Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308704932> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W4308704932 endingPage "103436" @default.
- W4308704932 startingPage "103436" @default.
- W4308704932 abstract "An early research in solid modeling led by Herbert Voelcker at the University of Rochester and later at Cornell suggested that every solid representation scheme corresponds to an algebra, where the elements of the algebra are solid representations constructed and edited using operations in the algebra. For example, every CSG representation describes an element in a finite Boolean algebra of closed regular sets, whereas every boundary representation describes an element of a vector space of 2-chains in an algebraic topological chain complex. In this paper, we elucidate the precise relationships (functors) between all algebras used for CSG and boundary representations of solids. Based on these properties, we show that many solid modeling operations, including boundary evaluation, reduce to straightforward algebraic operations or application of identified functors that are efficiently implemented using point membership tests and sparse matrix operations. To fully exploit the efficacy of the new algebraic approach to solid modeling, all algorithms are fully implemented in Julia, the modern language of choice for numerical and scientific computing. • New research direction in solid modeling. • Algebraic relationships between CSG and boundary representations of PL solids. • Arrangements are isomorphic to the finite Boolean algebra of regularized sets. • This algebra is isomorphic to a linear vector space of 3-chains. • Operations on CSG and b-reps reduce to composition of algebraic operations. operations." @default.
- W4308704932 created "2022-11-14" @default.
- W4308704932 creator A5034405971 @default.
- W4308704932 creator A5035988852 @default.
- W4308704932 creator A5037860974 @default.
- W4308704932 creator A5074046624 @default.
- W4308704932 creator A5076800717 @default.
- W4308704932 date "2023-02-01" @default.
- W4308704932 modified "2023-09-25" @default.
- W4308704932 title "Finite Algebras for Solid Modeling using Julia’s Sparse Arrays" @default.
- W4308704932 cites W1910479248 @default.
- W4308704932 cites W1982289281 @default.
- W4308704932 cites W1986644591 @default.
- W4308704932 cites W2000306582 @default.
- W4308704932 cites W2000358470 @default.
- W4308704932 cites W2003048988 @default.
- W4308704932 cites W2003782316 @default.
- W4308704932 cites W2007839801 @default.
- W4308704932 cites W2029322949 @default.
- W4308704932 cites W2072932164 @default.
- W4308704932 cites W2077002020 @default.
- W4308704932 cites W2081280922 @default.
- W4308704932 cites W2120575449 @default.
- W4308704932 cites W2135301926 @default.
- W4308704932 cites W2144829963 @default.
- W4308704932 cites W2152495224 @default.
- W4308704932 cites W2155657794 @default.
- W4308704932 cites W2475322788 @default.
- W4308704932 cites W2898321943 @default.
- W4308704932 cites W4239750358 @default.
- W4308704932 doi "https://doi.org/10.1016/j.cad.2022.103436" @default.
- W4308704932 hasPublicationYear "2023" @default.
- W4308704932 type Work @default.
- W4308704932 citedByCount "0" @default.
- W4308704932 crossrefType "journal-article" @default.
- W4308704932 hasAuthorship W4308704932A5034405971 @default.
- W4308704932 hasAuthorship W4308704932A5035988852 @default.
- W4308704932 hasAuthorship W4308704932A5037860974 @default.
- W4308704932 hasAuthorship W4308704932A5074046624 @default.
- W4308704932 hasAuthorship W4308704932A5076800717 @default.
- W4308704932 hasConcept C11413529 @default.
- W4308704932 hasConcept C136119220 @default.
- W4308704932 hasConcept C202444582 @default.
- W4308704932 hasConcept C33923547 @default.
- W4308704932 hasConcept C41008148 @default.
- W4308704932 hasConcept C459310 @default.
- W4308704932 hasConceptScore W4308704932C11413529 @default.
- W4308704932 hasConceptScore W4308704932C136119220 @default.
- W4308704932 hasConceptScore W4308704932C202444582 @default.
- W4308704932 hasConceptScore W4308704932C33923547 @default.
- W4308704932 hasConceptScore W4308704932C41008148 @default.
- W4308704932 hasConceptScore W4308704932C459310 @default.
- W4308704932 hasLocation W43087049321 @default.
- W4308704932 hasOpenAccess W4308704932 @default.
- W4308704932 hasPrimaryLocation W43087049321 @default.
- W4308704932 hasRelatedWork W1987949650 @default.
- W4308704932 hasRelatedWork W2045490848 @default.
- W4308704932 hasRelatedWork W2090649758 @default.
- W4308704932 hasRelatedWork W2333698505 @default.
- W4308704932 hasRelatedWork W2351491280 @default.
- W4308704932 hasRelatedWork W2371447506 @default.
- W4308704932 hasRelatedWork W2386767533 @default.
- W4308704932 hasRelatedWork W2963070987 @default.
- W4308704932 hasRelatedWork W303980170 @default.
- W4308704932 hasRelatedWork W3046926816 @default.
- W4308704932 hasVolume "155" @default.
- W4308704932 isParatext "false" @default.
- W4308704932 isRetracted "false" @default.
- W4308704932 workType "article" @default.