Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms

Geometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments -- An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations -- Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities -- If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints -- Otherwise, a diagnostic of inconsistency is expected -- The three main approaches used for this problem are numerical, procedural or operational and mathematical -- Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one -- The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations -- The common roots to this set of polynomials characterizes the solution space for such a problem -- That work presents the use of Groebner basis techniques for verifying the consistency of the constraints -- It also integrates subgroups of the Special Euclidean Group of Displacements SE(3) in the problem formulation to exploit the structure implied by geometric relations -- Although theoretically sound, these techniques require large amounts of computing resources -- This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities -- The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem -- Cluster identification can be related to identifying short cycles in the Spatial Con straint graph for the GCS/SF problem -- Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles -- Besides improving theefficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem -- This is illustrated by applying the discussed techniques to the analysis of the degrees of freedom of mechanism

EGCL: an extended G-Code Language with flow control, functions and mnemonic variables

In the context of computer numerical control (CNC) and computer aided manufacturing (CAM), the capabilities of programming languages such as symbolic and intuitive programming, program portability and geometrical portfolio have special importance -- They allow to save time and to avoid errors during part programming and permit code re-usage -- Our updated literature review indicates that the current state of art presents voids in parametric programming, program portability and programming flexibility -- In response to this situation, this article presents a compiler implementation for EGCL (Extended G-code Language), a new, enriched CNC programming language which allows the use of descriptive variable names, geometrical functions and flow-control statements (if-then-else, while) -- Our compiler produces low-level generic, elementary ISO-compliant Gcode, thus allowing for flexibility in the choice of the executing CNC machine and in portability -- Our results show that readable variable names and flow control statements allow a simplified and intuitive part programming and permit re-usage of the programs -- Future work includes allowing the programmer to define own functions in terms of EGCL, in contrast to the current status of having them as library built-in function

Fixed grid finite element analysis for 3D structural problems

Fixed Grid (FG) methodology was first introduced by García and Steven as an engine for numerical estimation of two-dimensional elasticity problems -- The advantages of using FG are simplicity and speed at a permissible level of accuracy -- Two dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources -- Moreover, FG has been used as the analytical kernel for different structural optimisation methods as Evolutionary Structural Optimisation, Genetic Algorithms (GA), and Evolutionary Strategies -- FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements -- Elements are assessed to be inside (I), outside (O) or neither inside nor outside (NIO) of the object -- Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem -- As a result of the subdivision NIO elements have non-continuous properties -- They can be approximated in different ways which range from simple setting of NIO elements as O to complex noncontinuous domain integration -- If homogeneously averaged material properties are used to approximate the NIO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes -- This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements -- In addition inclusion/exclusion of O elements in the global stiffness matrix is studied -- Preliminary results shown that non-continuous NIO elements improve the accuracy of the results with considerable savings in time -- Numerical examples are presented to illustrate the possibilities of the metho

On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface

We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifold

Edge and corner identification for tracking the line of sight

This article presents an edge-corner detector, implemented in the realm of the GEIST project (an Computer Aided Touristic Information System) to extract the information of straight edges and their intersections (image corners) from camera-captured (real world) and computer-generated images (from the database of Historical Monuments, using observer position and orientation data) -- Camera and computer-generated images are processed for reduction of detail, skeletonization and corner-edge detection -- The corners surviving the detection and skeletonization process from both images are treated as landmarks and fed to a matching algorithm, which estimates the sampling errors which usually contaminate GPS and pose tracking data (fed to the computer-image generatator) -- In this manner, a closed loop control is implemented, by which the system converges to exact determination of position and orientation of an observer traversing a historical scenario (in this case the city of Heidelberg) -- With this exact position and orientation, in the GEIST project other modules are able to project history tales on the view field of the observer, which have the exact intended scenario (the real image seen by the observer) -- In this way, the tourist “sees” tales developing in actual, material historical sites of the city -- To achieve these goals this article presents the modification and articulation of algorithms such as the Canny Edge Detector, SUSAN Corner Detector, 1-D and 2-D filters, etceter

