Matches in SemOpenAlex for { <https://semopenalex.org/work/W4323353630> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W4323353630 abstract "Abstract This paper studies the problem of computing an average (or mean) displacement from a set of given spatial displacements using three types of parametric representations: Euler angles and translation vectors, unit quaternions and translation vectors, and dual quaternions. It is shown that the use of Euclidean norm in the space of unit quaternions reduces the problem to that of computing the mean for each quaternion component separately and independently. While the resulting algorithm is simple, a change in the sign of a unit quaternion could lead to an incorrect result. A novel kinematic measure based on dual quaternions is introduced to capture the separation between two spatial displacements. This kinematic measure is used to define the variance of a set of displacements, which is then used to formulate a constrained least squares minimization problem. It is shown that the problem decomposes into that of finding the optimal translation vector and the optimal unit quaternion. The former is simply the centroid of the set of translation vectors and the latter is obtained as the eigenvector corresponding to the least eigenvalue of a 4 × 4 positive definite symmetric matrix. In addition, it is found that the weight factor used in combining rotations and translations in the formulation does not play a role in the final outcome. Examples are provided to show the comparisons of these methods." @default.
- W4323353630 created "2023-03-08" @default.
- W4323353630 creator A5015338018 @default.
- W4323353630 creator A5022546522 @default.
- W4323353630 creator A5038441318 @default.
- W4323353630 creator A5050521672 @default.
- W4323353630 date "2023-03-28" @default.
- W4323353630 modified "2023-10-14" @default.
- W4323353630 title "On the Computation of Mean and Variance of Spatial Displacements" @default.
- W4323353630 cites W1994374557 @default.
- W4323353630 cites W1996806128 @default.
- W4323353630 cites W2001682292 @default.
- W4323353630 cites W2014307172 @default.
- W4323353630 cites W2018801303 @default.
- W4323353630 cites W2037610551 @default.
- W4323353630 cites W2039050554 @default.
- W4323353630 cites W2041846944 @default.
- W4323353630 cites W2045688598 @default.
- W4323353630 cites W2050936461 @default.
- W4323353630 cites W2053269485 @default.
- W4323353630 cites W2065750785 @default.
- W4323353630 cites W2084004869 @default.
- W4323353630 cites W2144606943 @default.
- W4323353630 cites W2151285298 @default.
- W4323353630 cites W2160015218 @default.
- W4323353630 cites W2165167250 @default.
- W4323353630 cites W2820797251 @default.
- W4323353630 cites W3002158483 @default.
- W4323353630 cites W4246410535 @default.
- W4323353630 cites W4289519404 @default.
- W4323353630 doi "https://doi.org/10.1115/1.4057046" @default.
- W4323353630 hasPublicationYear "2023" @default.
- W4323353630 type Work @default.
- W4323353630 citedByCount "0" @default.
- W4323353630 crossrefType "journal-article" @default.
- W4323353630 hasAuthorship W4323353630A5015338018 @default.
- W4323353630 hasAuthorship W4323353630A5022546522 @default.
- W4323353630 hasAuthorship W4323353630A5038441318 @default.
- W4323353630 hasAuthorship W4323353630A5050521672 @default.
- W4323353630 hasConcept C104317684 @default.
- W4323353630 hasConcept C105580179 @default.
- W4323353630 hasConcept C11413529 @default.
- W4323353630 hasConcept C121332964 @default.
- W4323353630 hasConcept C145941777 @default.
- W4323353630 hasConcept C149364088 @default.
- W4323353630 hasConcept C158693339 @default.
- W4323353630 hasConcept C185592680 @default.
- W4323353630 hasConcept C200127275 @default.
- W4323353630 hasConcept C2524010 @default.
- W4323353630 hasConcept C28826006 @default.
- W4323353630 hasConcept C33923547 @default.
- W4323353630 hasConcept C45374587 @default.
- W4323353630 hasConcept C55493867 @default.
- W4323353630 hasConcept C62520636 @default.
- W4323353630 hasConcept C83633838 @default.
- W4323353630 hasConceptScore W4323353630C104317684 @default.
- W4323353630 hasConceptScore W4323353630C105580179 @default.
- W4323353630 hasConceptScore W4323353630C11413529 @default.
- W4323353630 hasConceptScore W4323353630C121332964 @default.
- W4323353630 hasConceptScore W4323353630C145941777 @default.
- W4323353630 hasConceptScore W4323353630C149364088 @default.
- W4323353630 hasConceptScore W4323353630C158693339 @default.
- W4323353630 hasConceptScore W4323353630C185592680 @default.
- W4323353630 hasConceptScore W4323353630C200127275 @default.
- W4323353630 hasConceptScore W4323353630C2524010 @default.
- W4323353630 hasConceptScore W4323353630C28826006 @default.
- W4323353630 hasConceptScore W4323353630C33923547 @default.
- W4323353630 hasConceptScore W4323353630C45374587 @default.
- W4323353630 hasConceptScore W4323353630C55493867 @default.
- W4323353630 hasConceptScore W4323353630C62520636 @default.
- W4323353630 hasConceptScore W4323353630C83633838 @default.
- W4323353630 hasFunder F4320337351 @default.
- W4323353630 hasIssue "1" @default.
- W4323353630 hasLocation W43233536301 @default.
- W4323353630 hasOpenAccess W4323353630 @default.
- W4323353630 hasPrimaryLocation W43233536301 @default.
- W4323353630 hasRelatedWork W151107383 @default.
- W4323353630 hasRelatedWork W1980109971 @default.
- W4323353630 hasRelatedWork W1988553069 @default.
- W4323353630 hasRelatedWork W1989173793 @default.
- W4323353630 hasRelatedWork W2074615279 @default.
- W4323353630 hasRelatedWork W2091132606 @default.
- W4323353630 hasRelatedWork W2381584688 @default.
- W4323353630 hasRelatedWork W2387323969 @default.
- W4323353630 hasRelatedWork W2607388023 @default.
- W4323353630 hasRelatedWork W2914794850 @default.
- W4323353630 hasVolume "16" @default.
- W4323353630 isParatext "false" @default.
- W4323353630 isRetracted "false" @default.
- W4323353630 workType "article" @default.