What's the difference between quaternion and rotation?
Quaternion
Definition:
(n.) The number four.
(n.) A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
(n.) A word of four syllables; a quadrisyllable.
(n.) The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
(v. t.) To divide into quaternions, files, or companies.
Example Sentences:
(1) During visually guided movements, arm follows gaze, and the nine-dimensional rotatory configuration space for eye-head-arm-synergies (three degrees of freedom for each system) is reduced to a two-dimensional plane in the space of quaternion vectors.
(2) Many testable predictions made by quaternion models also turn up in models based on other mathematics.
(3) Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion.
(4) The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements.
(5) In other words, angular eye positions in space (expressed as quaternions) were constrained to a two-dimensional surface.
(6) Findings 1 and 3 show that saccadic control signals accurately reflect the properties of three-dimensional rotations, as predicted by a new quaternion model of the saccadic system; models that approximate rotational kinematics using vectorial addition and integration do not predict these findings.
(7) Tweed and Vilis (Journal of Neurophysiology, 58, 832-849, 1987) have argued that quaternion algebra provides the most appropriate description of the rotations of the eye, and have derived a three-dimensional model of gaze control based on quaternion operations.
(8) A canonical unitary representation of the Euclidean group on the range space of the Gabor transform is constructed from mathematical properties of the Euclidean group and the quaternions.
(9) The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position.
(10) In this paper we present algorithms for computing eye position quaternions and eye angular velocity (not the derivative of position in three dimensions) from two search coils (not necessarily orthogonal) on one eye in two or three magnetic fields, and for locating primary position using quaternions.
(11) In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions.
Rotation
Definition:
(n.) The act of turning, as a wheel or a solid body on its axis, as distinguished from the progressive motion of a revolving round another body or a distant point; thus, the daily turning of the earth on its axis is a rotation; its annual motion round the sun is a revolution.
(n.) Any return or succesion in a series.
(a.) Pertaining to, or resulting from, rotation; of the nature of, or characterized by, rotation; as, rotational velocity.
Example Sentences:
(1) To determine the accuracy of double-contrast arthrography in complete rotator cuff tears, we studied 805 patients thought to have a complete rotator cuff tear who had undergone double-contrast shoulder arthrography (DCSA) between 1978 and 1983.
(2) When the posterior capsule was sectioned, no significant changes were noted in the severity of the sag or the rotation.
(3) The Ta loop was a smooth, elongated ellipse in configuration and showed clockwise rotation in all planes, as did the P loop.
(4) With this system, a brain region loaded with fura-2 was illuminated by a rotating disc bearing three different interference filters of 340, 360 and 380 nm at a rate of 600 rpm.
(5) The automatic half of both the motor which advances the trepan as well as the second motor which rotates the trepan is triggered by the sudden change in electrical resistance between the trepan and the patient's internal body fluid, at the final stage of penetration.
(6) This series of tests included tests for pathologic nystagmus, saccades, smooth pursuit, and optokinetic nystagmus, as well as bithermal caloric testing and rotational testing.
(7) The adherence of 51Cr-labeled platelets to rabbit aortae everted on probes rotated in platelet-red cell suspensions has been measured.
(8) We have used a modification of the rotating-frame imaging technique to measure PCr-to-ATP ratio non-invasively in human heart.
(9) Experimental evidence suggested that nucleosome rotational positioning is determined by the DNA sequence itself.
(10) The X-ray tube rotates outside the detector array at the rate of one revolution per second.
(11) The data collection scheme for the scanner uses multiple rotations of a linearly shifted, asymmetric fan beam permitting user-defined variable resolution.
(12) The purity and configuration of each isomer of the free acid and N-chloroacetylated derivative were ascertained by: (a) paper chromatography in five solvent systems, (b) elemental analysis, (c) Van Slyke nitrous acid determination of alpha-carbonyl carbon, and (d) Van Slyke ninhydrin determination of alpha-carbonyl carbon, and (e) optical rotation.
(13) Based on our experience with the mark I prosthesis we have designed and developed a mark II model which has freedom of axial rotation of the saddle.
(14) The reported study demonstrates that performance asymmetries between normal or reflected letters presented in the right and left visual field favors the right visual field when stimulus patterns are blocked and rotated 90 degrees clockwise and favors the left visual field when they are blocked and rotated 90 degrees counterclockwise.
(15) Moreover, the majority of the 'out of phase' units showed an increased discharge during side-up animal tilt and side-down neck rotation.
(16) 3-D curves were computed with an apparent rotation around the vertical axis Z.
(17) Subsequently, due to the rotation of the original polar axis in one hemisphere, the third cleavage plane through one half of the egg is transverse to the third cleavage plane through the other half.
(18) This suggests that S1 is a flexible protein with at least two domains that can rotate independently.
(19) Per-rotational nystagmus was recorded in rabbits with unilaterally narrowed vertebral arteries or following unilateral cervical sympathectomies.
(20) We found that the Gallie system generally allowed significantly more rotation in flexion, extension, axial rotation, and lateral bending than the other three fixation techniques.