Imaging techniques used to colocalize sites of brain functions or physiological activity with brain structures.
Investigative technique commonly used during ELECTROENCEPHALOGRAPHY in which a series of bright light flashes or visual patterns are used to elicit brain activity.
The act, process, or result of passing from one place or position to another. It differs from LOCOMOTION in that locomotion is restricted to the passing of the whole body from one place to another, while movement encompasses both locomotion but also a change of the position of the whole body or any of its parts. Movement may be used with reference to humans, vertebrate and invertebrate animals, and microorganisms. Differentiate also from MOTOR ACTIVITY, movement associated with behavior.
The awareness of the spatial properties of objects; includes physical space.
The selecting and organizing of visual stimuli based on the individual's past experience.
Awareness of oneself in relation to time, place and person.
The rotation of linearly polarized light as it passes through various media.
The coordination of a sensory or ideational (cognitive) process and a motor activity.
The time from the onset of a stimulus until a response is observed.
The properties, processes, and behavior of biological systems under the action of mechanical forces.
Mental process to visually perceive a critical number of facts (the pattern), such as characters, shapes, displays, or designs.
A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.
Non-invasive method of demonstrating internal anatomy based on the principle that atomic nuclei in a strong magnetic field absorb pulses of radiofrequency energy and emit them as radiowaves which can be reconstructed into computerized images. The concept includes proton spin tomographic techniques.
Computer-based representation of physical systems and phenomena such as chemical processes.
Theoretical representations that simulate the behavior or activity of the neurological system, processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.
The distance and direction to which a bone joint can be extended. Range of motion is a function of the condition of the joints, muscles, and connective tissues involved. Joint flexibility can be improved through appropriate MUSCLE STRETCHING EXERCISES.
Behavioral manifestations of cerebral dominance in which there is preferential use and superior functioning of either the left or the right side, as in the preferred use of the right hand or right foot.
Use of sound to elicit a response in the nervous system.
A technique of inputting two-dimensional images into a computer and then enhancing or analyzing the imagery into a form that is more useful to the human observer.
The relationships between symbols and their meanings.
Area of the parietal lobe concerned with receiving sensations such as movement, pain, pressure, position, temperature, touch, and vibration. It lies posterior to the central sulcus.
Relatively permanent change in behavior that is the result of past experience or practice. The concept includes the acquisition of knowledge.
Signals for an action; that specific portion of a perceptual field or pattern of stimuli to which a subject has learned to respond.
Voluntary or involuntary motion of head that may be relative to or independent of body; includes animals and humans.
Area of the OCCIPITAL LOBE concerned with the processing of visual information relayed via VISUAL PATHWAYS.
Voluntary or reflex-controlled movements of the eye.
Upper central part of the cerebral hemisphere. It is located posterior to central sulcus, anterior to the OCCIPITAL LOBE, and superior to the TEMPORAL LOBES.
The sensory discrimination of a pattern shape or outline.
The distal part of the arm beyond the wrist in humans and primates, that includes the palm, fingers, and thumb.
A species of the genus MACACA inhabiting India, China, and other parts of Asia. The species is used extensively in biomedical research and adapts very well to living with humans.
The anterior portion of the head that includes the skin, muscles, and structures of the forehead, eyes, nose, mouth, cheeks, and jaw.
A new pattern of perceptual or ideational material derived from past experience.
A cognitive process involving the formation of ideas generalized from the knowledge of qualities, aspects, and relations of objects.
A reflex wherein impulses are conveyed from the cupulas of the SEMICIRCULAR CANALS and from the OTOLITHIC MEMBRANE of the SACCULE AND UTRICLE via the VESTIBULAR NUCLEI of the BRAIN STEM and the median longitudinal fasciculus to the OCULOMOTOR NERVE nuclei. It functions to maintain a stable retinal image during head rotation by generating appropriate compensatory EYE MOVEMENTS.
The process of generating three-dimensional images by electronic, photographic, or other methods. For example, three-dimensional images can be generated by assembling multiple tomographic images with the aid of a computer, while photographic 3-D images (HOLOGRAPHY) can be made by exposing film to the interference pattern created when two laser light sources shine on an object.
The basic cellular units of nervous tissue. Each neuron consists of a body, an axon, and dendrites. Their purpose is to receive, conduct, and transmit impulses in the NERVOUS SYSTEM.
Area of the FRONTAL LOBE concerned with primary motor control located in the dorsal PRECENTRAL GYRUS immediately anterior to the central sulcus. It is comprised of three areas: the primary motor cortex located on the anterior paracentral lobule on the medial surface of the brain; the premotor cortex located anterior to the primary motor cortex; and the supplementary motor area located on the midline surface of the hemisphere anterior to the primary motor cortex.
Sensation of making physical contact with objects, animate or inanimate. Tactile stimuli are detected by MECHANORECEPTORS in the skin and mucous membranes.
Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.
Differential response to different stimuli.
Elements of limited time intervals, contributing to particular results or situations.
The region of the cerebral cortex that receives the auditory radiation from the MEDIAL GENICULATE BODY.
Complex mental function having four distinct phases: (1) memorizing or learning, (2) retention, (3) recall, and (4) recognition. Clinically, it is usually subdivided into immediate, recent, and remote memory.
A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.
Three-dimensional representation to show anatomic structures. Models may be used in place of intact animals or organisms for teaching, practice, and study.
The process whereby auditory stimuli are selected, organized, and interpreted by the organism.
A front limb of a quadruped. (The Random House College Dictionary, 1980)
The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.
The knowledge or perception that someone or something present has been previously encountered.
Sequential operating programs and data which instruct the functioning of a digital computer.
Set of cell bodies and nerve fibers conducting impulses from the eyes to the cerebral cortex. It includes the RETINA; OPTIC NERVE; optic tract; and geniculocalcarine tract.
Models used experimentally or theoretically to study molecular shape, electronic properties, or interactions; includes analogous molecules, computer-generated graphics, and mechanical structures.
Focusing on certain aspects of current experience to the exclusion of others. It is the act of heeding or taking notice or concentrating.
An abnormal twisting or rotation of a bodily part or member on its axis.
The real or apparent movement of objects through the visual field.
The total area or space visible in a person's peripheral vision with the eye looking straightforward.
Reactions of an individual or groups of individuals with relation to the immediate surrounding area including the animate or inanimate objects within that area.
The position or attitude of the body.
The science dealing with the correlation of the physical characteristics of a stimulus, e.g., frequency or intensity, with the response to the stimulus, in order to assess the psychologic factors involved in the relationship.
Lower lateral part of the cerebral hemisphere responsible for auditory, olfactory, and semantic processing. It is located inferior to the lateral fissure and anterior to the OCCIPITAL LOBE.
Sensory functions that transduce stimuli received by proprioceptive receptors in joints, tendons, muscles, and the INNER EAR into neural impulses to be transmitted to the CENTRAL NERVOUS SYSTEM. Proprioception provides sense of stationary positions and movements of one's body parts, and is important in maintaining KINESTHESIA and POSTURAL BALANCE.
An oval, bony chamber of the inner ear, part of the bony labyrinth. It is continuous with bony COCHLEA anteriorly, and SEMICIRCULAR CANALS posteriorly. The vestibule contains two communicating sacs (utricle and saccule) of the balancing apparatus. The oval window on its lateral wall is occupied by the base of the STAPES of the MIDDLE EAR.
Motion of an object in which either one or more points on a line are fixed. It is also the motion of a particle about a fixed point. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
Act of eliciting a response from a person or organism through physical contact.
The positioning and accommodation of eyes that allows the image to be brought into place on the FOVEA CENTRALIS of each eye.
The process of pictorial communication, between human and computers, in which the computer input and output have the form of charts, drawings, or other appropriate pictorial representation.
A specified list of terms with a fixed and unalterable meaning, and from which a selection is made when CATALOGING; ABSTRACTING AND INDEXING; or searching BOOKS; JOURNALS AS TOPIC; and other documents. The control is intended to avoid the scattering of related subjects under different headings (SUBJECT HEADINGS). The list may be altered or extended only by the publisher or issuing agency. (From Harrod's Librarians' Glossary, 7th ed, p163)
Abrupt changes in the membrane potential that sweep along the CELL MEMBRANE of excitable cells in response to excitation stimuli.
The misinterpretation of a real external, sensory experience.
The portion of an interactive computer program that issues messages to and receives commands from a user.
Numeric or quantitative entities, descriptions, properties, relationships, operations, and events.
The part of CENTRAL NERVOUS SYSTEM that is contained within the skull (CRANIUM). Arising from the NEURAL TUBE, the embryonic brain is comprised of three major parts including PROSENCEPHALON (the forebrain); MESENCEPHALON (the midbrain); and RHOMBENCEPHALON (the hindbrain). The developed brain consists of CEREBRUM; CEREBELLUM; and other structures in the BRAIN STEM.
Conceptual functions or thinking in all its forms.
The volatile portions of substances perceptible by the sense of smell. (Grant & Hackh's Chemical Dictionary, 5th ed)
The rotational force about an axis that is equal to the product of a force times the distance from the axis where the force is applied.
A concept that stands for or suggests something else by reason of its relationship, association, convention, or resemblance. The symbolism may be mental or a visible sign or representation. (From Webster, 3d ed)
A genus of the family CEBIDAE consisting of four species: S. boliviensis, S. orstedii (red-backed squirrel monkey), S. sciureus (common squirrel monkey), and S. ustus. They inhabit tropical rain forests in Central and South America. S. sciureus is used extensively in research studies.
The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
The thin layer of GRAY MATTER on the surface of the CEREBRAL HEMISPHERES that develops from the TELENCEPHALON and folds into gyri and sulchi. It reaches its highest development in humans and is responsible for intellectual faculties and higher mental functions.
A meshlike structure composed of interconnecting nerve cells that are separated at the synaptic junction or joined to one another by cytoplasmic processes. In invertebrates, for example, the nerve net allows nerve impulses to spread over a wide area of the net because synapses can pass information in any direction.
Neural tracts connecting one part of the nervous system with another.
NEURAL PATHWAYS and connections within the CENTRAL NERVOUS SYSTEM, beginning at the hair cells of the ORGAN OF CORTI, continuing along the eighth cranial nerve, and terminating at the AUDITORY CORTEX.
Three long canals (anterior, posterior, and lateral) of the bony labyrinth. They are set at right angles to each other and are situated posterosuperior to the vestibule of the bony labyrinth (VESTIBULAR LABYRINTH). The semicircular canals have five openings into the vestibule with one shared by the anterior and the posterior canals. Within the canals are the SEMICIRCULAR DUCTS.
Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
A genus of the subfamily CERCOPITHECINAE, family CERCOPITHECIDAE, consisting of 16 species inhabiting forests of Africa, Asia, and the islands of Borneo, Philippines, and Celebes.
An abrupt voluntary shift in ocular fixation from one point to another, as occurs in reading.
An increase in the rate of speed.
Set of nerve fibers conducting impulses from olfactory receptors to the cerebral cortex. It includes the OLFACTORY NERVE; OLFACTORY BULB; OLFACTORY TRACT; OLFACTORY TUBERCLE; ANTERIOR PERFORATED SUBSTANCE; and OLFACTORY CORTEX.
