3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective

The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a three- and four-dimensional space. Furthermore, we design a system of polynomial equations to construct occluding contours of algebraic surfaces in a 4-D perspective. The method is presented on a composed 3-D scene and three 4-D cases with gradual complexity. In general, our goal is to improve the understanding of spatial properties in a four-dimensional space

A Framework Using Tangible Interaction for Automatically Capturing and Embedding Design Intent in Parametric Models

The objective of this research is to address some of the challenges of parametric design associated with defining a model’s frameworks using mathematics and computer programming. This work proposes a tactile-based approach to automate the generation of such information. A design-based research method is implemented for this work, which involves developing research prototypes consisting of Tangible User-Interfaces (TUIs) to demonstrate and test the digital-physical workflow. Five prototypes were created each generating a type of information for setting up parametric models, including; linear and polynomial mathematical equations, algorithmic rules and seed configurations for a Cellular Automata (CA) component, geometric transformations (single and compound), and Non-Uniform Rational Basis Spline (NURBS) objects. During the progress of the work, prototypes were improved to include a higher level of automation by performing multiple and more complex modeling tasks. This research includes two levels of evaluation. The first is system correctness, which tests the prototypes for translating tangible interaction with design objects into modeling information. The second is a qualitative comparison between the developed method and the conventional parametric modeling approach using graph-based and/or text-based programming applications. The results of the research have shown the plausibility of the workflow and its potential benefits for parametric modeling practice and education. This work provides a proof-of-concept for a novel approach that translates design intents into mathematical and algorithmic modeling information for establishing parametric frameworks. The outcomes of this research include; detailed workflows describing algorithmic procedures for interpreting analog data, TUI specifications, and an overall theoretical framework of the method

Doctor of Philosophy

dissertationThe medial axis of an object is a shape descriptor that intuitively presents the morphology or structure of the object as well as intrinsic geometric properties of the object’s shape. These properties have made the medial axis a vital ingredient for shape analysis applications, and therefore the computation of which is a fundamental problem in computational geometry. This dissertation presents new methods for accurately computing the 2D medial axis of planar objects bounded by B-spline curves, and the 3D medial axis of objects bounded by B-spline surfaces. The proposed methods for the 3D case are the first techniques that automatically compute the complete medial axis along with its topological structure directly from smooth boundary representations. Our approach is based on the eikonal (grassfire) flow where the boundary is offset along the inward normal direction. As the boundary deforms, different regions start intersecting with each other to create the medial axis. In the generic situation, the (self-) intersection set is born at certain creation-type transition points, then grows and undergoes intermediate transitions at special isolated points, and finally ends at annihilation-type transition points. The intersection set evolves smoothly in between transition points. Our approach first computes and classifies all types of transition points. The medial axis is then computed as a time trace of the evolving intersection set of the boundary using theoretically derived evolution vector fields. This dynamic approach enables accurate tracking of elements of the medial axis as they evolve and thus also enables computation of topological structure of the solution. Accurate computation of geometry and topology of 3D medial axes enables a new graph-theoretic method for shape analysis of objects represented with B-spline surfaces. Structural components are computed via the cycle basis of the graph representing the 1-complex of a 3D medial axis. This enables medial axis based surface segmentation, and structure based surface region selection and modification. We also present a new approach for structural analysis of 3D objects based on scalar functions defined on their surfaces. This approach is enabled by accurate computation of geometry and structure of 2D medial axes of level sets of the scalar functions. Edge curves of the 3D medial axis correspond to a subset of ridges on the bounding surfaces. Ridges are extremal curves of principal curvatures on a surface indicating salient intrinsic features of its shape, and hence are of particular interest as tools for shape analysis. This dissertation presents a new algorithm for accurately extracting all ridges directly from B-spline surfaces. The proposed technique is also extended to accurately extract ridges from isosurfaces of volumetric data using smooth implicit B-spline representations. Accurate ridge curves enable new higher-order methods for surface analysis. We present a new definition of salient regions in order to capture geometrically significant surface regions in the neighborhood of ridges as well as to identify salient segments of ridges

