|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
three-dimensional Euclidean space
|
|
gptkbp:application
|
computer vision
mechanics
physics
robotics
|
|
gptkbp:compact
|
true
|
|
gptkbp:consistsOf
|
rotations and translations in 3D
|
|
gptkbp:dimensions
|
6
|
|
gptkbp:fullName
|
Special Euclidean group in three dimensions
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasIdentityComponent
|
itself
|
|
gptkbp:hasSubgroup
|
gptkb:Euclidean_group_E(3)
gptkb:SO(3)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SE(3) group
|
|
gptkbp:identityElement
|
inverse rotation and translation
no rotation, no translation
|
|
gptkbp:isLieGroupOver
|
real numbers
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isRealLieGroup
|
true
|
|
gptkbp:isSemidirectProductOf
|
SO(3) and R^3
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSmoothManifold
|
true
|
|
gptkbp:isSolvableGroup
|
false
|
|
gptkbp:isTopologicalGroup
|
true
|
|
gptkbp:Lie_algebra
|
se(3)
|
|
gptkbp:LieAlgebraDimension
|
6
|
|
gptkbp:matrixRepresentation
|
4x4 homogeneous transformation matrices
|
|
gptkbp:notation
|
gptkb:SE(3)
|
|
gptkbp:relatedConcept
|
gptkb:affine_group
isometry
homogeneous coordinates
rigid body motion
|
|
gptkbp:relatedGroup
|
composition of transformations
|
|
gptkbp:usedIn
|
gptkb:navigation
aerospace engineering
computer graphics
control theory
kinematics
motion planning
biomechanics
multibody dynamics
geometric mechanics
|
|
gptkbp:bfsParent
|
gptkb:Dual_quaternions
|
|
gptkbp:bfsLayer
|
8
|