Add to ORKGThe Minkowski product of unit quaternion sets is introduced and analyzed, motivated by the desire to characterize the overall variation of compounded spatial rotations that result from individual rotations subject to known uncertainties in their rotation axes and angles. For a special type of unit quaternion set, the spherical caps of the 3-sphere S3 in R4, closure under the Minkowski product is achieved. Products of sets characterized by fixing either the rotation axis or rotation angle, and allowing the other to vary over a given domain, are also analyzed. Two methods for visualizing unit quaternion sets and their Minkowski products in R3 are also discussed, based on stereographic projection and the Lie algebra formulation. Finally, some ...
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due t...
A one-parameter homothetic motion in three-dimensional Minkowski space is defined by means of the Ha...
A set of basic vectors locally describing metric properties of an arbitrary 2-dimensional (2D) surfa...
The Minkowski product can be viewed as a higher-dimensional version of inter-val arithmetic. We disc...
In this study, firstly, we give a different approach to the relationship between the split quaternio...
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of th...
The theory of quaternions was discovered in the middle of nineteenth century and they were commonly ...
In this paper the generalization of the rotations on any lightcone in Minkowski 3-space ℝ1,2 is give...
In a Minkowski three dimensional space, whose metric is based on a strictly convex and centrally sym...
This paper is written to aid the readers to understand application of Euler angles and quaternion in...
The Minkowski product can be viewed as a higher dimensional version of interval arithmetic. We discu...
The existing approaches support Minkowski sums for the boundary, set-theoretic, and ray representati...
Quaternions are a type of hypercomplex numbers. Unit quaternions, which describe rotations, were cal...
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due t...
Quaternions are presented in various ways: as pairs of complex numbers, using vectors, as 2 × 2-dime...
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due t...
A one-parameter homothetic motion in three-dimensional Minkowski space is defined by means of the Ha...
A set of basic vectors locally describing metric properties of an arbitrary 2-dimensional (2D) surfa...
The Minkowski product can be viewed as a higher-dimensional version of inter-val arithmetic. We disc...
In this study, firstly, we give a different approach to the relationship between the split quaternio...
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of th...
The theory of quaternions was discovered in the middle of nineteenth century and they were commonly ...
In this paper the generalization of the rotations on any lightcone in Minkowski 3-space ℝ1,2 is give...
In a Minkowski three dimensional space, whose metric is based on a strictly convex and centrally sym...
This paper is written to aid the readers to understand application of Euler angles and quaternion in...
The Minkowski product can be viewed as a higher dimensional version of interval arithmetic. We discu...
The existing approaches support Minkowski sums for the boundary, set-theoretic, and ray representati...
Quaternions are a type of hypercomplex numbers. Unit quaternions, which describe rotations, were cal...
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due t...
Quaternions are presented in various ways: as pairs of complex numbers, using vectors, as 2 × 2-dime...
Solid object rotations or rotations of unit real vectors are often used in robotic moves. Yet, due t...
A one-parameter homothetic motion in three-dimensional Minkowski space is defined by means of the Ha...
A set of basic vectors locally describing metric properties of an arbitrary 2-dimensional (2D) surfa...