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

Heterogeneous Material Modeling with Distance Fields

We propose a universal approach to the outstanding problem of computer modeling of continuously varying distributions of material properties satisfying prescribed material quantities and rates on a finite collection of geometric features. The central notion is a parameterization of the shape’s interior by distances from the material features - either exactly or approximately; this parameterization supports specification, interpolation, and optimization of desired material distributions in a systematic and controlled fashion. We demonstrate how the approach can be implemented within the existing framework of solid modeling and its numerous advantages, including: • precise and intuitive control using explicit, analytic, differential, and integral constraints specified on the original (not discretized) geometric model; • applicability to material features of arbitrary dimension, shape, and topology; and • guaranteed smoothness and analytic properties for superior performance, analysis and optimization. Last, but not least, the proposed approach subsumes and generalizes a number of other proposals for heterogeneous material modeling for FGM, heterogeneous solid modeling, and solid free-form fabrication.Mechanical Engineerin

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

Источник регулируемого тока для катушек Гельмгольца

Разрабатываемое устройство позволит с высокой точностью задавать значение магнитного поля в системе катушек Гельмогольца.The device under development will allow with high accuracy to set the value of the magnetic field in the Helmogoltz coil system

Integrality theorems in the theory of topological strings

We give a simplified derivation of the expression of instanton numbers and of mirror map in terms of Frobenius map on p-adic cohomology and use this expression to prove integrality theorems. Modifying this proof we verify that the Aganagic-Vafa formulas for the number of holomorphic disks can be expressed in terms of Frobenius map on p-adic relative cohomology; this expression permits us to prove integrality of this number.Comment: 33 pages, new results in the last section. Appendix adde

Un recueil de papiers sur le systeme d'exploitation reparti a objets SOS

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