Comparison of Current Gravity Estimation and Determination Models

This paper will discuss the history of gravity estimation and determination models while analyzing methods that are in development. Some fundamental methods for calculating the gravity field include spherical harmonics solutions, local weighted interpolation, and global point mascon modeling (PMC). Recently, high accuracy measurements have become more accessible, and the requirements for high order geopotential modeling have become more stringent. Interest in irregular bodies, accurate models of the hydrological system, and on-board processing has demanded a comprehensive model that can quickly and accurately compute the geopotential with low memory costs. This trade study of current geopotential modeling techniques will reveal that each modeling technique has a unique use case. It is notable that the spherical harmonics model is relatively accurate but poses a cumbersome inversion problem. PMC and interpolation models, on the other hand, are computationally efficient, but require more research to become robust models with high levels of accuracy. Considerations of the trade study will suggest further research for the point mascon model. The PMC model should be improved through mascon refinement, direct solutions that stem from geodetic measurements, and further validation of the gravity gradient. Finally, the potential for each model to be implemented with parallel computation will be shown to lead to large improvements in computing time while reducing the memory cost for each technique.Aerospace Engineering and Engineering Mechanic

ADAM: a general method for using various data types in asteroid reconstruction

We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple and universal since it handles all disk-resolved data types (adaptive optics or other images, interferometry, and range-Doppler radar data) in a uniform manner via the 2D Fourier transform, enabling fast convergence in model optimization. The resolved data can be combined with disk-integrated data (photometry). In the reconstruction process, the difference between each data type is only a few code lines defining the particular generalized projection from 3D onto a 2D image plane. Occultation timings can be included as sparse silhouettes, and thermal infrared data are efficiently handled with an approximate algorithm that is sufficient in practice due to the dominance of the high-contrast (boundary) pixels over the low-contrast (interior) ones. This is of particular importance to the raw ALMA data that can be directly handled by ADAM without having to construct the standard image. We study the reliability of the inversion by using the independent shape supports of function series and control-point surfaces. When other data are lacking, one can carry out fast nonconvex lightcurve-only inversion, but any shape models resulting from it should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&

Revisión de literatura de jerarquía volúmenes acotantes enfocados en detección de colisiones

(Eng) A bounding volume is a common method to simplify object representation by using the composition of geometrical shapes that enclose the object; it encapsulates complex objects by means of simple volumes and it is widely useful in collision detection applications and ray tracing for rendering algorithms. They are popular in computer graphics and computational geometry. Most popular bounding volumes are spheres, Oriented-Bounding Boxe s (OBB’ s), Axis-Align ed Bound ing Boxes (AABB’ s); moreover , the literature review includes ellipsoids, cylinders, sphere packing, sphere shells , k-DOP’ s, convex hulls, cloud of points, and minimal bounding boxe s, among others. A Bounding Volume Hierarchy is ussualy a tree in which the complete object is represented thigter fitting every level of the hierarchy. Additionally, each bounding volume has a cost associated to construction, update, and interference te ts. For instance, spheres are invariant to rotation and translations, then they do not require being updated ; their constructions and interference tests are more straightforward then OBB’ s; however, their tightness is lower than other bounding volumes. Finally , three comparisons between two polyhedra; seven different algorithms were used, of which five are public libraries for collision detection.(Spa) Un volumen acotante es un método común para simplificar la representación de los objetos por medio de composición de formas geométricas que encierran el objeto; estos encapsulan objetos complejos por medio de volúmenes simples y son ampliamente usados en aplicaciones de detección de colisiones y trazador de rayos para algoritmos de renderización. Los volúmenes acotantes son populares en computación gráfica y en geometría computacional; los más populares son las esferas, las cajas acotantes orientadas (OBB’s) y las cajas acotantes alineadas a los ejes (AABB’s); no obstante, la literatura incluye elipses, cilindros empaquetamiento de esferas, conchas de esferas, k-DOP’s, convex hulls, nubes de puntos y cajas acotantes mínimas, entre otras. Una jerarquía de volúmenes acotantes es usualmente un árbol, en el cual la representación de los objetos es más ajustada en cada uno de los niveles de la jerarquía. Adicionalmente, cada volumen acotante tiene asociado costos de construcción, actualización, pruebas de interferencia. Por ejemplo, las esferas so invariantes a rotación y translación, por lo tanto no requieren ser actualizadas en comparación con los AABB no son invariantes a la rotación. Por otro lado la construcción y las pruebas de solapamiento de las esferas son más simples que los OBB’s; sin embargo, el ajuste de las esferas es menor que otros volúmenes acotantes. Finalmente, se comparan dos poliedros con siete algoritmos diferentes de los cuales cinco son librerías públicas para detección de colisiones

Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are verified by numerical simulations

An Innovative Solution to NASA's NEO Impact Threat Mitigation Grand Challenge and Flight Validation Mission Architecture Development

This final technical report describes the results of a NASA Innovative Advanced Concept (NIAC) Phase 2 study entitled "An Innovative Solution to NASA's NEO Impact Threat Mitigation Grand Challenge and Flight Validation Mission Architecture Development." This NIAC Phase 2 study was conducted at the Asteroid Deflection Research Center (ADRC) of Iowa State University in 2012-2014. The study objective was to develop an innovative yet practically implementable solution to the most probable impact threat of an asteroid or comet with short warning time (less than 5 years). The technical materials contained in this final report are based on numerous technical papers, which have been previously published by the project team of the NIAC Phase 1 and 2 studies during the past three years. Those technical papers as well as a NIAC Phase 2 Executive Summary report can be downloaded from the ADRC website (www.adrc.iastate.edu)