Theoretical representations that simulate psychological processes and/or social processes. These include the use of mathematical equations, computers, and other electronic equipment.
The articulation between the head of the HUMERUS and the glenoid cavity of the SCAPULA.
Stiff hairs projecting from the face around the nose of most mammals, acting as touch receptors.
The process by which the nature and meaning of tactile stimuli are recognized and interpreted by the brain, such as realizing the characteristics or name of an object being touched.
Remembrance of information for a few seconds to hours.
Perception of three-dimensionality.
A twisting deformation of a solid body about an axis. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
The superior part of the upper extremity between the SHOULDER and the ELBOW.
Specific languages used to prepare computer programs.
Theory and development of COMPUTER SYSTEMS which perform tasks that normally require human intelligence. Such tasks may include speech recognition, LEARNING; VISUAL PERCEPTION; MATHEMATICAL COMPUTING; reasoning, PROBLEM SOLVING, DECISION-MAKING, and translation of language.
A verbal or nonverbal means of communicating ideas or feelings.
A type of non-ionizing radiation in which energy is transmitted through solid, liquid, or gas as compression waves. Sound (acoustic or sonic) radiation with frequencies above the audible range is classified as ultrasonic. Sound radiation below the audible range is classified as infrasonic.
The process of discovering or asserting an objective or intrinsic relation between two objects or concepts; a faculty or power that enables a person to make judgments; the process of bringing to light and asserting the implicit meaning of a concept; a critical evaluation of a person or situation.
The terms, expressions, designations, or symbols used in a particular science, discipline, or specialized subject area.
An appreciable lateral deviation in the normally straight vertical line of the spine. (Dorland, 27th ed)
In INFORMATION RETRIEVAL, machine-sensing or identification of visible patterns (shapes, forms, and configurations). (Harrod's Librarians' Glossary, 7th ed)
Four or five slender jointed digits in humans and primates, attached to each HAND.
Ability to determine the specific location of a sound source.
The upper part of the human body, or the front or upper part of the body of an animal, typically separated from the rest of the body by a neck, and containing the brain, mouth, and sense organs.
The characteristic 3-dimensional shape of a protein, including the secondary, supersecondary (motifs), tertiary (domains) and quaternary structure of the peptide chain. PROTEIN STRUCTURE, QUATERNARY describes the conformation assumed by multimeric proteins (aggregates of more than one polypeptide chain).
The observable response an animal makes to any situation.
The ability to estimate periods of time lapsed or duration of time.
The detailed examination of observable activity or behavior associated with the execution or completion of a required function or unit of work.
A form of glaucoma in which the intraocular pressure increases because the angle of the anterior chamber is blocked and the aqueous humor cannot drain from the anterior chamber.
The analysis of a critical number of sensory stimuli or facts (the pattern) by physiological processes such as vision (PATTERN RECOGNITION, VISUAL), touch, or hearing.
A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.
A collection of NEURONS, tracts of NERVE FIBERS, endocrine tissue, and blood vessels in the HYPOTHALAMUS and the PITUITARY GLAND. This hypothalamo-hypophyseal portal circulation provides the mechanism for hypothalamic neuroendocrine (HYPOTHALAMIC HORMONES) regulation of pituitary function and the release of various PITUITARY HORMONES into the systemic circulation to maintain HOMEOSTASIS.
A dimension of auditory sensation varying with cycles per second of the sound stimulus.
Physical motion, i.e., a change in position of a body or subject as a result of an external force. It is distinguished from MOVEMENT, a process resulting from biological activity.
A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.
Intellectual or mental process whereby an organism obtains knowledge.
The non-genetic biological changes of an organism in response to challenges in its ENVIRONMENT.
The capacity of the NERVOUS SYSTEM to change its reactivity as the result of successive activations.
The principle that items experienced together enter into a connection, so that one tends to reinstate the other.
Organized activities related to the storage, location, search, and retrieval of information.
Posterior portion of the CEREBRAL HEMISPHERES responsible for processing visual sensory information. It is located posterior to the parieto-occipital sulcus and extends to the preoccipital notch.
Invisible boundaries surrounding the individual's body which are maintained in relation to others.
Methods developed to aid in the interpretation of ultrasound, radiographic images, etc., for diagnosis of disease.
An outbred strain of rats developed in 1915 by crossing several Wistar Institute white females with a wild gray male. Inbred strains have been derived from this original outbred strain, including Long-Evans cinnamon rats (RATS, INBRED LEC) and Otsuka-Long-Evans-Tokushima Fatty rats (RATS, INBRED OLETF), which are models for Wilson's disease and non-insulin dependent diabetes mellitus, respectively.
Sense of movement of a part of the body, such as movement of fingers, elbows, knees, limbs, or weights.
The sensory interpretation of the dimensions of objects.
The ability to detect scents or odors, such as the function of OLFACTORY RECEPTOR NEURONS.
Performance of complex motor acts.
Application of statistical procedures to analyze specific observed or assumed facts from a particular study.
Recording of the changes in electric potential of muscle by means of surface or needle electrodes.
The interactions between the anterior pituitary and adrenal glands, in which corticotropin (ACTH) stimulates the adrenal cortex and adrenal cortical hormones suppress the production of corticotropin by the anterior pituitary.
Surgically placed electric conductors through which ELECTRIC STIMULATION is delivered to or electrical activity is recorded from a specific point inside the body.
The process in which light signals are transformed by the PHOTORECEPTOR CELLS into electrical signals which can then be transmitted to the brain.
A discipline concerned with relations between messages and the characteristics of individuals who select and interpret them; it deals directly with the processes of encoding (phonetics) and decoding (psychoacoustics) as they relate states of messages to states of communicators.
Mental processing of chromatic signals (COLOR VISION) from the eye by the VISUAL CORTEX where they are converted into symbolic representations. Color perception involves numerous neurons, and is influenced not only by the distribution of wavelengths from the viewed object, but also by its background color and brightness contrast at its boundary.
Part of the body in humans and primates where the arms connect to the trunk. The shoulder has five joints; ACROMIOCLAVICULAR joint, CORACOCLAVICULAR joint, GLENOHUMERAL joint, scapulathoracic joint, and STERNOCLAVICULAR joint.
Learning that is manifested in the ability to respond differentially to various stimuli.
A dead body, usually a human body.
The part of the cerebral hemisphere anterior to the central sulcus, and anterior and superior to the lateral sulcus.
Involuntary rhythmical movements of the eyes in the normal person. These can be naturally occurring as in end-position (end-point, end-stage, or deviational) nystagmus or induced by the optokinetic drum (NYSTAGMUS, OPTOKINETIC), caloric test, or a rotating chair.
The electric response evoked in the CEREBRAL CORTEX by ACOUSTIC STIMULATION or stimulation of the AUDITORY PATHWAYS.
The blending of separate images seen by each eye into one composite image.
The measurement of magnetic fields over the head generated by electric currents in the brain. As in any electrical conductor, electric fields in the brain are accompanied by orthogonal magnetic fields. The measurement of these fields provides information about the localization of brain activity which is complementary to that provided by ELECTROENCEPHALOGRAPHY. Magnetoencephalography may be used alone or together with electroencephalography, for measurement of spontaneous or evoked activity, and for research or clinical purposes.
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
Scattering of a beam of electromagnetic or acoustic RADIATION, or particles, at small angles by particles or cavities whose dimensions are many times as large as the wavelength of the radiation or the de Broglie wavelength of the scattered particles. Also know as low angle scattering. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Small angle scattering (SAS) techniques, small angle neutron (SANS), X-ray (SAXS), and light (SALS, or just LS) scattering, are used to characterize objects on a nanoscale.
The sum or the stock of words used by a language, a group, or an individual. (From Webster, 3d ed)
A synovial hinge connection formed between the bones of the FEMUR; TIBIA; and PATELLA.
The rostral part of the frontal lobe, bounded by the inferior precentral fissure in humans, which receives projection fibers from the MEDIODORSAL NUCLEUS OF THE THALAMUS. The prefrontal cortex receives afferent fibers from numerous structures of the DIENCEPHALON; MESENCEPHALON; and LIMBIC SYSTEM as well as cortical afferents of visual, auditory, and somatic origin.
Linear POLYPEPTIDES that are synthesized on RIBOSOMES and may be further modified, crosslinked, cleaved, or assembled into complex proteins with several subunits. The specific sequence of AMINO ACIDS determines the shape the polypeptide will take, during PROTEIN FOLDING, and the function of the protein.
Computer-assisted processing of electric, ultrasonic, or electronic signals to interpret function and activity.
A whiplike motility appendage present on the surface cells. Prokaryote flagella are composed of a protein called FLAGELLIN. Bacteria can have a single flagellum, a tuft at one pole, or multiple flagella covering the entire surface. In eukaryotes, flagella are threadlike protoplasmic extensions used to propel flagellates and sperm. Flagella have the same basic structure as CILIA but are longer in proportion to the cell bearing them and present in much smaller numbers. (From King & Stansfield, A Dictionary of Genetics, 4th ed)
The process whereby an utterance is decoded into a representation in terms of linguistic units (sequences of phonetic segments which combine to form lexical and grammatical morphemes).
Communication through a system of conventional vocal symbols.
Malocclusion in which the mandible and maxilla are anteroposteriorly normal as reflected by the relationship of the first permanent molar (i.e., in neutroclusion), but in which individual teeth are abnormally related to each other.
The science pertaining to the interrelationship of psychologic phenomena and the individual's response to the physical properties of sound.
Theoretical representations that simulate the behavior or activity of chemical processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.
The domestic cat, Felis catus, of the carnivore family FELIDAE, comprising over 30 different breeds. The domestic cat is descended primarily from the wild cat of Africa and extreme southwestern Asia. Though probably present in towns in Palestine as long ago as 7000 years, actual domestication occurred in Egypt about 4000 years ago. (From Walker's Mammals of the World, 6th ed, p801)
The study of the generation and behavior of electrical charges in living organisms particularly the nervous system and the effects of electricity on living organisms.
The science or study of speech sounds and their production, transmission, and reception, and their analysis, classification, and transcription. (Random House Unabridged Dictionary, 2d ed)
The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.
Nerve structures through which impulses are conducted from a peripheral part toward a nerve center.
Continuous frequency distribution of infinite range. Its properties are as follows: 1, continuous, symmetrical distribution with both tails extending to infinity; 2, arithmetic mean, mode, and median identical; and 3, shape completely determined by the mean and standard deviation.
The joint that is formed by the articulation of the head of FEMUR and the ACETABULUM of the PELVIS.
The process by which the nature and meaning of olfactory stimuli, such as odors, are recognized and interpreted by the brain.
The act of knowing or the recognition of a distance by recollective thought, or by means of a sensory process which is under the influence of set and of prior experience.
Computer processing of a language with rules that reflect and describe current usage rather than prescribed usage.
Examination of the angle of the anterior chamber of the eye with a specialized optical instrument (gonioscope) or a contact prism lens.
The physical state of supporting an applied load. This often refers to the weight-bearing bones or joints that support the body's weight, especially those in the spine, hip, knee, and foot.
