A subdivision scheme for continuous-scale B-splines and affine invariant progressive

Caption title.Includes bibliographical references (p. 19-22).Partially supported by the Rothschild Foundation-Yad Hanadiv. Partially supported by the Army Research Office. DAAL03-92-G-0115Guillermo Sapiro, Albert Cohen, Alfred M. Bruckstein

Uncovering the specificities of CAD tools for industrial design with design theory – style models for generic singularity

International audienceAccording to some casual observers, computer-aided design (CAD) tools are very similar. These tools are used to design new artifacts in a digital environment; hence, they share typical software components, such as a computing engine and human-machine interface. However, CAD software is dedicated to specific professionals—such as engineers, three-dimensional (3D) artists, and industrial designers (IDs)—who claim that, despite their apparent similarities, CAD tools are so different that they are not substitutable. Moreover, CAD tools do not fully meet the needs of IDs. This paper aims at better characterizing CAD tools by taking into account their underlying design logic, which involves relying on recent advances in design theory. We show that engineering CAD tools are actually modeling tools that design a generic variety of products; 3D artist CAD tools not only design but immediately produce single digital artefacts; and ID CAD tools are neither a mix nor an hybridization of engineering CAD and 3D artist CAD tools but have their own logic, namely to create new conceptual models for a large variety of products, that is, the creation of a unique original style that leads to a generic singularity. Such tools are useful for many creative designers beyond IDs

Introductory lectures to loop quantum gravity

We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.Comment: Based on lectures given at the 3eme Ecole de Physique Theorique de Jijel, Algeria, 26 Sep -- 3 Oct, 2009. 52 pages, many figures. v2 minor corrections. To be published in the proceeding

A variational model for fracture and debonding of thin films under in-plane loadings

We study fracture and debonding of a thin stiff film bonded to a rigid substrate through a thin compliant layer, introducing a two-dimensional variational fracture model in brittle elasticity. Fractures are naturally distinguished between transverse cracks in the film (curves in 2D) and debonded surfaces (2D planar regions). In order to study the mechanical response of such systems under increasing loads, we formulate a dimension-reduced, rate-independent, irreversible evolution law accounting for both transverse fracture and debonding. We propose a numerical implementation based on a regularized formulation of the fracture problem via a gradient damage functional, and provide an illustration of its capabilities exploring complex crack patterns, showing a qualitative comparison with geometrically involved real life examples. Moreover, we justify the underlying dimension-reduced model in the setting of scalar-valued displacement fields by a rigorous asymptotic analysis using Γ-convergence, starting from the three-dimensional variational fracture (free-discontinuity) problem under precise scaling hypotheses on material and geometric parameters. © 2014 Elsevier Ltd

A variational approach for viewpoint-based visibility maximization

We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface from a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. This latter contribution receives significant focus in this thesis as it is crucial to obtain the desired unfolding effect derived from the first energy functional and flow. Without it, the resulting topology changes render the unconstrained evolution uninteresting for the purpose of cortical visualization, exploration, and inspection. The third is a method that dramatically improves the computational speed of the 3D topology-preservation approach by creating a tree structure of the triangulated surface and using a recursion technique.Ph.D.Committee Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Yezzi; Committee Member: Gregory Turk; Committee Member: Joel R. Jackson; Committee Member: Patricio A. Vel

A variational technique for three-dimensional reconstruction of local structure

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 1999.Includes bibliographical references (leaves 66-70).by Eric Raphaël Amram.S.M

Kaijus as environments: design & production of a colossal monster functioning as a boss level