Efficient algorithms for occlusion culling and shadows

The goal of this research is to develop more efficient techniques for computing the visibility and shadows in real-time rendering of three-dimensional scenes. Visibility algorithms determine what is visible from a camera, whereas shadow algorithms solve the same problem from the viewpoint of a light source. In rendering, a lot of computational resources are often spent on primitives that are not visible in the final image. One visibility algorithm for reducing the overhead is occlusion culling, which quickly discards the objects or primitives that are obstructed from the view by other primitives. A new method is presented for performing occlusion culling using silhouettes of meshes instead of triangles. Additionally, modifications are suggested to occlusion queries in order to reduce their computational overhead. The performance of currently available graphics hardware depends on the ordering of input primitives. A new technique, called delay streams, is proposed as a generic solution to order-dependent problems. The technique significantly reduces the pixel processing requirements by improving the efficiency of occlusion culling inside graphics hardware. Additionally, the memory requirements of order-independent transparency algorithms are reduced. A shadow map is a discretized representation of the scene geometry as seen by a light source. Typically the discretization causes difficult aliasing issues, such as jagged shadow boundaries and incorrect self-shadowing. A novel solution is presented for suppressing all types of aliasing artifacts by providing the correct sampling points for shadow maps, thus fully abandoning the previously used regular structures. Also, a simple technique is introduced for limiting the shadow map lookups to the pixels that get projected inside the shadow map. The fillrate problem of hardware-accelerated shadow volumes is greatly reduced with a new hierarchical rendering technique. The algorithm performs per-pixel shadow computations only at visible shadow boundaries, and uses lower resolution shadows for the parts of the screen that are guaranteed to be either fully lit or fully in shadow. The proposed techniques are expected to improve the rendering performance in most real-time applications that use 3D graphics, especially in computer games. More efficient algorithms for occlusion culling and shadows are important steps towards larger, more realistic virtual environments.reviewe

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues

The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave) shapes in both 2D and 3D cases. By choosing such a contact energy function, the full normal contact features can be determined without the need to introduce any additional assumptions/parameters. By further exploiting the geometric properties of the contact surfaces concerned, more effective integration schemes are developed to reduce the evaluation costs involved. When a linear contact energy function of the contact volume is adopted, a linear contact model is derived in which only the intersection between two contact shapes is needed, thereby substantially improving both efficiency and applicability of the proposed contact model. A comparison of this linear energy-conserving contact model with some existing models for discs and spheres further reveals the nature of the proposed model, and provides insights into how to appropriately choose the stiffness parameter included in the energy function. For general non-spherical shapes, mesh representations are required. The corresponding computational aspects are described when shapes are discretised into volumetric meshes, while new developments are presented and recommended for shapes that are represented by surface triangular meshes. Owing to its additive property of the contact geometric features involved, the proposed contact model can be conducted locally in parallel using GPU or GPGPU computing without occurring much communication overhead for shapes represented as either a volumetric or surface triangular mesh. A set of examples considering the elastic impact of two shapes are presented to verify the energy-conserving property of the proposed model for a wide range of concave shapes and contact scenarios, followed by examples involving large numbers of arbitrarily shaped particles to demonstrate the robustness and applicability for more complex and realistic problems

Multi-resolution mapping and planning for UAV navigation in attitude constrained environments

In this thesis we aim to bridge the gap between high quality map reconstruction and Unmanned Aerial Vehicles (UAVs) SE(3) motion planning in challenging environments with narrow openings, such as disaster areas, which requires attitude to be considered. We propose an efficient system that leverages the concept of adaptive-resolution volumetric mapping, which naturally integrates with the hierarchical decomposition of space in an octree data structure. Instead of a Truncated Signed Distance Function (TSDF), we adopt mapping of occupancy probabilities in log-odds representation, which allows representation of both surfaces, as well as the entire free, i.e.\ observed space, as opposed to unobserved space. We introduce a method for choosing resolution -on the fly- in real-time by means of a multi-scale max-min pooling of the input depth image. The notion of explicit free space mapping paired with the spatial hierarchy in the data structure, as well as map resolution, allows for collision queries, as needed for robot motion planning, at unprecedented speed. Our mapping strategy supports pinhole cameras as well as spherical sensor models. Additionally, we introduce a first-of-a-kind global minimum cost path search method based on A* that considers attitude along the path. State-of-the-art methods incorporate attitude only in the refinement stage. To make the problem tractable, our method exploits an adaptive and coarse-to-fine approach using global and local A* runs, plus an efficient method to introduce the UAV attitude in the process. We integrate our method with an SE(3) trajectory optimisation method based on a safe-flight-corridor, yielding a complete path planning pipeline. We quantitatively evaluate our mapping strategy in terms of mapping accuracy, memory, runtime performance, and planning performance showing improvements over the state-of-the-art, particularly in cases requiring high resolution maps. Furthermore, extensive evaluation is undertaken using the AirSim flight simulator under closed loop control in a set of randomised maps, allowing us to quantitatively assess our path initialisation method. We show that it achieves significantly higher success rates than the baselines, at a reduced computational burden.Open Acces

A Parallel Feature-preserving Mesh Variable Offsetting Method with Dynamic Programming

Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and normal vector, a new calculation of offset position is proposed by using dynamic programming and quadratic programming, and the sharp feature can be preserved after offsetting. Instead of distance implicit field, a spatial coverage region represented by polyhedral for computing offsets is proposed. Our method can generate an offsetting model with smaller mesh size, and also can achieve high quality without gaps, holes, and self-intersections. Moreover, several acceleration techniques are proposed for the efficient mesh offsetting, such as the parallel computing with grid, AABB tree and rays computing. In order to show the efficiency and robustness of the proposed framework, we have tested our method on the quadmesh dataset, which is available at [https://www.quadmesh.cloud]. The source code of the proposed algorithm is available on GitHub at [https://github.com/iGame-Lab/PFPOffset]