Recording of electric currents developed in the brain by means of electrodes applied to the scalp, to the surface of the brain, or placed within the substance of the brain.
The interference of one perceptual stimulus with another causing a decrease or lessening in perceptual effectiveness.
Electrical responses recorded from nerve, muscle, SENSORY RECEPTOR, or area of the CENTRAL NERVOUS SYSTEM following stimulation. They range from less than a microvolt to several microvolts. The evoked potential can be auditory (EVOKED POTENTIALS, AUDITORY), somatosensory (EVOKED POTENTIALS, SOMATOSENSORY), visual (EVOKED POTENTIALS, VISUAL), or motor (EVOKED POTENTIALS, MOTOR), or other modalities that have been reported.
Extensive collections, reputedly complete, of facts and data garnered from material of a specialized subject area and made available for analysis and application. The collection can be automated by various contemporary methods for retrieval. The concept should be differentiated from DATABASES, BIBLIOGRAPHIC which is restricted to collections of bibliographic references.
A species of the genus MACACA which typically lives near the coast in tidal creeks and mangrove swamps primarily on the islands of the Malay peninsula.
The part of a limb or tail following amputation that is proximal to the amputated section.
The science that investigates the principles governing correct or reliable inference and deals with the canons and criteria of validity in thought and demonstration. This system of reasoning is applicable to any branch of knowledge or study. (Random House Unabridged Dictionary, 2d ed & Sippl, Computer Dictionary, 4th ed)
Use of electric potential or currents to elicit biological responses.
Dominance of one cerebral hemisphere over the other in cerebral functions.
The process whereby a representation of past experience is elicited.
Also called the shoulder blade, it is a flat triangular bone, a pair of which form the back part of the shoulder girdle.
The distal extremity of the leg in vertebrates, consisting of the tarsus (ANKLE); METATARSUS; phalanges; and the soft tissues surrounding these bones.
A branch of biology dealing with the structure of organisms.
The difference between two images on the retina when looking at a visual stimulus. This occurs since the two retinas do not have the same view of the stimulus because of the location of our eyes. Thus the left eye does not get exactly the same view as the right eye.
The phenomenon of an organism's responding to all situations similar to one in which it has been conditioned.
The central part of the body to which the neck and limbs are attached.
A research and development program initiated by the NATIONAL LIBRARY OF MEDICINE to build knowledge sources for the purpose of aiding the development of systems that help health professionals retrieve and integrate biomedical information. The knowledge sources can be used to link disparate information systems to overcome retrieval problems caused by differences in terminology and the scattering of relevant information across many databases. The three knowledge sources are the Metathesaurus, the Semantic Network, and the Specialist Lexicon.
A mechanism of communicating one's own sensory system information about a task, movement or skill.
An illusion of vision usually affecting spatial relations.
The science of language, including phonetics, phonology, morphology, syntax, semantics, pragmatics, and historical linguistics. (Random House Unabridged Dictionary, 2d ed)
A gelatinous membrane overlying the acoustic maculae of SACCULE AND UTRICLE. It contains minute crystalline particles (otoliths) of CALCIUM CARBONATE and protein on its outer surface. In response to head movement, the otoliths shift causing distortion of the vestibular hair cells which transduce nerve signals to the BRAIN for interpretation of equilibrium.
Electrodes with an extremely small tip, used in a voltage clamp or other apparatus to stimulate or record bioelectric potentials of single cells intracellularly or extracellularly. (Dorland, 28th ed)
Improvement of the quality of a picture by various techniques, including computer processing, digital filtering, echocardiographic techniques, light and ultrastructural MICROSCOPY, fluorescence spectrometry and microscopy, scintigraphy, and in vitro image processing at the molecular level.
The processes occurring in early development that direct morphogenesis. They specify the body plan ensuring that cells will proceed to differentiate, grow, and diversify in size and shape at the correct relative positions. Included are axial patterning, segmentation, compartment specification, limb position, organ boundary patterning, blood vessel patterning, etc.
The electric response evoked in the cerebral cortex by visual stimulation or stimulation of the visual pathways.
Tests designed to assess neurological function associated with certain behaviors. They are used in diagnosing brain dysfunction or damage and central nervous system disorders or injury.
Lack of correspondence between the way a stimulus is commonly perceived and the way an individual perceives it under given conditions.
Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.
The vestibular part of the 8th cranial nerve (VESTIBULOCOCHLEAR NERVE). The vestibular nerve fibers arise from neurons of Scarpa's ganglion and project peripherally to vestibular hair cells and centrally to the VESTIBULAR NUCLEI of the BRAIN STEM. These fibers mediate the sense of balance and head position.
... the rotation angle α + γ {\displaystyle \alpha +\gamma } changes, but the rotation axis remains in the Z {\displaystyle Z} ... A rotation in 3D space can be represented numerically with matrices in several ways. One of these representations is: R = [ 1 0 ... To apply angular changes, the orientation is modified by a delta angle/axis rotation. The resulting orientation must be re- ... axes. The same holds true for rotations: all the rotations can be described using three numbers α {\displaystyle \alpha } , β ...
The corresponding 3-dimensional rotation has the angle 2a about the axis r in axis-angle representation. In case a = π/2, the ... The 3-dimensional rotation defined by the versor has the angle two times the arc's subtended angle, and preserves the same ... the same a as in the unit vector-angle representation of a versor explained above. That's why it may be natural to understand ... from Mathematical Reviews Rotation representation Lyons, David W. (April 2003), "An Elementary Introduction to the Hopf ...
... along φ2 in Euler angles, at increments of rotation angle for axis/angle, and at constant ρ3 (parallel to ) for Rodrigues. Due ... The following is an example of the algorithm for determining the axis/angle representation of misorientation between two ... Euler angles, Rodrigues vectors, axis/angle (where the axis is specified as a crystallographic direction), or unit quaternions ... Discrete misorientations or the misorientation distribution can be fully described as plots in the Euler angle, axis/angle, or ...
The mirror axis in the pattern is rotated by the angle ϕ {\displaystyle ~\phi } with respect to the vertical direction. This ... By rotation of the plane pattern about the meridian the scattering data collected in 4 s fill an almost spherical volume of s- ... From the Polanyi representation of fiber diffraction geometry the relations of the fiber mapping are established by elementary ... as the sample is rotated about a unique axis (the fiber axis). Such uniaxial symmetry is frequent with filaments or fibers ...
In this article the axis-angle representation is used for ρ. The rotation is about an axis in the direction of a unit vector e ... axis-angle representation, or Euler angles, etc.). A combination of a rotation and boost is a homogeneous transformation, which ... while ρ and ρ are rotation parameters (e.g. axis-angle variables, Euler angles, etc.). The rotation in block matrix form is ... The parameter ζ is the hyperbolic angle of rotation, analogous to the ordinary angle for circular rotations. This ...
The rotation vector, from the axis-angle representation of rotations, is a compact way of representing rotations in three ... angle of rotation θ, so that the magnitude of the overall rotation vector θω equals the (unsigned) rotation angle. The ... Let Ω be a unit bivector in the plane of rotation, and let θ be the angle of rotation. Then the rotation bivector is Ωθ. The ... is that in odd dimensions every rotation has a fixed axis - it is misleading to call it an axis of rotation as in higher ...
Let X = 2πM12 so that X generates a rotation around the z-axis by an angle of 2π. Then Λ = eiX = I ∈ SO(3;1)+ but eiπ(X) = −I ... a bispinor representation. Now using the recipe of exponentiation of the Lie algebra representation to obtain a representation ... one can speculate that a rotation of an angle 2π will turn a bispinor into minus itself, and that it requires a 4π rotation to ... This representation space is related to, but not identical to, the (½,0) ⊕ (0,½) representation space contained in the Clifford ...
The rotation is given by is a 4×4 rotation matrix R in the axis-angle representation, and coordinate systems are taken to be ... The axis-angle vector Δθ parametrizes the rotation, its magnitude Δθ is the angle Σ′′ has rotated, and direction is parallel to ... the rotation axis, in this case the axis is parallel to the cross product (−β)×(β + Δβ) = −β×Δβ. If the angles are negative, ... which is similar to the rotation of the swing plane of a Foucault pendulum. The angle of rotation in both cases is determined ...
To retrieve the axis-angle representation of a rotation matrix, calculate the angle of rotation from the trace of the rotation ... When a rigid body rotates around a fixed axis, its axis-angle data are a constant rotation axis and the rotation angle ... The rotation axis is sometimes called the Euler axis. It is one of many rotation formalisms in three dimensions. The axis-angle ... rotation axis and the angle are represented by a vector codirectional with the rotation axis whose length is the rotation angle ...
The color histogram of an image is relatively invariant with translation and rotation about the viewing axis, and varies only ... 1. What is a histogram? A histogram is a graphical representation of the number of pixels in an image. In a more simple way to ... slowly with the angle of view. By comparing histograms signatures of two images and matching the color content of one image ... In image processing and photography, a color histogram is a representation of the distribution of colors in an image. For ...
... rotation formula Plane of rotation Axis-angle representation Rotation group SO(3) Rotation formalisms in three dimensions ... There are several methods to compute the axis and angle from a rotation matrix (see also axis-angle representation). Here, we ... fixing the x-axis, the y-axis, and the z-axis, respectively. The rotation axis need not be a coordinate axis; if u = (x,y,z) is ... a vector along this axis is unchanged by the rotation), and its angle - the amount of rotation about that axis (Euler rotation ...
Axis-angle representation (pictured at the right) specifies an angle with the axis about which the rotation takes place. It can ... Above-mentioned Euler angles and axis-angle representations can be easily converted to a rotation matrix. Another possibility ... A general rotation in four dimensions has only one fixed point, the centre of rotation, and no axis of rotation; see rotations ... The axis (where present) and the plane of a rotation are orthogonal. A representation of rotations is a particular formalism, ...
3 rotation matrix. In this article the axis-angle representation is used, and θ = θe is the "axis-angle vector", the angle θ ... The angle of a rotation matrix in the axis-angle representation can be found from the trace of the rotation matrix, the general ... For this specific rotation, let the angle be ε and the axis be defined by the unit vector e, so the axis-angle vector is ε = εe ... This rotation is called Thomas rotation, Thomas-Wigner rotation or Wigner rotation. The rotation was discovered by Llewellyn ...
... the group of all rotation matrices, from an axis-angle representation. In other words, the Rodrigues' formula provides an ... which enables the extraction of both the axis of rotation and the sine of the angle of the rotation from the rotation matrix ... given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation ... and the axis of rotation is perpendicular to their plane. Let k be a unit vector defining a rotation axis, and let v be any ...
Axis-angle representation (pictured at the right) specifies an angle with the axis about which the rotation takes place. It can ... Above-mentioned Euler angles and axis-angle representations can be easily converted to a rotation matrix. ... A general rotation in four dimensions has only one fixed point, the centre of rotation, and no axis of rotation; see rotations ... They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the ...
