Matches in SemOpenAlex for { <https://semopenalex.org/work/W2510276203> ?p ?o ?g. }
- W2510276203 abstract "We study schemes for interpolating functions that take values in the special orthogonal group $SO(n)$. Our focus is on interpolation schemes obtained by embedding $SO(n)$ in a linear space, interpolating in the linear space, and mapping the result onto $SO(n)$ via the closest point projection. The resulting interpolants inherit both the order of accuracy and the regularity of the underlying interpolants on the linear space. The values and derivatives of the interpolants admit efficient evaluation via either explicit formulas or iterative algorithms, which we detail for two choices of embeddings: the embedding of $SO(n)$ in the space of $n times n$ matrices and, when $n=3$, the identification of $SO(3)$ with the set of unit quaternions. Along the way, we point out a connection between these interpolation schemes and geodesic finite elements. We illustrate the utility of these interpolation schemes by numerically computing minimum acceleration curves on $SO(n)$, a task which is handled naturally with $SO(n)$-valued finite elements having $C^1$-continuity." @default.
- W2510276203 created "2016-09-16" @default.
- W2510276203 creator A5047012686 @default.
- W2510276203 creator A5055428521 @default.
- W2510276203 date "2016-08-19" @default.
- W2510276203 modified "2023-09-27" @default.
- W2510276203 title "Embedding-Based Interpolation on the Special Orthogonal Group" @default.
- W2510276203 cites W1483804921 @default.
- W2510276203 cites W1538701695 @default.
- W2510276203 cites W1557324374 @default.
- W2510276203 cites W1970439956 @default.
- W2510276203 cites W1981467185 @default.
- W2510276203 cites W1982729005 @default.
- W2510276203 cites W1984417059 @default.
- W2510276203 cites W2006022270 @default.
- W2510276203 cites W2012294177 @default.
- W2510276203 cites W2017587562 @default.
- W2510276203 cites W2024871754 @default.
- W2510276203 cites W2027661541 @default.
- W2510276203 cites W2030394252 @default.
- W2510276203 cites W2034940548 @default.
- W2510276203 cites W2036881824 @default.
- W2510276203 cites W2043312091 @default.
- W2510276203 cites W2054689585 @default.
- W2510276203 cites W2064445894 @default.
- W2510276203 cites W2088748973 @default.
- W2510276203 cites W2102162313 @default.
- W2510276203 cites W2115096653 @default.
- W2510276203 cites W2119135605 @default.
- W2510276203 cites W2147774191 @default.
- W2510276203 cites W2151394936 @default.
- W2510276203 cites W2152394501 @default.
- W2510276203 cites W2158958880 @default.
- W2510276203 cites W2164266004 @default.
- W2510276203 cites W2170039048 @default.
- W2510276203 cites W2236623899 @default.
- W2510276203 cites W2511201564 @default.
- W2510276203 cites W76980395 @default.
- W2510276203 hasPublicationYear "2016" @default.
- W2510276203 type Work @default.
- W2510276203 sameAs 2510276203 @default.
- W2510276203 citedByCount "2" @default.
- W2510276203 countsByYear W25102762032016 @default.
- W2510276203 countsByYear W25102762032017 @default.
- W2510276203 crossrefType "posted-content" @default.
- W2510276203 hasAuthorship W2510276203A5047012686 @default.
- W2510276203 hasAuthorship W2510276203A5055428521 @default.
- W2510276203 hasConcept C104114177 @default.
- W2510276203 hasConcept C111919701 @default.
- W2510276203 hasConcept C11413529 @default.
- W2510276203 hasConcept C118615104 @default.
- W2510276203 hasConcept C134306372 @default.
- W2510276203 hasConcept C137800194 @default.
- W2510276203 hasConcept C146561895 @default.
- W2510276203 hasConcept C154945302 @default.
- W2510276203 hasConcept C171836373 @default.
- W2510276203 hasConcept C176370821 @default.
- W2510276203 hasConcept C178790620 @default.
- W2510276203 hasConcept C185592680 @default.
- W2510276203 hasConcept C202444582 @default.
- W2510276203 hasConcept C2778572836 @default.
- W2510276203 hasConcept C2781311116 @default.
- W2510276203 hasConcept C33923547 @default.
- W2510276203 hasConcept C41008148 @default.
- W2510276203 hasConcept C41608201 @default.
- W2510276203 hasConcept C57493831 @default.
- W2510276203 hasConcept C90119067 @default.
- W2510276203 hasConceptScore W2510276203C104114177 @default.
- W2510276203 hasConceptScore W2510276203C111919701 @default.
- W2510276203 hasConceptScore W2510276203C11413529 @default.
- W2510276203 hasConceptScore W2510276203C118615104 @default.
- W2510276203 hasConceptScore W2510276203C134306372 @default.
- W2510276203 hasConceptScore W2510276203C137800194 @default.
- W2510276203 hasConceptScore W2510276203C146561895 @default.
- W2510276203 hasConceptScore W2510276203C154945302 @default.
- W2510276203 hasConceptScore W2510276203C171836373 @default.
- W2510276203 hasConceptScore W2510276203C176370821 @default.
- W2510276203 hasConceptScore W2510276203C178790620 @default.
- W2510276203 hasConceptScore W2510276203C185592680 @default.
- W2510276203 hasConceptScore W2510276203C202444582 @default.
- W2510276203 hasConceptScore W2510276203C2778572836 @default.
- W2510276203 hasConceptScore W2510276203C2781311116 @default.
- W2510276203 hasConceptScore W2510276203C33923547 @default.
- W2510276203 hasConceptScore W2510276203C41008148 @default.
- W2510276203 hasConceptScore W2510276203C41608201 @default.
- W2510276203 hasConceptScore W2510276203C57493831 @default.
- W2510276203 hasConceptScore W2510276203C90119067 @default.
- W2510276203 hasLocation W25102762031 @default.
- W2510276203 hasOpenAccess W2510276203 @default.
- W2510276203 hasPrimaryLocation W25102762031 @default.
- W2510276203 hasRelatedWork W111171389 @default.
- W2510276203 hasRelatedWork W169231747 @default.
- W2510276203 hasRelatedWork W183223787 @default.
- W2510276203 hasRelatedWork W186592689 @default.
- W2510276203 hasRelatedWork W1976273847 @default.
- W2510276203 hasRelatedWork W2008550913 @default.
- W2510276203 hasRelatedWork W2019343873 @default.
- W2510276203 hasRelatedWork W2024068274 @default.
- W2510276203 hasRelatedWork W2041042918 @default.
- W2510276203 hasRelatedWork W2068693617 @default.