Boss fights are a staple in most video game genres. They are milestones in the adventure, designed and intended to test the skills that the player has acquired throughout their adventure. In some cases, they even define the whole experience of the game, especially one type of enemy that has appeared in several instances and every genre: colossal bosses, monsters of giant proportions usually used as a matter of spectacle and a simple yet effective way to showcase the sheer power that players have achieved up until that point in the adventure. Titles like God of War, Shadow of the Colossus and even many Super Mario titles use this concept in their video games in imaginative ways to create Kaiju-like creatures working as a living environment the player has to traverse to defeat them. However, what is the process behind creating a colossal boss that works as a breathing environment, and how can it be achieved? This project aims to study the process of colossal boss creation and design and apply level design and asset creation. To do this, the author will investigate the main aspects and key-defining features of these bosses, analyzing the strengths and weaknesses of existing bosses in videogames such as God of War 3’s Cronos and Shadow of the Colossus and Solar Ash’s bosses in terms of art production and game design. From this study and following the art process for creating creatures in the video game industry, the author will conceptualize, design and produce a working, playable prototype of a boss fight, showcased in the final presentation

Isogeometric Approximation of Variational Problems for Shells

The interaction of applied geometry and numerical simulation is a growing field in the interplay of com- puter graphics, computational mechanics and applied mathematics known as isogeometric analysis. In this thesis we apply and analyze Loop subdivision surfaces as isogeometric tool because they provide great flexibility in handling surfaces of arbitrary topology combined with higher order smoothness. Compared with finite element methods, isogeometric methods are known to require far less degrees of freedom for the modeling of complex surfaces but at the same time the assembly of the isogeo- metric matrices is much more time-consuming. Therefore, we implement the isogeometric subdivision method and analyze the experimental convergence behavior for different quadrature schemes. The mid-edge quadrature combines robustness and efficiency, where efficiency is additionally increased via lookup tables. For the first time, the lookup tables allow the simulation with control meshes of arbitrary closed connectivity without an initial subdivision step, i.e. triangles can have more than one vertex with valence different from six. Geometric evolution problems have many applications in material sciences, surface processing and modeling, bio-mechanics, elasticity and physical simulations. These evolution problems are often based on the gradient flow of a geometric energy depending on first and second fundamental forms of the surface. The isogeometric approach allows a conforming higher order spatial discretization of these geometric evolutions. To overcome a time-error dominated scheme, we combine higher order space and time discretizations, where the time discretization based on implicit Runge-Kutta methods. We prove that the energy diminishes in every time-step in the fully discrete setting under mild time-step restrictions which is the crucial characteristic of a gradient flow. The overall setup allows for a general type of fourth-order energies. Among others, we perform experiments for Willmore flow with respect to different metrics. In the last chapter of this thesis we apply the time-discrete geodesic calculus in shape space to the space of subdivision shells. By approximating the squared Riemannian distance by a suitable energy, this approach defines a discrete path energy for a consistent computation of geodesics, logarithm and exponential maps and parallel transport. As approximation we pick up an elastic shell energy, which measures the deformation of a shell by membrane and bending contributions of its mid-surface. Bézier curves are a fundamental tool in computer-aided geometric design. We extend these to the subdivision shell space by generalizing the de Casteljau algorithm. The evaluation of Bézier curves depends on all input data. To solve this problem, we introduce B-splines and cardinal splines in shape space by gluing together piecewise Bézier curves in a smooth way. We show examples of quadratic and cubic Bézier curves, quadratic and cubic B-splines as well as cardinal splines in subdivision shell space

2D growth processes: SLE and Loewner chains

This review provides an introduction to two dimensional growth processes. Although it covers a variety processes such as diffusion limited aggregation, it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner evolutions (SLE) which are Markov processes describing interfaces in 2D critical systems. It starts with an informal discussion, using numerical simulations, of various examples of 2D growth processes and their connections with statistical mechanics. SLE is then introduced and Schramm's argument mapping conformally invariant interfaces to SLE is explained. A substantial part of the review is devoted to reveal the deep connections between statistical mechanics and processes, and more specifically to the present context, between 2D critical systems and SLE. Some of the SLE remarkable properties are explained, as well as the tools for computing with SLE. This review has been written with the aim of filling the gap between the mathematical and the physical literatures on the subject.Comment: A review on Stochastic Loewner evolutions for Physics Reports, 172 pages, low quality figures, better quality figures upon request to the authors, comments welcom