Continuous collision detection for ellipsoids

We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop a real-time algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples. © 2006 IEEE.published_or_final_versio

Subdivision methods for solving polynomial equations

International audienceThis paper presents a new algorithm for solving a system of polynomials, in a domain of $^n$. It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke and Patrikalakis . It uses a powerful reduction strategy based on univariate root finder using Bernstein basis representation and Descarte's rule. We analyse the behavior of the method, from a theoretical point of view, shows that for simple roots, it has a local quadratic convergence speed and gives new bounds for the complexity of approximating real roots in a box of $^n$. The improvement of our approach, compared with classical subdivision methods, is illustrated on geometric modeling applications such as computing intersection points of implicit curves, self-intersection points of rational curves, and on the classical parallel robot benchmark problem

Silhouette-Informed Trajectory Generation Through a Wire Maze for Small UAS

Current rapidly-exploring random tree (RRT) algorithms rely on proximity query packages that often include collision checkers, tolerance verification, and distance computation algorithms for the generation of safe paths. In this paper, we broaden the information available to the path-planning algorithm by incorporating silhouette information of nearby obstacles in conflict. A silhouette-informed tree (SIT) is generated through the flight-safe region of a wire maze for a single unmanned aerial system (UAS). The silhouette is used to extract local geometric information of nearby obstacles and provide path alternatives around these obstacles. Thus, focusing the search for the generation of new tree branches near these obstacles, and decreasing the number of samples required to explore the narrow corridors within the wire maze. The SIT is then processed to extract a path that connects the initial location of the UAS with the goal, reduce the number of line segments in this path if possible, and smooth the resulting path using Pythagorean Hodograph Bezier curves. To ensure that the smoothed path remains in the flight-safe region of the configuration space, a tolerance verification algorithm for Bezier curves and convex polytopes in three dimensions is proposed. Lastly, temporal specifications are imposed on the smoothed path in the shape of an arbitrary speed profile

Registration of spatial image sequences for quantitative evaluation of free-form surfaces

This contribution describes an iterative registration method of spatial image sequences in view of accurate measurements and 3D reconstruction of free-form surfaces. Each image is represented by a set of 3D points characterizing the surface to be analyzed, gained with a technique based on the use of a structured light. The novelty of our registration method lies in interpolation of the imaged surfaces for the matching step and in the automated determination of the overlap region between two consecutive images of the sequence. The use of a statistical criterion enables to discard the matchings of bad quality. The actual displacement is computed using a least-squares technique based on unit quaternions and knowing a priori and approximately the displacement between two positions of the sensor. Processing the whole sequence enables to express the points of all images in a common reference frame. Results on both synthetic and real sequences assess efficiency and robustness of this registration procedure.Cette contribution décrit une méthode itérative de recalage de séquences spatiales d'images en vue d'une mesure 3D précise et d'une reconstruction de surfaces gauches quelconques. Chaque image est représentée par une collection de points 3D caractérisant la surface à analyser, obtenue par une technique de projection de lumière structurée. La nouveauté de notre méthode de recalage réside dans l'interpolation des surfaces imagées pour l'étape d'appariement et dans la détermination automatique de la zone de recouvrement entre deux images consécutives de la séquence. L'utilisation d'un critère statistique permet d'éliminer les appariements de mauvaise qualité. Le déplacement effectif est calculé par une technique de moindres carrés reposant sur les quaternions unitaires en connaissant a priori et approximativement le déplacement entre deux positions du système de prise de vues. Le traitement de la séquence complète permet d'exprimer les points de toutes les images dans un même référentiel. Des résultats expérimentaux sur des données synthétiques et réelles montrent que cette méthode de recalage est robuste et précise

Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface

We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the capillary surface. Using a single graph representation, we interpret this geometric motion as a gradient flow on a Hilbert manifold. We propose unconditionally stable first/second order numerical schemes to simulate this geometric motion of the droplet, which is described using motion by mean curvature coupled with moving contact lines. The schemes are based on (i) explicit moving boundaries, which decouple the dynamic updates of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with a nonlinear elliptic solver upto second order accuracy. For the case of quasi-static dynamics with continuous spatial variable in the numerical schemes, we prove the stability and convergence of the first/second order numerical schemes. To demonstrate the accuracy and long-time validation of the proposed schemes, several challenging computational examples - including breathing droplets, droplets on inhomogeneous rough surfaces and quasi-static Kelvin pendant droplets - are constructed and compared with exact solutions to quasi-static dynamics obtained by desingularized differential-algebraic system of equations (DAEs).Comment: 8 figures, 48 page

Robust interrogation of differential properties for design and manufacture

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1994, and Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1994.Includes bibliographical references (leaves 120-123).by George D. Margetis.M.S

Digital Alchemy: Matter and Metamorphosis in Contemporary Digital Animation and Interface Design

The recent proliferation of special effects in Hollywood film has ushered in an era of digital transformation. Among scholars, digital technology is hailed as a revolutionary moment in the history of communication and representation. Nevertheless, media scholars and cultural historians have difficulty finding a language adequate to theorizing digital artifacts because they are not just texts to be deciphered. Rather, digital media artifacts also invite critiques about the status of reality because they resurrect ancient problems of embodiment and transcendence.In contrast to scholarly approaches to digital technology, computer engineers, interface designers, and special effects producers have invented a robust set of terms and phrases to describe the practice of digital animation. In order to address this disconnect between producers of new media and scholars of new media, I argue that the process of digital animation borrows extensively from a set of preexisting terms describing materiality that were prominent for centuries prior to the scientific revolution. Specifically, digital animators and interface designers make use of the ancient science, art, and technological craft of alchemy. Both alchemy and digital animation share several fundamental elements: both boast the power of being able to transform one material, substance, or thing into a different material, substance, or thing. Both seek to transcend the body and materiality but in the process, find that this elusive goal (realism and gold) is forever receding onto the horizon.The introduction begins with a literature review of the field of digital media studies. It identifies a gap in the field concerning disparate arguments about new media technology. On the one hand, scholars argue that new technologies like cyberspace and digital technology enable radical new forms of engagement with media on individual, social, and economic levels. At the same time that media scholars assert that our current epoch is marked by a historical rupture, many other researchers claim that new media are increasingly characterized by ancient metaphysical problems like embodiment and transcendence. In subsequent chapters I investigate this disparity