Matches in SemOpenAlex for { <https://semopenalex.org/work/W2979781648> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W2979781648 abstract "3D frame fields are auxiliary for hexahedral mesh generation. There mainly exist three ways to represent 3D frames: combination of rotations, spherical harmonics and fourth order tensor. We propose here a representation carried out by the special unitary group. The article strongly relies on cite{du1964homographies}. We first describe the rotations with quaternions, cite[§ 13-15]{du1964homographies}. We define and show the isomorphism between unit quaternions and the special unitary group, cite[§16]{du1964homographies}. The frame field space is identified as the quotient group of rotations by the octahedral group, cite[§20]{du1964homographies}. The invariant forms of the vierer, tetrahedral and octahedral groups are successively built, without using homographies cite[§ 39]{du1964homographies}. Modifying the definition of the isomorphism between unit quaternions and the special unitary group allows to use the invariant forms of the octahedral group as a unique parameterization of the orientation of 3D frames. The parameterization consists in three complex values, corresponding to a coordinate of a variety which is embedded in a three complex valued dimensional space. The underlined variety is the model surface of the octahedral group, which can be expressed with an implicit equation. We prove that from a coordinate of the surface, we may identify all the quaternions giving the corresponding 3D frames. We show that the euclidean distance between two coordinates does not correspond to the actual distance of the corresponding 3D frames. We derive the expression of three components of a coordinate in the case of frames sharing an even direction. We then derive a way to ensure that a coordinate corresponds to the special unitary group. Finally, the attempted numerical schemes to compute frame fields are given." @default.
- W2979781648 created "2019-10-18" @default.
- W2979781648 creator A5037121552 @default.
- W2979781648 creator A5043553994 @default.
- W2979781648 creator A5045471884 @default.
- W2979781648 creator A5087893927 @default.
- W2979781648 date "2019-10-14" @default.
- W2979781648 modified "2023-09-27" @default.
- W2979781648 title "Quaternionic octahedral fields: SU(2) parameterization of 3D frames." @default.
- W2979781648 cites W2065234731 @default.
- W2979781648 cites W2075768929 @default.
- W2979781648 cites W2549535666 @default.
- W2979781648 cites W2962696410 @default.
- W2979781648 hasPublicationYear "2019" @default.
- W2979781648 type Work @default.
- W2979781648 sameAs 2979781648 @default.
- W2979781648 citedByCount "0" @default.
- W2979781648 crossrefType "posted-content" @default.
- W2979781648 hasAuthorship W2979781648A5037121552 @default.
- W2979781648 hasAuthorship W2979781648A5043553994 @default.
- W2979781648 hasAuthorship W2979781648A5045471884 @default.
- W2979781648 hasAuthorship W2979781648A5087893927 @default.
- W2979781648 hasConcept C105239961 @default.
- W2979781648 hasConcept C115624301 @default.
- W2979781648 hasConcept C121332964 @default.
- W2979781648 hasConcept C17744445 @default.
- W2979781648 hasConcept C185592680 @default.
- W2979781648 hasConcept C190470478 @default.
- W2979781648 hasConcept C191948623 @default.
- W2979781648 hasConcept C198819137 @default.
- W2979781648 hasConcept C199539241 @default.
- W2979781648 hasConcept C200127275 @default.
- W2979781648 hasConcept C202444582 @default.
- W2979781648 hasConcept C203436722 @default.
- W2979781648 hasConcept C207570611 @default.
- W2979781648 hasConcept C2524010 @default.
- W2979781648 hasConcept C2781311116 @default.
- W2979781648 hasConcept C33923547 @default.
- W2979781648 hasConcept C37914503 @default.
- W2979781648 hasConcept C62520636 @default.
- W2979781648 hasConcept C67820243 @default.
- W2979781648 hasConcept C8010536 @default.
- W2979781648 hasConcept C84316537 @default.
- W2979781648 hasConcept C99072794 @default.
- W2979781648 hasConceptScore W2979781648C105239961 @default.
- W2979781648 hasConceptScore W2979781648C115624301 @default.
- W2979781648 hasConceptScore W2979781648C121332964 @default.
- W2979781648 hasConceptScore W2979781648C17744445 @default.
- W2979781648 hasConceptScore W2979781648C185592680 @default.
- W2979781648 hasConceptScore W2979781648C190470478 @default.
- W2979781648 hasConceptScore W2979781648C191948623 @default.
- W2979781648 hasConceptScore W2979781648C198819137 @default.
- W2979781648 hasConceptScore W2979781648C199539241 @default.
- W2979781648 hasConceptScore W2979781648C200127275 @default.
- W2979781648 hasConceptScore W2979781648C202444582 @default.
- W2979781648 hasConceptScore W2979781648C203436722 @default.
- W2979781648 hasConceptScore W2979781648C207570611 @default.
- W2979781648 hasConceptScore W2979781648C2524010 @default.
- W2979781648 hasConceptScore W2979781648C2781311116 @default.
- W2979781648 hasConceptScore W2979781648C33923547 @default.
- W2979781648 hasConceptScore W2979781648C37914503 @default.
- W2979781648 hasConceptScore W2979781648C62520636 @default.
- W2979781648 hasConceptScore W2979781648C67820243 @default.
- W2979781648 hasConceptScore W2979781648C8010536 @default.
- W2979781648 hasConceptScore W2979781648C84316537 @default.
- W2979781648 hasConceptScore W2979781648C99072794 @default.
- W2979781648 hasLocation W29797816481 @default.
- W2979781648 hasOpenAccess W2979781648 @default.
- W2979781648 hasPrimaryLocation W29797816481 @default.
- W2979781648 hasRelatedWork W1985802214 @default.
- W2979781648 hasRelatedWork W2002409257 @default.
- W2979781648 hasRelatedWork W2032157811 @default.
- W2979781648 hasRelatedWork W2036758406 @default.
- W2979781648 hasRelatedWork W2052943184 @default.
- W2979781648 hasRelatedWork W2058139805 @default.
- W2979781648 hasRelatedWork W2078772248 @default.
- W2979781648 hasRelatedWork W2087211681 @default.
- W2979781648 hasRelatedWork W2087999907 @default.
- W2979781648 hasRelatedWork W2128308160 @default.
- W2979781648 hasRelatedWork W2131839137 @default.
- W2979781648 hasRelatedWork W2189600060 @default.
- W2979781648 hasRelatedWork W2476575366 @default.
- W2979781648 hasRelatedWork W2490048 @default.
- W2979781648 hasRelatedWork W2555590552 @default.
- W2979781648 hasRelatedWork W2955884132 @default.
- W2979781648 hasRelatedWork W2968811798 @default.
- W2979781648 hasRelatedWork W2971884972 @default.
- W2979781648 hasRelatedWork W1644076242 @default.
- W2979781648 hasRelatedWork W1708471149 @default.
- W2979781648 isParatext "false" @default.
- W2979781648 isRetracted "false" @default.
- W2979781648 magId "2979781648" @default.
- W2979781648 workType "article" @default.