The linear operator "rotation by angle θ around the axis defined by ê3" has the matrix representation [ Y 1 Y 2 Y 3 ] = [ cos ... The rotation matrix by angle θ around a general axis of rotation k is given by Rodrigues' rotation formula. R = I cos ⁡ θ + [ k ... "rotation by angle θ around a specified axis" discussed above is an orthogonal mapping and its matrix relative to any base ... and thence the rotation axis. Defining E4 as cos θ the matrix for the rotation operator is 1 − E 4 E 1 2 + E 2 2 + E 3 2 [ E 1 ...
The vector cross product, used to define the axis-angle representation, does confer an orientation ("handedness") to space: in ... a zero angle rotation). Just as in the case of the identity rotation, no axis of rotation is defined, and the angle of rotation ... Let the quaternion associated with a spatial rotation R be constructed from its rotation axis S with the rotation angle φ {\ ... Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation ...
Each vertex represents a rotation about the axis pointing from the center to that vertex, by an angle equal to the distance ... so there is a representation A 5 → S O 3 ( R ) {\displaystyle A_{5}\to SO_{3}(\mathbb {R} )} In this picture the vertices of ... The reason for this redundancy is that the corresponding rotations are by π {\displaystyle \pi } radians, and so can be ... generated by a cyclic rotation of three objects) with any distinct nontrivial element generates the whole group. For all n > 4 ...
The angle θ which appears in the eigenvalue expression corresponds to the angle of the Euler axis and angle representation. The ... The angle adds the third degree of freedom to this rotation representation. One may wish to express rotation as a rotation ... From Euler's rotation theorem we know that any rotation can be expressed as a single rotation about some axis. The axis is the ... The a n g l e ∗ a x i s {\displaystyle angle*axis} scaling each point gives a unique coordinate in Angle-Angle-Angle notation. ...
Anatomical terms of motion Artificial gravity by rotation Axle Axial precession Axial tilt Axis-angle representation Carousel, ... if two rotations are forced at the same time, a new axis of rotation will appear. This article assumes that the rotation is ... To maintain rotation around a fixed axis, the total torque vector has to be along the axis, so that it only changes the ... The axis of rotation need not go through the body. In general, any rotation can be specified completely by the three angular ...
... an arbitrary 3-dimensional rotation can be specified by an axis of rotation together with an angle of rotation about this axis ... Representations of SO(3) Euler angles Rodrigues' rotation formula Infinitesimal rotation Pin group Quaternions and spatial ... and its angle of rotation. Composing two rotations results in another rotation; every rotation has a unique inverse rotation; ... Let the quaternion associated with a spatial rotation R is constructed from its rotation axis S and the rotation angle φ this ...
Spatial rotations can be parametrized by the axis-angle representation, the angle θ and a unit vector a pointing in the ... direction of the axis, which combine into an "axis-angle vector" θ = θ a {\displaystyle {\boldsymbol {\theta }}=\theta \mathbf ... If the angle between ω and x is θ (assumed to be nonzero, otherwise u would be zero corresponding to no motion at all), then ,u ... These transformations are true for all v, not just for motion along the xx′ axes. Considering L as a tensor, we get a similar ...
The physics of the rotation around a fixed axis is mathematically described with the axis-angle representation of rotations. ... Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, and ... If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results. The ... Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a ...
Axis-angle representation Conversion between quaternions and Euler angles Davenport chained rotations Euler's rotation theorem ... The Z axis is now at angle β with respect to the z axis. The XYZ system rotates a third time, about the z axis again, by angle ... axis, γ (intrinsic rotation) represents a rotation around the Z or z″ axis. If β is zero, there is no rotation about N. As a ... represents a rotation around the z″ axis. Extrinsic rotations are elemental rotations that occur about the axes of the fixed ...
... by an angle of ±120°: 4 axes, 2 per axis, together 8 ((1 2 3), etc.; 1 ± i ± j ± k/2) rotation by an angle of 180° such that an ... and the unit quaternion representation): identity (identity; 1) rotation about an axis through a vertex, perpendicular to the ... angle OAB\cdot \sin \angle OBC\cdot \sin \angle OCA=\sin \angle OAC\cdot \sin \angle OCB\cdot \sin \angle OBA.\,} One may view ... rotation about an axis perpendicular to the plane: 3 axes, 2 per axis, together 6; equivalently, they are 90° rotations ...
"Axis of rotation" redirects here. For a mathematical context, see Axis-angle representation. ... Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a ... To maintain rotation around a fixed axis, the total torque vector has to be along the axis, so that it only changes the ... The axis of rotation need not go through the body. In general, any rotation can be specified completely by the three angular ...
... called axis-angle representation, describes a rotation or orientation using a unit vector aligned with the rotation axis, and a ... One scheme for orienting a rigid body is based upon body-axes rotation; successive rotations three times about the axes of the ... using two rotations to fix the vertical axis and another to fix the other two axes). The values of these three rotations are ... This gives one common way of representing the orientation using an axis-angle representation. Other widely used methods include ...
Angular velocity Rotation around a fixed axis Matrix exponential Axis-angle representation 3D rotation group Chasles' theorem ( ... The axis of rotation is known as an Euler axis, typically represented by a unit vector ê. Its product by the rotation angle is ... A finite rotation through angle θ about this axis may be seen as a succession of small rotations about the same axis. ... Suppose we specify an axis of rotation by a unit vector [x, y, z], and suppose we have an infinitely small rotation of angle Δθ ...
... rotation about an axis from the center of a face to the center of the opposite face by an angle of 90°: 3 axes, 2 per axis, ... in parentheses are given the permutations of the body diagonals and the unit quaternion representation): identity (identity; 1 ... rotation about an axis from the center of an edge to the center of the opposite edge by an angle of 180°: 6 axes, 1 per axis, ... rotation about a body diagonal by an angle of 120°: 4 axes, 2 per axis, together 8 ((1 2 3), etc.; (1 ± i ± j ± k)/2) The same ...
Groups whose representations are of particular importance include the rotation group SO(3) (or its double cover SU(2)), the ... Using the rotation angle φ {\displaystyle \varphi } as a parameter, this group can be parametrized as follows: SO ⁡ ( 2 , R ... Examples of symmetries include rotation about an axis. What must be understood is the nature of 'small' transformations, for ... Here, the representations of the Lie group (or of its Lie algebra) are especially important. Representation theory is used ...
Pure rotations about an arbitrary axisEdit. For two frames rotated by a fixed angle θ about an axis defined by the unit vector ... It corresponds to the dual representation of the standard representation. However, for the Lorentz group the dual of any ... the spacelike part of the Lorentz matrix reduces to the rotation matrix about the z-axis: (. A. ′. 0. A. ′. 1. A. ′. 2. A. ′. 3 ... Then without rotations, the matrix Λ has components given by:[5]. Λ. 00. =. γ. ,. Λ. 0. i. =. Λ. i. 0. =. −. γ. β. i. ,. Λ. i. ...
... γ represent the angle opposite the respective crystallographic axis (e.g. α is the angle opposite the a-axis, viz. the angle ... Cyclic twins are caused by repeated twinning around a rotation axis. This type of twinning occurs around three, four, five, six ... Coordination polyhedra are geometric representations of how a cation is surrounded by an anion. In mineralogy, coordination ... These families can be described by the relative lengths of the three crystallographic axes, and the angles between them; these ...
a b c Three dimensional rotations occur around an axis line. Four dimensional rotations may occur around a plane. So in three ... so if their dihedral angle is 90 degrees in the boundary 3-space, it is some other angle in 4-space, and they are not ... has a real representation as a 24-cell in 4-dimensional space. 3{4}3 has 24 vertices, and 24 3-edges. Its symmetry is 3[4]3, ... But in four dimensions there is yet another way in which rotations can occur, called a double rotation. Double rotations are an ...
The peptide bond has two resonance forms that contribute some double-bond character and inhibit rotation around its axis, so ... Left: All-atom representation colored by atom type. Middle: Simplified representation illustrating the backbone conformation, ... The other two dihedral angles in the peptide bond determine the local shape assumed by the protein backbone.[4] The end with a ... A representation of the 3D structure of the protein myoglobin showing turquoise α-helices. This protein was the first to have ...
V∗ is a (counter clockwise) rotation by an angle alpha where alpha satisfies tan(α) = −φ. U is a rotation by an angle beta with ... Σ along the coordinate axes, and a final rotation U. The lengths σ1 and σ2 of the semi-axes of the ellipse are the singular ... Mode-k representation[edit]. M. =. U. S. V. T. {\displaystyle M=USV^{\textsf {T}}}. can be represented using mode-k ... followed by a single rotation (unitary matrix R = UV∗). If the rotation is done first, M = P'R, then R is the same and P' = UΣU ...
The matrix inverse for a rotation is the rotation with the negative of the angle ... These formulae show that these matrices form a representation of the rotation group in the plane (technically, the special ... where the angle is that determined by a parallel to the given line through the origin and the positive x-axis. If a line ( ... Double-angle, triple-angle, and half-angle formulaeEdit. Double-angle formulaeEdit. Formulae for twice an angle.[25] ...
... of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and ... From his measurements of this distance and of the width of the rope, he could calculate the angle subtended by the star at his ... Electronic representation of Galilei's notes on motion (MS. 72). *Galileo's c. 1590 De Motu translation ... 1611 - David Fabricius publishes Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun prior to ...
Rotation (degrees). Projections. Image resolution. Time per projection (s) Bone scan. technetium-99m. 140. 6 hours. ... This data set may then be manipulated to show thin slices along any chosen axis of the body, similar to those obtained from ... SPECT can be used to complement any gamma imaging study, where a true 3D representation can be helpful, e.g., tumor imaging, ... from multiple angles. A computer is then used to apply a tomographic reconstruction algorithm to the multiple projections, ...
the angle to the z axis in spherical coordinates (mathematics). *the angle to the x axis in the xy-plane in spherical or ... the ring representation of a representation module. *the population mean or expected value in probability and statistics ... the rotation rate of an object, particularly a planet, in dynamics. *the omega constant 0.5671432904097838729999686622... ... the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics) ...
"Alignment Solution for CT Image Reconstruction using Fixed Point and Virtual Rotation Axis". Scientific Reports. 7: 41218. ... Left image is a sinogram which is a graphic representation of the raw data obtained from a CT scan. At right is an image sample ... For example, the bones of the pelvis could be displayed as semi-transparent, so that, even at an oblique angle, one part of the ... of the inside of the object from a large series of two-dimensional radiographic images taken around a single axis of rotation.[ ...
New inflection points cannot be created by the curve-shortening flow.[22] Each of the angles in the representation of the total ... remain self-similar with more complicated motions including rotation or combinations of rotation, shrinking or expansion, and ... Curves evolved in this way will in general develop sharp corners, the trace of which forms the medial axis of the curve.[63] A ... This representation is updated by alternating two steps: *Convolve the pixelated image with a heat kernel to simulate its ...
... the φ angle about the loop/capillary axis. When the κ angle is zero, the ω and φ axes are aligned. The κ rotation allows for ... The data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice. The position of ... which offers three angles of rotation: the ω angle, which rotates about an axis perpendicular to the beam; the κ angle, about ... The rotation axis should be changed at least once, to avoid developing a "blind spot" in reciprocal space close to the rotation ...