Finite Element Modeling of Composite Materials using Kinematic Constraints

El propósito de este artículo es presentar simulaciones del comportamiento de materiales compuestos basado en restricciones cinemáticas entre las mismas fibras y entre las fibras y la resina circundante -- En la revisión de literatura, los autores han encontrado que las restricciones cinemáticas no han sido plenamente explotadas para modelar materiales compuestos, probablemente debido a su alto costo computacional -- El propósito de este artículo es exponer la implementación y resultados de tal modelo, usando Análisis por Elementos Finitos de restricciones geométricas prescritas a los nodos de la resina y las fibras -- Las descripciones analíticas del comportamiento de materiales compuestos raramente aparecen -- Muchas aproximaciones para describir materiales compuestos en capas son basadas en la teoría de funciones C1 Z y C0Z, tal como la Teoría Clásica de Capas (CLT) -- Estas teorías de funciones contienen significativas simplificaciones del material, especialmente para compuestos tejidos -- Una aproximación hibrida para modelar materiales compuestos con Elementos Finitos (FEA) fue desarrollada por Sidhu y Averill [1] y adaptada por Li y Sherwood [2] para materiales compuestos tejidos con polipropileno de vidrio -- Este artículo presenta un método para obtener valores para las propiedades de los materiales compuestos -- Tales valores son usados para simular las fibras reforzadas tejidas aplicando elementos de capas en el software ANSYS -- El presente modelo requiere menos simplificaciones que las teorías C1Z y C0Z -- En el artículo presente, a diferencia del modelo Li–Sherwood, el tejido es modelado geométricamente -- Una Representación por la Frontera (B-Rep del modelo “Hand”) con genus 1 (con geometría compleja) fue usada para aplicar restricciones geométricas a las capas de resina, fibra, etcétera, mostrando que es apropiada para simular estructuras complejas -- En el futuro, las propiedades no–lineales de los materiales deben ser consideradas, y el trabajo experimental requerido debe ser realizad

Optical Enhancement of Exoskeleton-Based Estimation of Glenohumeral Angles

In Robot-Assisted Rehabilitation (RAR) the accurate estimation of the patient limb joint angles is critical for assessing therapy efficacy. In RAR, the use of classic motion capture systems (MOCAPs) (e.g., optical and electromagnetic) to estimate the Glenohumeral (GH) joint angles is hindered by the exoskeleton body, which causes occlusions and magnetic disturbances. Moreover, the exoskeleton posture does not accurately reflect limb posture, as their kinematic models differ. To address the said limitations in posture estimation, we propose installing the cameras of an optical marker-based MOCAP in the rehabilitation exoskeleton. Then, the GH joint angles are estimated by combining the estimated marker poses and exoskeleton Forward Kinematics. Such hybrid system prevents problems related to marker occlusions, reduced camera detection volume, and imprecise joint angle estimation due to the kinematic mismatch of the patient and exoskeleton models. This paper presents the formulation, simulation, and accuracy quantification of the proposed method with simulated human movements. In addition, a sensitivity analysis of the method accuracy to marker position estimation errors, due to system calibration errors and marker drifts, has been carried out. The results show that, even with significant errors in the marker position estimation, method accuracy is adequate for RAR

Real-time volume rendering and tractography visualization on the web

In the field of computer graphics, Volume Rendering techniques allow the visualization of 3D datasets, and specifically, Volume Ray-Casting renders images from volumetric datasets, typically used in some scientific areas, such as medical imaging -- This article aims to describe the development of a combined visualization of tractography and volume rendering of brain T1 MRI images in an integrated way -- An innovative web viewer for interactive visualization of neuro-imaging data has been developed based on WebGL -- This recently developed standard enables the clients to use the web viewer on a wide range of devices, with the only requirement of a compliant web-browser -- As the majority of the rendering tasks take place in the client machine, the effect of bottlenecks and server overloading are minimized -- The web application presented is able to compete with desktop tools, even supporting high graphical demands and facing challenges regarding performance and scalability -- The developed software modules are available as open source code and include MRI volume data and tractography generated by the Diffusion Toolkit, and connectivity data from the Connectome Mapping Toolkit -- Our contribution for the Volume Web Viewer implements early ray termination step according to the tractography depthmap, combining volume images and estimated white matter fibers -- Furthermore, the depthmap system extension can be used for visualization of other types of data, where geometric and volume elements are displayed simultaneousl

DigitLAB, an Environment and Language for Manipulation of 3D Digitizations

In Computer Aided Geometric Design the fitting of surfaces to massive series of data points has many applications, ranging from medicine to aerophotogrametry -- However, even the mathematical meaning of fitting a surface to a set of points is dependent on functional considerations, and not only on the geometric properties of the point set -- Also, characteristics of some parts of the data set must be interpreted as stochastic in nature, while others must be taken as literal and therefore they become constraints of the surface -- For these reasons, among others, automated surface fitting alone does not produce results usable at industrial level -- At the same time, it does not take advantage of sampling patterns, particular shapes of the cross sections, functionally different regions within the object, etc -- The latest literature reviews show the need for utilities to process point data sets that must be asynchronous, (applicable at any time and upon any region of the point set) -- Addressing this need, this article reports new tools developed within DigitLAB, a language that allows topological traversal, retrieval and statistical modifications to the data, and surface fitting -- They can handle arbitrary topology, as case studies in medicine, mathematics, landscaping, etc discussed here demonstrat