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Geometric Objects (geometric + object)

Distribution by Scientific Domains
Engineering40%

Selected Abstracts

Variable Resolution 4- k Meshes: Concepts and Applications

COMPUTER GRAPHICS FORUM, Issue 4 2000
Luiz Velho
In this paper we introduce variable resolution 4-k meshes, a powerful structure for the representation of geometric objects at multiple levels of detail. It combines most properties of other related descriptions with several advantages, such as more flexibility and greater expressive power. The main unique feature of the 4-k mesh structure lies in its variable resolution capability, which is crucial for adaptive computation. We also give an overview of the different methods for constructing the 4-k mesh representation, as well as the basic algorithms necessary to incorporate it in modeling and graphics applications. [source]

Urban Textural Analysis from Remote Sensor Data: Lacunarity Measurements Based on the Differential Box Counting Method

GEOGRAPHICAL ANALYSIS, Issue 4 2006
Soe W. Myint
Lacunarity is related to the spatial distribution of gap or hole sizes. For low lacunarity, all gap sizes are the same and geometric objects are deemed homogeneous; conversely, for high lacunarity, gap sizes are variable and objects are therefore heterogeneous. Textures that are homogeneous at small scales can be quite heterogeneous at large scales and vice versa, and hence, lacunarity can be considered a scale-dependent measure of heterogeneity or texture. In this article, we use a lacunarity method based on a differential box counting approach to identify urban land-use and land-cover classes from satellite sensor data. Our methodology focuses on two different gliding box methods to compute lacunarity values and demonstrate a mirror extension approach for a local moving window. The extension approach overcomes, or at least minimizes, the boundary problem. The results from our study suggest that the overlapping box approach is more effective than the skipping box approach, but that there is no significant difference between window sizes. Our work represents a contribution to not only advances in textural and spatial metrics as used in remote-sensing pattern interpretation but also for broadening understanding of the computational geometry of nonlinear shape models of which lacunarity is the reciprocal of fractal theory. [source]

Visualization of material stiffness in geomechanics analysis

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2006
Donald C. Wotring
Abstract This paper presents novel visualization techniques to simplify representation of the fourth-order material stiffness tensor as a set of three-dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non-linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three-dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non-linear and path dependent material models. The proposed stiffness visualization can be represented as 3-D, 2-D and 1-D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Surface wavelets: a multiresolution signal processing tool for 3D computational modelling

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001
Kevin Amaratunga
Abstract In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN) 7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Statistical Mechanical Modeling of Protein Adsorption

MATERIALWISSENSCHAFT UND WERKSTOFFTECHNIK, Issue 12 2003
P. R. Van TasselArticle first published online: 5 JAN 200
Abstract We present rationale for and a derivation of a statistical mechanical model of protein adsorption. Proteins are modeled as rigid geometric objects adsorbing initially in a reversible manner and subsequently undergoing an irreversible change in shape to a permanently adsorbed state. Both adsorption and shape change occur subject to energetic interactions with previously adsorbed proteins. We evaluate the model quantitatively for proteins with disk-shaped projections within the scaled particle theory and compare the predictions to experimental measurements taken via optical waveguide lightmode spectroscopy. [source]