Such complexes distort along one of the molecular fourfold axes (always labelled the z axis), which has the effect of removing ... When the barrier is sufficiently small, this is called (free) pseudorotation (not to be confused with the rotation of a rigid ... Their model, using a pseudospin representation for the local orbitals, leads to a Heisenberg-like model in which the ground ... From spectra with rotational resolution, moments of inertia and hence bond lengths and angles can be determined "directly" (at ...
... this representation preserves distances and angles from the geometry of the RGB cube.[23][25] I. =. 1. 3. (. R. +. G. +. B. ). ... with neutrals running from black to white in a central axis, and hues corresponding to angles around that axis. Similar ... In the image on the right (c), we make the same rotation to the HSL/HSV hue of each color, but then we force the CIELAB ... then measured the hue of the colors in the cube by their angle around that axis, starting with red at 0°. Then they came up ...
In addition, moment of inertia considerations mean that rotation along the major axis is more easily perturbed than rotation ... is the polar angle, and φ. {\displaystyle \varphi }. is the azimuth angle of the point (x, y, z) of the ellipsoid. ... which were wanted for the parametric representation of the intersection ellipse. How to find the vertices and semi-axes of the ... The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, or simply axes of ...
Thus, by the principal axis theorem, the second fundamental form is I. I. ⁡. (. X. ,. X. ). =. k. 1. (. X. ⋅. u. 1. ). 2. +. k ... In the limit dT/ds will be in the direction N and the curvature describes the speed of rotation of the frame. ... In the first definition, the curvature of a circle is equal to the ratio of the angle of an arc to its length. Likewise, the ... which here means that there exists a parametric representation of C by a pair of functions γ(t) = (x(t), y(t)) such that the ...
The rotation angles required to get to this equivalent position now appear in the three vectors and can be read out as the x, y ... The three axes of the ellipsoid are now directly along the main orthogonal axes of the coordinate system so we can easily infer ... There are numerous different possible representations of a tensor (of rank 2), but among these, this discussion focuses on the ... The ellipsoid itself has a principal long axis and then two more small axes that describe its width and depth. All three of ...
The rotation axis of the Earth is centered and vertical. The dense clusters of lines are within the Earth's core.[2] ... The best fitting dipole is tilted at an angle of about 10° with respect to the rotational axis, as described earlier.[12] ... Schematic representation of spherical harmonics on a sphere and their nodal lines. P. ℓ m. is equal to 0 along m. great circles ... Its angle relative to true North is the declination (. D. ) or variation. Facing magnetic North, the angle the field makes with ...
"Effects of the axis of rotation and primordially solicited limb of high level athletes in a mental rotation task" (PDF). Human ... "Greater superior than inferior parietal lobule activation with increasing rotation angle during mental rotation: An fMRI study" ... Mental rotation is the ability to rotate mental representations of two-dimensional and three-dimensional objects as it is ... In a mental rotation test, the participant compares two 3D objects (or letters), often rotated in some axis, and states if they ...
It is also possible to associate a sign to an angle of rotation in three dimensions, assuming the axis of rotation has been ... discrete number representations (see also signed number representations.) ... particularly an oriented angle or an angle of rotation. In such a situation, the sign indicates whether the angle is in the ... Sign of an angleEdit. Measuring from the x-axis, angles on the unit circle count as positive in the counterclockwise direction ...
is the rotation matrix about an axis defined by the unit vector n. ^. {\displaystyle {\hat {\boldsymbol {n}}}}. and angle θ. ... Representation theory. ReferencesEdit. *^ a b c d Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum ... Rotation (I = moment of inertia) T. ^. x. x. =. J. ^. x. 2. 2. I. x. x. T. ^. y. y. =. J. ^. y. 2. 2. I. y. y. T. ^. z. z. =. J ... Rotation T. ^. =. J. ^. ⋅. J. ^. 2. I. {\displaystyle {\hat {T}}={\frac {\mathbf {\hat {J}} \cdot \mathbf {\hat {J}} }{2I ...
The width (or breadth, or diameter) is the maximum measurement of the shell at right angles to the central axis. Both terms are ... Schematic representation of the apical, apertural and basal view of a shell, showing 14 different commonly used measurements. ... Whorl: each one of the complete rotations of the shell spiral. Shape of the shellEdit. The overall shape of the shell varies. ... The central axis is an imaginary axis along the length of a shell, around which, in a coiled shell, the whorls spiral. The ...
Moreover, even with no alternation in the angle of the interaural axis (i.e. without tilting one's head) the hearing system can ... As long as the dynamic changes in binaural cues accompanied a perceived head rotation, the synthesized elevation was perceived. ... a feat that likely requires spatially resolving individual object features and integration into a holistic representation of ... elevation angle φ. {\displaystyle \varphi }. , distance between source and center of the head r. {\displaystyle r}. , the ...
... then a series of 3D representations with different angles have been made and assembled into a GIF file to produce this ... If the beam enters the sample perpendicular to the surface, then the activated region is uniform about the axis of the beam and ... Many instruments have chambers that can tilt an object of that size to 45° and provide continuous 360° rotation. ... As the angle of incidence increases, the interaction volume increases and the "escape" distance of one side of the beam ...
... rotation. The identity matrices have determinant 1, and are pure rotations by an angle zero. ... Reflection through the vertical axis Squeeze mapping with r = 3/2 Scaling by a factor of 3/2 Rotation by π/6 = 30° ... Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical ... Every finite group is isomorphic to a matrix group, as one can see by considering the regular representation of the symmetric ...
Bond Angles, and Internal-Rotation Angles". Biopolymers. 5 (7): 673-679. doi:10.1002/bip.1967.360050708.. ... The helical wheel represents a helix by a projection of the Cα backbone structure down the helix axis, while the wenxiang ... The amino acids that make up a particular helix can be plotted on a helical wheel, a representation that illustrates the ... In more general terms, they adopt dihedral angles such that the ψ dihedral angle of one residue and the φ dihedral angle of the ...
and a suitable rotation around the origin such that the transformed parabola has the origin as vertex and the y-axis as axis of ... Angle VPF is complementary to θ, and angle PVF is complementary to angle VPF, therefore angle PVF is θ. Since the length of PV ... opening to the right) has the polar coordinate representation:. r. =. 2. p. cos. ⁡. φ. sin. 2. ⁡. φ. with φ. ∈. [. −. π. 2. ,. ... is parallel to the axis of the parabola (axis of symmetry through the vertex).. In general the two vectors f. →. 1. ,. f. →. 2 ...
called semimajor axis), and polar radius b. {\displaystyle b}. (called semiminor axis); ... The angle between the plumb line which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to ... Earth rotation and Earth's interior[edit]. Further information: Structure of the Earth ... is the distance from the center of the ellipsoid to the equator (semi-major axis), and b. {\displaystyle b}. is the distance ...
The Earth's rotation relative to this shape causes the daily tidal cycle. The ocean surface moves because of the changing tidal ... The Moon orbits the Earth in the same direction as the Earth rotates on its axis, so it takes slightly more than a day-about 24 ... Their representation as a Fourier series having only one fundamental frequency and its (integer) multiples would require many ... During this time, it has passed overhead (culmination) once and underfoot once (at an hour angle of 00:00 and 12:00 ...
An elevation is a view of a building seen from one side, a flat representation of one façade. This is the most common view used ... In many cases a different scale is required for different axes, and again this can be calculated but in practice was often ... This is sometimes called a planometric or plan oblique view, and allows freedom to choose any suitable angle to present the ... unusually and exaggerated rotations of the plan, and exploded elements. The axonometric view is not readily generated by CAD ...
I need to calculate to be able to calculate a rotation vector from a set of rotation around 3 axes (x,y,z) with z being up, x ... axis-angle representation of rotation. This is a normalized vector (x,y,z) representing the axis of rotation, and a scalar ... angle r that represents the amount to rotate around that axis.*Euler angle representation of rotation. These are the triplets ... a rotation vector from a set of rotation around 3 axes (x,y,z) with z.. To represent a rotation operation in 3D space, you ...
"Axis of rotation" redirects here. For a mathematical context, see Axis-angle representation. ... Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a ... To maintain rotation around a fixed axis, the total torque vector has to be along the axis, so that it only changes the ... The axis of rotation need not go through the body. In general, any rotation can be specified completely by the three angular ...
90 Along the orientation of the current angles of my object. Which is already rotated along is local axis. Simply setting... ... Ive been spending quite a lot of time trying to figure out how i can convert the following angles: X, Y, Z: 0, 0, ... in my project i want to rotate around a local-axis. ... axis you can use the axis/angle representation of rotations. ... For the coherences of the various rotation representations see e.g. here, and especially for conversion from axis/angle to ...
Axis-angle representation (pictured at the right) specifies an angle with the axis about which the rotation takes place. It can ... Above-mentioned Euler angles and axis-angle representations can be easily converted to a rotation matrix. ... A general rotation in four dimensions has only one fixed point, the centre of rotation, and no axis of rotation; see rotations ... They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the ...
While converting rotation matrix to angle-axis representation how to find axis of rotation when angle of rotation is Pi? ... And yes, the conversion unit quaternion (SU(2)) ,--, axis-angle (su(2)) is easier than rotation matrix (SO(3)) ,--, axis-angle ... Rotations around x-axis and y-axis give a rotation around z-axis [Exercise 1.38 "Vector Calculus…"-Hubbard&Hubbard] ... We can calculate the rotation vector $\omega$ (axis-angle representation) as follows:. $$\omega = \begin{cases} \left(\frac{1}{ ...
Defining a rotation vector as a function of theta. 0. Rotation matrix from axis-angle representation ... First note that a rotation about an axis of angle $\theta$ and a rotation about the same axis of angle $-\theta$ have the same ... begingroup$ Ive written that skew-symmetric part of 3D rotation matrix has 3DOF from components of an axis, but these ... is the axis of rotation. It remains to recover $\operatorname{sin}(\theta)$, up to a sign. Well, in $\operatorname{sym}(R)-I$, ...
... rotation angle [deg] of the lower arm around the elbow axis_LU = [0 0 1]; % rotation axis of the lower arm around the elbow ... if choice_representation == 1 % rotations and translations operators % rotation, translation and rotational velocities dual ... rotation angle [deg] of the hand around the wrist axis_HL = [0 0 1]; % rotation axis of the hand around the wrist Omega_speed_ ... rotation angle [deg] of the upper arm around the shoulder axis_UB = [0 0 1]; % rotation axis of the upper arm around the ...
A Schematic Representation of Helix Tilting, Rotation around the Channel Axis, and Self-Rotation Angles ... A) Helix tilting angle. (B) Rotation around the channel axis angle. (C) Self-rotation angle. ... Glu45, Lys46, Lys145, Tyr188, and Arg206 are shown in ball-and-stick representation. Pro269 is shown in sphere representation. ... The triad of conserved residues is shown in stick representation. The tip of C-loop, to which the targeted force is applied ( ...
1 Rotation. *2 Other representations *2.1 Euler vector. *2.2 Axis plus Angle ... Axis plus Angle. In this method you define an axis of rotation, like defining the axis about which the earth spins, and use ... global rotation of prim global rotation of prim global rotation of avatar global rotation of avatar * global rotation of prim ( ... The vector part (R.x,R.y,R.z) is the product of the normalized axis of rotation and the sine of half the angle of rotation. You ...
