, a method has be proposed to solve the difficulty of geodesic equation solving. the solving result can be used in antenna’s mesh dividing, meanwhile the solving result can be used in Robot trajectory planning, Air route planning,Navigation route planning,Architectural structure design,etc. great care should be taken in constructing both.

Technologies for supporting high-order geodesic mesh frameworks for computational astrophysics and space sciences

Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical schemes based on a spherical mesh. Despite its orthogonality property, the polar (latitude-longitude) mesh is ill suited for computation because of the singularity on the polar axis, leading to a highly non-uniform distribution of zone sizes. The consequences are (a) loss of accuracy due to large variations in zone aspect ratios, and (b) poor computational efficiency from a severe limitations on the time stepping. Geodesic meshes, based on a central projection using a Platonic solid as a template, solve the anisotropy problem, but increase the complexity of the resulting computer code. We describe a new finite volume implementation of Euler and MHD systems of equations on a triangular geodesic mesh (TGM) that is accurate up to fourth order in space and time and conserves the divergence of magnetic field to machine precision. The paper discusses in detail the generation of a TGM, the domain decomposition techniques, three-dimensional conservative reconstruction, and time stepping.

Efficient, divergence-free, high-order MHD on 3D spherical meshes with optimal geodesic meshing

ABSTRACT There is a great need in several areas of astrophysics and space physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh quality and numerical algorithms. Methods have been designed that fundamentally integrate high-order isoparametric mappings with the other high accuracy algorithms that are needed for divergence-free MHD simulations on geodesic meshes. The goal of this paper is to document such algorithms that are implemented in the geodesic mesh version of the RIEMANN code. The fluid variables are reconstructed using a special kind of WENO-AO algorithm that integrates the mesh geometry into the reconstruction process from the ground-up. A novel divergence-free reconstruction strategy for the magnetic field that performs efficiently at all orders, even on isoparametrically mapped meshes, is then presented. The MHD equations are evolved in space and time using a novel ADER predictor algorithm that is efficiently adapted to the isoparametrically mapped geometry. The application of one-dimensional and multidimensional Riemann solvers at suitable locations on the mesh then provides the corrector step. The corrector step for the magnetic field uses a Yee-type staggering of magnetic fields. This results in a scheme with divergence-free update for the magnetic field. The use of ADER enables a one-step update that only requires one messaging operation per complete timestep. This is very beneficial for parallel processing. Several accuracy tests are presented as are stringent test problems. PetaScale performance is also demonstrated on the largest available supercomputers.

Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images

In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the minimal path approach. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. This approach can also be used for finding an open curve giving extra information as stopping criteria. Detection of a variety of objects on real images is demonstrated. Using a similar idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.

Visualizing curvature on the Lorenz manifold

The Lorenz manifold is an intriguing two-dimensional surface that illustrates chaotic dynamics in the well-known Lorenz system. While it is not possible to find an explicit analytic expression for the Lorenz manifold, we have developed a method for calculating a numerical approximation that builds the surface up as successive geodesic level sets. The resulting mesh approximation can be read as crochet instructions, which means that we are able to generate a three-dimensional model of the Lorenz manifold. The crocheted model directly motivated us to investigate the curvature properties of the Lorenz manifold by means of determining an approximation to the Gaussian curvature from our geodesic mesh representation. We then translate this information to colour, which leads to a new visualization of the geometry of the Lorenz manifold. This colouring enhances the aesthetics of the visualization by revealing a striking pattern of regions of positive and negative Gaussian curvature.