๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Closure of Boolean operations on geometric entities

โœ Scribed by R.B. Tilove; A.A.G. Requicha

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
811 KB
Volume
12
Category
Article
ISSN
0010-4485

No coin nor oath required. For personal study only.

โœฆ Synopsis

Boolean operations akin to set intersection, union, and difference play an important role in CAD/CAM. Geometric entities of practical interest (e.g. polygons or polyhedra) are not algebraically closed under the conventional set operators, and therefore algorithms cannot implement conventional set operations if they are to produce results that can be used in subsequent calculations. This paper demonstrates that closure raises delicate issues, and presents a correct mathematical approach based on the topological notion of regularity.

๐Ÿ“œ SIMILAR VOLUMES

On representation and approximation of o
On representation and approximation of operations in Boolean algebras
โœ I. R. Goodman; Vladik Kreinovich ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 78 KB ๐Ÿ‘ 1 views

Several universal approximation and universal representation results are known for non-Boolean multivalued logics such as fuzzy logics. In this paper, we show that similar results can be proven for multivalued Boolean logics as well.

On Certain Closure Operators Defined by
On Certain Closure Operators Defined by Families of Semiring Morphisms
โœ Georg Karner; Werner Kuich ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 153 KB

Given a continuous semiring A and a collection แ‘ข of semiring morphisms mapping the elements of A into finite matrices with entries in A we define แ‘ข-closed semirings. These are fully rationally closed semirings that are closed under the following operation: each morphism in แ‘ข maps an element of the แ‘ข

Analytical properties of measure geometr
Analytical properties of measure geometric Krein-Feller-operators on the real line
โœ Uta Freiberg ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 163 KB

## Abstract We investigate analytical properties of a measure geometric Laplacian which is given as the second derivative $ {d \over {d \mu}} {d \over {d \nu}} $ w.r.t. two atomless finite Borel measures __ฮผ__ and __ฮฝ__ with compact supports supp __ฮผ__ โŠ‚ supp __ฮฝ__ on the real line. This class of o