This equivalence described above is like mapping 3D rotations to the axis-angle representation. ... Calculate rotation around the axis of rotation.. *Translate the point to the rotation plane, rotate in the plane, then apply ... angles. euler. axis angle. direction cosines. conversions. frame-of-. reference. theory. in n. dimensions. in a. plane. as 2. ... Finite rotations. In 2 dimensions rotations can be combined by adding the angles. In 3 dimensions we need to multiply ...
To retrieve the axis-angle representation of a rotation matrix, calculate the angle of rotation from the trace of the rotation ... When a rigid body rotates around a fixed axis, its axis-angle data are a constant rotation axis and the rotation angle ... The rotation axis is sometimes called the Euler axis. It is one of many rotation formalisms in three dimensions. The axis-angle ... rotation axis and the angle are represented by a vector codirectional with the rotation axis whose length is the rotation angle ...
... the rotation angle α + γ {\displaystyle \alpha +\gamma } changes, but the rotation axis remains in the Z {\displaystyle Z} ... A rotation in 3D space can be represented numerically with matrices in several ways. One of these representations is: R = [ 1 0 ... To apply angular changes, the orientation is modified by a delta angle/axis rotation. The resulting orientation must be re- ... axes. The same holds true for rotations: all the rotations can be described using three numbers α {\displaystyle \alpha } , β ...
ii)In Figure 3(b) for backward rotation, and .(iii)In Figure 3(c) for rotation along -axis, and , which means the angle of such ... In quaternion representation, describes the orientation of frame relative to frame [25]. Any orientation of frame relative to ... axis, respectively. Figure 3(c) represents a rotation along -axis. Assume the absolute values of angles for all rotations are ... Then, we find the angle between and by slightly updating (7) as follows:. In this way,. ...
Bottom sections, cartoon representation of boxes in top sections. The angle between a fibrillar structure and the long axis of ... B, Rotation over time of fibrillar staining in elongation zone epidermal cells stained with S4B. Top sections, time points (0 ... 3B; Supplemental Movie S1). We measured the change in fiber angle relative to the long axis of the cell for 22 fibers in ... This arrangement allows the cell wall to resist forces along its radial axis better than along its longitudinal axis. When ...
... and a rotation angle Δφ of the case in which the obtained θ′ is transformed to rotation-axis rotation-angle representation is ... rotation angle ra and rotation axis vector raxis) and the 3×3 rotation transform matrix R can be expressed: R. =. ⁢. [. R. 11. ... Given a rotation axis vector raxis=[rx ry rz]t, the relationship between raxis and ω can be expressed: [ωxωyωz ]=[r a r x r a r ... around the x-axis, y-axis, and z-axis:. R. =. R. roll. ·. R. pitch. ·. R. yaw. =. [. cos. ⁢. ⁢. γ. -. sin. ⁢. ⁢. γ. 0. sin. ⁢. ...
Rotation in three dimensions can be represented using pauli matrices \sigma^{i},... ... could use either of the known paramentrizations of rotations: complex numbers (Cayley-Klein parameters), axis-angle, or Euler ... So rotations in 3 dimensions and the rotational symmetry of space-time should be linked 1-1 to representations of SO(3). But we ... Or is there a more general result which relates all representations of SO(3) to rotation in three dimensions (like the one two- ...
For rotations in four dimensional Euclidean space, see SO(4). For rotations in higher dimensions, see orthogonal group. In ... This article is about rotations in three dimensional Euclidean space. ... mechanics and geometry, the rotation group is the… ... by axis and rotation angle. *in quaternion algebra with versors ... Representations of rotations. Main article: Rotation representation (mathematics). We have seen that there are a variety of ...
... rotation, translation, view angle, lighting, colors, specific graphical representations, labels and parameters. The vector and ... The graphical information includes the vector and coordinate description of a representation of at least one three dimensional ... the rotation axis is determined and the rotation angle is interpolated linearly around this rotation axis. To interpolate ... According to these embodiments, the user can at any point alter rotation including Z-axis rotation, rocking, initiate or ...
mm and the rotations a maximum rotation angle of , , , or around the -axis. The prior knowledge in SMCR is set accordingly, ... that is, the absolute value of the angle of the axis-angle representation of . Let be the basis vectors of the base coordinate ... with a random angle onto and If sample in . Otherwise, sample in (5)Build the rotation matrix If the rotation angle holds ... be the space of rotations in the remainder. The -neighborhood of a rotation is defined as. with being the rotational difference ...
1, by rotation of the mandrel 2 about its longitudinal axis. Due to the angle which is present between the axis of the mandrel ... The representations are not to scale.. In FIG. 1 a schematic depiction of an operating sequence of an embodiment of the ... The tape 11 is joined at an angle θ to the axis of the longitudinally extending mandrel 2. Subsequently, the tape 11 is coiled ... in such a way that tape extends at an angle of greater or smaller than 90° to the axis of the pipe-shaped body. Thereby a body ...
The first shape is rotated on the X -, Y -, or Z -axis to second shape, which is shown to demonstrate the rotation pattern. ... right orientation of axis, (b) use of correct proportion, (c) accurate angle used for isometric perspective, (d) appropriate ... were presented with a visual representation of an object (drafting model) and were asked to rotate the model and create a ... Mental Rotation Test. The Mental Rotation Test (MRT) consists of 20 items that require the learner to compare two-dimensional ...
The different vertical sections are taken at different angles of rotation about the center axis 5 of the object. The computer ... Efficient data representation of teeth model. US7702492. Mar 11, 2004. Apr 20, 2010. Geodigm Corporation. System and method for ... The object is reproduced through its different contours at different angles of rotation in a horizontal plane through the ... The junctions (angles) 38b, 39b and 40b must also be formed with great precision in order to give a well-functioning cone ...
... compensation of images recorded sequentially by an electronic camera randomly displaced in a scene and provided with a rotation ... Method for producing a rotation-compensated image sequence allowing simplified reconstruction of the translation of a camera by ... Euler angle, see FIG. 1. a) or by rotating about a rotation axis in space (see FIG. 1. b, axis-angle representation (A, α), ... During camera rotation the rotation sensor immediately supplies measured data for the angles rotated about each of the axes ...
Angular offsets were defined as the difference between the angle from the x-axis (90° to the right of the starting orientation ... The starting orientation was along the y-axis. (b) First-person view of the virtual environment as seen by the participants. (c ... The starting orientation was along the y-axis. (b) First-person view of the virtual environment as seen by the participants. (c ... The starting orientation was along the y-axis. (b) First-person view of the virtual environment as seen by the participants. (c ...
... section of the vessel due to the oblique angle between the vessel segment central axis and the imaging system axis of rotation ... with minor axis length indicated). C: schematic representation of minor axis length is equivalent to the diameter of the vessel ... rotation angle (angle between the plane of branching of the branch division and the plane of branching of the parent branch ... and total branch angle (minor plus major angle, ∼70°) were not statistically different between human and pig (P , 0.5 for all ...
Various approaches exist such as rotation matrices, Euler angles, helical (or screw) axis and quaternions, but some have ... involve 3-D motion analysis which requires precise representation of an objects position and orientation. Mathematical ... Helical axis descriptions are handy for user interaction but do not provide a unique way to combine rotations into a single ... Two rotations can be combined simply by multiplying two quaternions together. Averaging and curve fitting rotations become ...
about the x axis and a rotation matrix A.sub.z-axis that may be used to provide a rotation of an angle .beta. about the z axis ... about the y axis by .alpha. degrees to cancel out pitch error. FIG. 13 is a graphical representation of the transformation of ... axis if necessary. Below are examples of a rotation matrix A.sub.x-axis that may be used to provide a rotation of an angle . ... Different rotation matrices may be used to provide rotation about the x (roll) axis and the z (yaw) ...
... alternative ways to represent rotations such as Euler- and Kardan-angles, angle and axis representation, and unit quaternions ...
... with angles and rotations are introduced and the equivalence of unit quaternion representation and unit ball representation is ... It is based on a specific, novel representation of rotations, called ,em,unit ball representation,/em,, which allows to ... intersecting axes is derived by describing the set of singular orientations as two tori that separate two-solvable from non- ... solvable orientations within $SO(3)$. Therefore, the tori provide the boundary of the workspace of the axes constellation. The ...
Orientation → rotation angles around a set of orthogonal axes. Sphericity = how spherical is a particle. Wadells sphericity:. ... Representations such as octrees or BSP are used to simplify the geometry and topology.. Lossy and lossless methods preserve. ... the three representative axes of an object.. OBB computed with the covariance method using extreme vertices instead of voxels. ... Boundary Representations. Kd-tree. Contructive Solid Geometry (CSG). etc.. B-Rep. Chain Codes. Semi-boundary and Shell. Extreme ...