Advances in Robot Kinematics : Proceedings of the 15th international conference on Advances in Robot Kinematics

International audienceThe motion of mechanisms, kinematics, is one of the most fundamental aspect of robot design, analysis and control but is also relevant to other scientific domains such as biome- chanics, molecular biology, . . . . The series of books on Advances in Robot Kinematics (ARK) report the latest achievement in this field. ARK has a long history as the first book was published in 1991 and since then new issues have been published every 2 years. Each book is the follow-up of a single-track symposium in which the participants exchange their results and opinions in a meeting that bring together the best of world’s researchers and scientists together with young students. Since 1992 the ARK symposia have come under the patronage of the International Federation for the Promotion of Machine Science-IFToMM.This book is the 13th in the series and is the result of peer-review process intended to select the newest and most original achievements in this field. For the first time the articles of this symposium will be published in a green open-access archive to favor free dissemination of the results. However the book will also be o↵ered as a on-demand printed book.The papers proposed in this book show that robot kinematics is an exciting domain with an immense number of research challenges that go well beyond the field of robotics.The last symposium related with this book was organized by the French National Re- search Institute in Computer Science and Control Theory (INRIA) in Grasse, France

A methodology for the Lower Limb Robotic Rehabilitation system

The overall goal of this thesis is to develop a new functional lower limb robot-assisted rehabilitation system for people with a paretic lower limb. A unilateral rehabilitation method is investigated, where the robot acts as an assistive device to provide the impaired leg therapeutic training through simulating the kinematics and dynamics of the ankle and lower leg movements. Foot trajectories of healthy subjects and post-stroke patients were recorded by a dedicated optical motion tracking system in a clinical gait measurement laboratory. A prototype 6 degrees of freedom parallel robot was initially built in order to verify capability of achieving singularity-free foot trajectories of healthy subjects in various exercises. This was then followed by building and testing another larger parallel robot to investigate the real-sized foot trajectories of patients. The overall results verify the designed robot’s capability in successfully tracking foot trajectories during different exercises. The thesis finally proposes a system of bilateral rehabilitation based on the concept of self-learning, where a passive parallel mechanism follows and records motion signatures of the patient’s healthy leg, and an active parallel mechanism provides motion for the impaired leg based on the kinematic mapping of the motion produced by the passive mechanism

A Robotic System for Learning Visually-Driven Grasp Planning (Dissertation Proposal)

We use findings in machine learning, developmental psychology, and neurophysiology to guide a robotic learning system\u27s level of representation both for actions and for percepts. Visually-driven grasping is chosen as the experimental task since it has general applicability and it has been extensively researched from several perspectives. An implementation of a robotic system with a gripper, compliant instrumented wrist, arm and vision is used to test these ideas. Several sensorimotor primitives (vision segmentation and manipulatory reflexes) are implemented in this system and may be thought of as the innate perceptual and motor abilities of the system. Applying empirical learning techniques to real situations brings up such important issues as observation sparsity in high-dimensional spaces, arbitrary underlying functional forms of the reinforcement distribution and robustness to noise in exemplars. The well-established technique of non-parametric projection pursuit regression (PPR) is used to accomplish reinforcement learning by searching for projections of high-dimensional data sets that capture task invariants. We also pursue the following problem: how can we use human expertise and insight into grasping to train a system to select both appropriate hand preshapes and approaches for a wide variety of objects, and then have it verify and refine its skills through trial and error. To accomplish this learning we propose a new class of Density Adaptive reinforcement learning algorithms. These algorithms use statistical tests to identify possibly interesting regions of the attribute space in which the dynamics of the task change. They automatically concentrate the building of high resolution descriptions of the reinforcement in those areas, and build low resolution representations in regions that are either not populated in the given task or are highly uniform in outcome. Additionally, the use of any learning process generally implies failures along the way. Therefore, the mechanics of the untrained robotic system must be able to tolerate mistakes during learning and not damage itself. We address this by the use of an instrumented, compliant robot wrist that controls impact forces