57,792 research outputs found
Chain-Based Representations for Solid and Physical Modeling
In this paper we show that the (co)chain complex associated with a
decomposition of the computational domain, commonly called a mesh in
computational science and engineering, can be represented by a block-bidiagonal
matrix that we call the Hasse matrix. Moreover, we show that
topology-preserving mesh refinements, produced by the action of (the simplest)
Euler operators, can be reduced to multilinear transformations of the Hasse
matrix representing the complex. Our main result is a new representation of the
(co)chain complex underlying field computations, a representation that provides
new insights into the transformations induced by local mesh refinements. Our
approach is based on first principles and is general in that it applies to most
representational domains that can be characterized as cell complexes, without
any restrictions on their type, dimension, codimension, orientability,
manifoldness, connectedness
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
The goal of this paper is to introduce a new method in computer-aided
geometry of solid modeling. We put forth a novel algebraic technique to
evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with
regularized operators of union, intersection, and difference, i.e., any CSG
tree. The result is obtained in three steps: first, by computing an independent
set of generators for the d-space partition induced by the input; then, by
reducing the solid expression to an equivalent logical formula between Boolean
terms made by zeros and ones; and, finally, by evaluating this expression using
bitwise operators. This method is implemented in Julia using sparse arrays. The
computational evaluation of every possible solid expression, usually denoted as
CSG (Constructive Solid Geometry), is reduced to an equivalent logical
expression of a finite set algebra over the cells of a space partition, and
solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig
On relating functional modeling approaches: abstracting functional models from behavioral models
This paper presents a survey of functional modeling approaches and describes a strategy to establish functional knowledge exchange between them. This survey is focused on a comparison of function meanings and representations. It is argued that functions represented as input-output flow transformations correspond to behaviors in the approaches that characterize functions as intended behaviors. Based on this result a strategy is presented to relate the different meanings of function between the approaches, establishing functional knowledge exchange between them. It is shown that this strategy is able to preserve more functional information than the functional knowledge exchange methodology of Kitamura, Mizoguchi, and co-workers. The strategy proposed here consists of two steps. In step one, operation-on-flow functions are translated into behaviors. In step two, intended behavior functions are derived from behaviors. The two-step strategy and its benefits are demonstrated by relating functional models of a power screwdriver between methodologies
BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning
The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples
Review of research in feature-based design
Research in feature-based design is reviewed. Feature-based design is regarded as a key factor towards CAD/CAPP integration from a process planning point of view. From a design point of view, feature-based design offers possibilities for supporting the design process better than current CAD systems do. The evolution of feature definitions is briefly discussed. Features and their role in the design process and as representatives of design-objects and design-object knowledge are discussed. The main research issues related to feature-based design are outlined. These are: feature representation, features and tolerances, feature validation, multiple viewpoints towards features, features and standardization, and features and languages. An overview of some academic feature-based design systems is provided. Future research issues in feature-based design are outlined. The conclusion is that feature-based design is still in its infancy, and that more research is needed for a better support of the design process and better integration with manufacturing, although major advances have already been made
A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters
This paper proposes a hierarchical, multi-resolution framework for the
identification of model parameters and their spatially variability from noisy
measurements of the response or output. Such parameters are frequently
encountered in PDE-based models and correspond to quantities such as density or
pressure fields, elasto-plastic moduli and internal variables in solid
mechanics, conductivity fields in heat diffusion problems, permeability fields
in fluid flow through porous media etc. The proposed model has all the
advantages of traditional Bayesian formulations such as the ability to produce
measures of confidence for the inferences made and providing not only
predictive estimates but also quantitative measures of the predictive
uncertainty. In contrast to existing approaches it utilizes a parsimonious,
non-parametric formulation that favors sparse representations and whose
complexity can be determined from the data. The proposed framework in
non-intrusive and makes use of a sequence of forward solvers operating at
various resolutions. As a result, inexpensive, coarse solvers are used to
identify the most salient features of the unknown field(s) which are
subsequently enriched by invoking solvers operating at finer resolutions. This
leads to significant computational savings particularly in problems involving
computationally demanding forward models but also improvements in accuracy. It
is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling
which is embarrassingly parallelizable and circumvents issues with slow mixing
encountered in Markov Chain Monte Carlo schemes
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Hybrid Prototypes to Assist Modeling Automotive Seats
The development of new modular seats is an important issue in the automotive industry.
However, is very time consuming and costly. Virtual models and hybrid prototypes could
accelerate the car seats development process. The hybrid prototypes are mainly manufactured by
rapid prototyping with multi materials. The objective of this paper is to establish a methodology
to develop innovative lightweight multi-functional, modular car seats to be used in Multi-Purpose
Vehicles (MPV), by means of FEA simulation and rapid prototyping additive/subtractive
technologies utilizing multi materials. A case study is presented to validate the developed
methodology. The manufactured hybrid prototype’s reproduces the main functionalities of the
MPV modular seat, namely its three key positions: normal, stored and table.Mechanical Engineerin
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