  • Euler angle representation of rotation. (
  • The rotation axis is sometimes called the Euler axis. (
  • The axis-angle representation is equivalent to the more concise rotation vector, also called the Euler vector. (
  • This is called the Euler representation of a 3D angle. (
  • Some coordinate systems in mathematics behave as if there were real gimbals used to measure the angles, notably Euler angles. (
  • Specifically, the Wigner functions (matrix elements of representation operators in case of SU(2)) could use either of the known paramentrizations of rotations: complex numbers (Cayley-Klein parameters), axis-angle, or Euler angles. (
  • Various approaches exist such as rotation matrices, Euler angles, helical (or screw) axis and quaternions, but some have significant limitations. (
  • Euler angles can be defined in 12 different ways and each will give a different answer. (
  • G. Piovan and F. Bullo, On coordinate-free rotation decomposition: Euler angles about arbitrary axes,, IEEE Transactions on Robotics , 28 (2012), 728. (
  • There are getters for quaternion components, of course, but there are also getters for Cardan angles, for Euler angles, for vector and axis and for matrix, none of them are stored in the instance, they are recomputed on the fly. (
  • This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). (
  • The 3D heading is here described using either the direction cosine matrix (DCM) or the Euler angle sets. (
  • So now if you think about a sequential, how do I go from Euler angles to a DCM? (
  • The values of these three rotations are called Euler angles . (
  • The simplest is to think of a rotation as being equivalent to a set of 3 rotations around the x, y, and z axes (known as the Euler representation). (
  • Unfortunately, the Euler representation has drawbacks when it comes to combining rotations (see below). (
  • If you are going to be working in euler co-ordinates as a generalized representation that is. (
  • Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors James Diebel These are (1) the rotation matrix, (2) a triple of Euler angles, derivation of rotation matrix using polar coordinates. (
  • The Euler representation of the joint angles in MVN is generally calculated using the Euler sequence ZXY. (
  • An Euler sequence explains in which order the angle is calculated. (
  • Even though the shoulder joint is the only joint with that sequence that can be shown in MVN, users have the option to export all the joint angles using the Euler sequence XZY. (
  • To answer your latest question, I did some research and from the limited information I found I'd say the matrix is direct (same as OpenGL) and has the following order of rotations: X, Y, Z. I am currently looking into the link you sent me and some additional info about Euler. (
  • Euler angles and quaternion specifications are simple lists of the corresponding numerical parameters, whereas DCM invokes an instance of the above mentioned matrix CT and angle-axis parameterization makes use of the vector CT for the rotation axis vector. (
  • SpinXML makes no attempt to rectify the well-documented ambiguities inherent in Euler angles [10], it only serves as a container. (
  • This is a normalized vector (x,y,z) representing the axis of rotation, and a scalar angle r that represents the amount to rotate around that axis. (
  • This can easily be converted into a quaternion or rotation matrix, whatever you use to handle rotations. (
  • You can read about them at . (
  • You are right that quaternion are a great replacement for rotation matrices. (
  • For good reasons, such as being able to easily combine rotations, the four number version, the quaternion rotation , is better, though perhaps harder for a beginner to grasp. (
  • In the context of inertial navigation systems, that can be done by mounting the inertial sensors directly to the body of the vehicle (this is called a strapdown system) and integrating sensed rotation and acceleration digitally using quaternion methods to derive vehicle orientation and velocity. (
  • Quaternion mathematics expands the possibilities of how we can represent and manipulate rotations. (
  • For further reading on quaternions, see: Shoemake, K. 'Animating Rotation with Quaternion Curves. (
  • In an appendix, tools for dealing with angles and rotations are introduced and the equivalence of unit quaternion representation and unit ball representation is described. (
  • rotation quaternion. (
  • We would like to base the rotation upon the new Quaternion object. (
  • A rotation quaternion is a special case of a quaternion. (
  • The fact that Rotation uses quaternion formalism (but for now not an independent class Quaternion) is an implementation detail and should not be visible from outside. (
  • Adding the Quaternion as the storage part of the Rotation class would also add another layer, with two different memory handling (which is significant for very small objects) and two levels of method delegations. (
  • Calling getQ is a very rare need and most users directly use the specialized Rotation operation to deal with rotation, and not with extra Quaternion only operations, as general quaternion operations are not Rotation oriented. (
  • If I understand you correctly, you're looking for a quaternion that will rotate a Z-axis-aligned object to face along a given vector. (
  • You can build the quaternion directly as: q.w = cos(theta/2) q.v = sin(theta/2)*normalize(a) The only real problem with this is that there's no control over the 'roll' component of the rotation. (
  • The rotation matrix R is defined in Representations of Body Motion and The quaternion derivative is also related to the Derivative Kinematics in Relatively Rotating 3. (
  • the time derivative of θ around y' and the time derivative of φ % __Quaternion to Rotation Matrix In motion Kinematics, it is well-known that the time derivative of a 3x3rotation matrix equals a skew-symmetric matrix multiplied by the rotation matrix where the skew symmetric matrix is a linear (matrix valued) function of the angular velocity and the ro The angle of rotation, Angle of Rotation Calculator. (
  • The following example uses ReactiveModule.rotation(w,x,y,z) to construct a rotation // from a quaternion-based representation of it. (
  • Construct a Rotation object from a quaternion-based values. (
  • 3x3 rotation matrices (if rotating around an axis passing through the origin). (
  • 3x4 rotation matrices with a translation (if rotating around an axis passing through an arbitrary point). (
  • Of course, if a group structure is desired, then unit quaternions are a nice replacement for rotation matrices. (
  • The group of all 3 × 3 orthogonal matrices is denoted O(3), and consists of all proper and improper rotations. (
  • Improper rotations correspond to orthogonal matrices with determinant −1, and they do not form a group because the product of two improper rotations is a proper rotation. (
  • Rotation matrices can drift numerically when repetitively multiplying matrices, resulting in undesired scaling or shearing. (
  • This means that applying multiple matrices in succession to a spinor is the same as applying the single matrix which corresponds to the resultant rotation--the matrices compose with each other in the same way that rotations do. (
  • Therefore, we have defined a set of matrices which is isomorphic to 3-dimensional rotations, on a 2-dimensional object. (
  • The generic term for this process is called representation theory , and in this case we say that the matrices [itex]D(R(e\theta))[/itex] form a 2-dimensional representation of the 3-dimensional rotation group, which is known as SO(3). (
  • There's also a 3-dimensional representation of SO(3): the plain old set of rotation matrices we all know and love. (
  • Rotation Matrices Suppose that ↵ 2 R. Search. (
  • Multiplication of Rotation Matrices Recall from above that the dot product of any two different rows or columns of a rotation matrix is zero, while the dot product of any row or column with itself is one. (
  • An \(n\)-dimensional representation of a group \(\Gamma\) is a homomorphism from \(\Gamma\) to the group of \(n \times n\) matrices defined on a field \(\Bbb F\ .\) Typically \(\Bbb F\) is \(\Bbb R\) or \(\Bbb C\ ,\) that is, the matrices have either real or complex entries. (
  • A representation is faithful if this mapping is an isomorphism onto a subgroup of \(n \times n\) matrices. (
  • You should consider the set of unit quaternions to encode the rotations. (
  • For both types, the user can choose to use rotations and translation dual quaternions, or to use screw motion dual quaternions. (
  • To do this we need to map the rotations to points on a hypersphere, that is what quaternions do. (
  • Two rotations can be combined simply by multiplying two quaternions together. (
  • Most importantly, because quaternions lie on a surface, interpolations of 3D rotations can be uniquely defined. (
  • Quaternions provide notational convenience and also provide a deeper mathematical foundation for 3D rotations. (
  • J. B. Kuipers, Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality ,, Princeton University Press , (2002). (
  • Quaternions in 3D are only rotation quaternions. (
  • To avoid these problems, LSL represents rotations using mathematical entities known as quaternions, which consists of 4 elements: x, y, z, and s. (
  • However, you can use rotations without dealing with the individual elements of quaternions. (
  • 1 1 We can Dual Quaternions for Rigid Transformation Blending Log-matrix Blending (b) † Constant speed if the derivative of bothα(t) If we re-write it as a matrix form by omitting , it becomes a 2x2 rotation matrix that we are familiar with. (
  • Then the radius vectors from the axis to all particles undergo the same angular displacement at the same time. (
  • By Rodrigues' rotation formula, the angle and axis determine a transformation that rotates three-dimensional vectors. (
  • Many rotation vectors correspond to the same rotation. (
  • Thus, there are at least a countable infinity of rotation vectors corresponding to any rotation. (
  • Furthermore, all rotations by 2πM are the same as no rotation at all, so, for a given integer M, all rotation vectors of length 2πM, in all directions, constitute a two-parameter uncountable infinity of rotation vectors encoding the same rotation as the zero vector. (
  • Another way to represent the same 3D angle is to use three vectors, showing what the front is pointing at (fwd), what the top is pointing at (up), and what the left side is pointing at (left). (
  • [ 1 ] By definition, a rotation about the origin is a linear transformation that preserves length of vectors (it is an isometry ) and preserves orientation (i.e. handedness ) of space. (
  • Besides just preserving length, rotations also preserve the angles between vectors. (
  • It follows that any length-preserving transformation in R 3 preserves the dot product, and thus the angle between vectors. (
  • We then find the angle α (in degrees) between vectors T1T2 and the positive z-axis by computing the scalar product of vectors T1T2 and OP where P is an arbitrary point along the positive z-axis, which is typically (0,0,p), where p is the approximate length of the rod-shaped protein under investigation. (
  • Then we compute the cross product of the two vectors to determine the axis about which we should rotate vector T1T2 so it coincides with the positive z-axis. (
  • The image in my head is of the z axis, and how no two vectors purely along the z axis can ever add up to a vector along the x axis. (
  • in figure 1 the arm of a subject is rotated according to the shown rotation vectors. (
  • Preston, 1982 ) postulates that in longitudinally expanding cells, cellulose microfibrils are synthesized in a transverse pattern and are then reoriented toward the longitudinal axis due to the strain generated by turgor pressure ( Green, 1960 ). (
  • 3. The system of claim 2 , wherein the plurality of dental position appliances further includes at least one appliance with cavities shaped to apply force to rotate the tooth around its center of rotation so that the longitudinal axis is substantially perpendicular to the gingival plane at the desired location, during or subsequent to translation of the tooth from the first location toward the desired location along the gingival plane. (
  • This corresponds to respectively 90 degrees rotation around a frontal, sagittal and longitudinal axis. (
  • The final position after a combination of 90 degrees about a, respectively, frontal, sagittal and longitudinal axis. (
  • The fixed axis hypothesis excludes the possibility of an axis changing its orientation, and cannot describe such phenomena as wobbling or precession . (
  • Along the orientation of the current angles of my object. (
  • Simply setting it to the above changes it according to world angles, which isn't relative to the objects orientation. (
  • If anyone can help it is greatly appreciated, i need to set the exact current rotation and still maintain the objects current orientation. (
  • To get the correct axis you have to transform the local axis (e.g. [0 0 1] for the z axis) by the same rotation that has caused the current orientation of the model. (
  • The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions . (
  • But a (proper) rotation also has to preserve the orientation structure . (
  • The " improper rotation " term refers to isometries that reverse (flip) the orientation. (
  • The LSL rotation type is one of several ways to represent an orientation in 3D. (
  • The rotation can be viewed as a discrete twist in three dimensional space, and the orientation of an object is how much it has been twisted around from whichever axes we are using - normally the region's axes. (
  • Nevertheless, because of the parallel orientation of two of the gimbals' axes there is no gimbal available to accommodate rotation about one axis. (
  • Finite rotations, that is a change from one angular orientation to another. (
  • A length-preserving transformation which reverses orientation is an improper rotation , that is a reflection or more generally a rotoinversion. (
  • In addition to preserving length, proper rotations must also preserve orientation. (
  • Technically, one needs to specify an orientation for the axis and whether the rotation is taken to be clockwise or counterclockwise with respect to this orientation). (
  • Many tasks in biomedical data analysis, such as kinematic data collection, involve 3-D motion analysis which requires precise representation of an object's position and orientation. (
  • B. Alpern, L. Carter, M. Grayson and C. Pelkie, Orientation maps: Techniques for visualizing rotations (a consumer's guide),, in VIS '93: Proceedings of the 4th conference on Visualization , (1993), 183. (
  • Orientation → rotation angles around a set of orthogonal axes. (
  • The operations of primary visual cortex generate continuous representations of orientation, ocular dominance, and retinotopy that, to fit in two dimensions, organize at separate but overlapping scales (e.g., 20-500 μm, 200 μm to 5 mm, and 2-33 mm). (
  • iso-orientation contours cross ocular dominance columns at right angles, and ocular dominance columns distort retinotopy near the V1/V2 border. (
  • We carried out further investigations on the effect of the polarization orientation, by rotating the crystal around the propagation axis. (
  • is the object's current orientation relative to this null rotation. (
  • An object is rotated by multiplying its current orientation with the desired rotation. (
  • This rotates the object around its local x-axis, which depends on its current orientation. (
  • Like previously, this would rotate your object along the x-axis based on its current orientation, but in the opposite direction. (
  • We are grateful to J. For a 3×3 matrix, The goal is to get rotation matrix from axis of rotation and angle of rotation I This means the rotation matrix is that the derivative of the which Representations of Body Orientation. (
  • For example the 9 KINEMATICS OF MOVING FRAMES 67 rotation matrix R is universal to all representations of orientation, resultant derivative is in the moving body frame. (
  • 8, Osnabrück, Germany article info abstract Article history: Received 9 May 01 Received in revised form 5 December 01 Available online 1 March 013 Keywords: Natural image statistics Natural vision Power spectrum Orientation The efficient coding hypothesis posits that sensory systems are adapted to the regularities of their signal input so as to reduce redundancy in the resulting representations. (
  • This convention for specifying an orientation is, in this example, called an orientation ZXY fixed angles. (
  • The initial view orientation is looking down the negative z axis with positive x to the right and positive y up. (
  • Consider a case of a level-sensing platform on an aircraft flying due north with its three gimbal axes mutually perpendicular (i.e., roll, pitch and yaw angles each zero). (
  • where M is the total mass and I C is the moment of inertia about an axis perpendicular to the movement of the rigid system and through the center of mass. (
  • 5) Polar second moment of area and perpendicular axis theorem. (
  • 7) Using the perpendicular axis theorem for calculating the planar second moment of area of a circle with respect to a diameter. (
  • But I just wanted to make clear that infinitesimal rotations (=axis-angle) are useful in either way, e.g. to formulate incremental updates in optimization. (
  • Continuous and infinitesimal rotations, such as when an object is continuously rotating. (
  • However it turns out that continuous and infinitesimal rotations are easily combined using vector addition. (
  • First note that a rotation about an axis of angle $\theta$ and a rotation about the same axis of angle $-\theta$ have the same symmetric parts. (
  • displaystyle (\mathrm {axis} ,\mathrm {angle} )=\left({\begin{bmatrix}e_{x}\\e_{y}\\e_{z}\end{bmatrix}},\theta \right)=\left({\begin{bmatrix}0\\0\\1\end{bmatrix}},{\frac {\pi }{2}}\right). (
  • That gives you an axis a and a rotation magnitude cos(theta). (
  • For a mathematical context, see Axis-angle representation . (
  • There are a number of mathematical notations and algebras that we could use, some are nearer to an angle like measure of rotation and some are nearer to the mapping of points. (
  • Mathematical operations such as interpolation, averaging and curve fitting, applied to translation are straightforward but are troublesome when applied to rotation. (
  • C. D. Mladenova and I. M. Mladenov, Vector decomposition of finite rotations,, Reports on Mathematical Physics , 68 (2011), 107. (
  • Then if you turn to your left, you will rotate π/2 radians (or 90°) about the z axis. (
  • The angle of rotation is a separate number given in radians, eg. (
  • In LSL, these three angles are expressed in radians instead of degrees, that is, a right angle is PI/2. (
  • Fortunately it's very seldom necessary to do anything with the actual internal representation of rotations and there are functions for converting easily back and forth between the three LSL types, and between degrees and radians. (
  • Note: LSL expects angles to be specified in terms of radians rather than degrees. (
  • The comparison between figure 1 and 2 shows us the order of rotations has an effect on the final position. (
  • It is one of many rotation formalisms in three dimensions. (
  • However finite rotations are more complicated and require other types of algebra. (
  • begingroup$ @Tpofofn: The exponential map from the Lie algebra so(3) (=axis-angle) to the Lie group SO(3) is surjective, so all possible rotations CAN nicely represented using three parameters only (… ). (
  • This hypersphere represents all possible rotations and all the possible paths between rotations. (
  • Note that this is a shape rather than a point because we need to be able to specify a rotation θ in the spherical plane in addition to Latitude and Longitude. (
  • Rotation between two orientations can be performed with spherical linear interpolation on the surface of this sphere (red line). (
  • Our research group is trying to use alternative representations for proteins structures, and has made progress on representing spheroproteins using spherical coordinates (ρ,φ,θ) (1). (
  • which represent the amount which the object is rotated around each axis. (
  • To rotate around an "arbitrary" axis you can use the axis/angle representation of rotations. (
  • Since every 2-dimensional rotation can be represented by an angle φ, an arbitrary 3-dimensional rotation can be specified by an axis of rotation together with an angle of rotation about this axis. (
  • There are a number of ways to visualize an arbitrary rotation in three dimensions. (
  • Note: An object can be rotated around an arbitrary point by multiplying a vector by a rotation in the manner described above. (
  • Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant. (
  • Hence, the interaction of interoception and stress represents bi-directional communication on the brain-body axis. (
  • Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion. (
  • The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. (
  • rotational motion around a single axis even has a work-energy theorem analogous to that of particle dynamics. (
  • They are also subject to gimbal lock, which is when two of the rotational axes align and you lose the ability to continue rotating freely. (
  • 3) To describe the boundaries of tilt and torsion using a model representation-disclination as an element of rotational plasticity [ [3] p. 254]. (
  • The wingstroke of an insect is typically divided into four kinematic portions: two translational phases (upstroke and downstroke), when the wings sweep through the air with a high angle of attack, and two rotational phases (pronation and supination), when the wings rapidly rotate and reverse direction. (
  • 3D rotation, specified as a 3-by-3 columnwise-defined matrix, also known as a direction cosine matrix. (
  • begingroup$ I is impossible to encode a rotation in 3-space with only 3 parameters without running into these types of problems. (
  • These assumptions are used throughout the Rotation class (see for example the constructors that add some specific parameters to deal with normalization. (
  • The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. (
  • These two types of rotation are called active and passive transformations . (
  • It is useful to both characterize rotations, and also for converting between different representations of rigid body motion, such as homogeneous transformations[clarification needed] and twists. (
  • Rotations are often defined as linear transformations that preserve the inner product on R 3 . (
  • The rotation group is a group under function composition (or equivalently the product of linear transformations). (
  • The important thing about spinors is that there are transformations on them which recreate the behavior of 3-dimensional rotations. (
  • So in your case, if you start with the state (1,0) and arbitrarily decide that that means 'downward', and apply a 90-degree Y-rotation to it, then it makes sense to say that it now points 'rightward', etc., because we know that the transformations will follow the right pattern when composed on top of each other. (
  • Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space. (
  • A gimbal is a ring that is suspended so it can rotate about an axis. (
  • When a set of gimbals is close to the locked configuration, small rotations of the gimbal platform require large motions of the surrounding gimbals. (
  • Gimbal lock can occur in gimbal systems with two degrees of freedom such as a theodolite with rotations about an azimuth and elevation in two dimensions. (
  • These systems can gimbal lock at zenith and nadir, because at those points azimuth is not well-defined, and rotation in the azimuth direction does not change the direction the theodolite is pointing. (
  • If the aircraft pitches up 90 degrees, the aircraft and platform's yaw axis gimbal becomes parallel to the roll axis gimbal, and changes about yaw can no longer be compensated for. (
  • This problem may be overcome by use of a fourth gimbal, actively driven by a motor so as to maintain a large angle between roll and yaw gimbal axes. (
  • Gimbal lock is the loss of one degree of freedom in a three degrees-of-freedom mechanism that occurs when two axes are driven into a parallel configuration, resulting in no available rotation about one axis ( Wiki: Gimbal Lock) . (
  • This results in a Gimbal Lock because the Y- and Z- axis are aligned. (
  • The following method actually rotates around the global equivalent of the chosen local axis. (
  • When a rigid body rotates around a fixed axis, its axis-angle data are a constant rotation axis and the rotation angle continuously dependent on time. (
  • For instance, if a given rotation rotates a point through 180 about the origin, then applying it twice will take it back to its original location, definitely not linear. (
  • This rotates the object around the global x-axis (the axis which runs from west to east). (
  • The composition rule is different when the second axis is fixed with respect to the vector, i.e. rotates with it during the first rotation. (
  • R a and R b rotates the vector through the angle a + b, or more formally R a R b - R a + b . (
  • Moreover, since composition of rotations corresponds to matrix multiplication , the rotation group is isomorphic to the special orthogonal group SO(3). (
  • For manual rotation I use matrix multiplication based on the user's mouse positions (positionY, positionX). (
  • According to Euler's rotation theorem , simultaneous rotation along a number of stationary axes at the same time is impossible. (
  • The axis-angle representation is predicated on Euler's rotation theorem, which dictates that any rotation or sequence of rotations of a rigid body in a three-dimensional space is equivalent to a pure rotation about a single fixed axis. (
  • Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R 3 which is called the axis of rotation (this is Euler's rotation theorem ). (
  • A representation is absolutely irreducible on \(\Bbb F^n\) if all linear maps \(A\) on \(\Bbb F^n\) that commute with all \(\gamma \in G\) are scalar multiples of the identity matrix. (
  • Any direct Euclidean motion can be represented as a composition of a rotation about the fixed point and a translation. (
  • In mathematics, the axis-angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle θ describing the magnitude of the rotation about the axis. (
  • Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a Euclidean vector, given a rotation axis and an angle of rotation. (
  • This article is about rotations in three-dimensional Euclidean space. (
  • For rotations in four-dimensional Euclidean space, see SO(4) . (
  • In mechanics and geometry , the rotation group is the group of all rotations about the origin of three-dimensional Euclidean space R 3 under the operation of composition. (
  • In general, any rotation can be specified completely by the three angular displacements with respect to the rectangular-coordinate axes x , y , and z . (
  • For example, during a single sensor event the accelerometer returns acceleration force data for the three coordinate axes, and the gyroscope returns rate of rotation data for the three coordinate axes. (
  • You can think of your viewpoint as carrying a set of coordinate axes with it. (
  • These facts must be taken into account when inverting the exponential map, that is, when finding a rotation vector that corresponds to a given rotation matrix. (
  • For most joint angles this corresponds to flexion/extension, which is a motion about the Z-axis (pointing to the right). (
  • orients the object so that its local axes are aligned with the global axes. (
  • The order in which the operands are specified depends if a rotation is performed around the global axes or the local axes. (
  • Cubic interpolation on the sphere surface can represent smooth rotation through multiple orientations (yellow line). (
  • To proceed to a tomographic reconstruction of the refractive index of the sample based on this quantitative phase measurement, such 2-dimentionnal data must be recorded for different sample orientations covering an angle of 180° to cover all the object spatial frequencies in the reciprocal space. (
  • they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body . (
  • Any displacement of a rigid body may be arrived at by first subjecting the body to a displacement followed by a rotation, or conversely, to a rotation followed by a displacement. (
  • The axis-angle representation is convenient when dealing with rigid body dynamics. (
  • There is a 1:1 equivalence (a morphism) between the rotation of a 3D rigid body and the movement of a shape on the surface of a sphere. (
  • I want to implement the Inverse Rodrigues Rotation Formula (also known as Log map from SO(3) to so(3)), in double precision code (MATLAB is fine for the example) preferably as a 3-parameter vector with the unit direction vector scaled by the magnitude of rotation. (
  • A clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. (
  • We describe a method using polarimetric radar to measure the polarizability angle, the relative phase, and the target magnitude. (
  • It struck me that perhaps I need to take the inverse of that transform first and then use the rotation angles. (
  • This creates a transpose matrix, which for rotations, happens to be the inverse matrix also, and inverting it again gives you the rotation you really wanted all along. (
  • Calculate the rotation as a sequence of two reflections. (
  • The reason why the shoulder joint is the only joint that shows the XZY sequence in MVN is because the rotation with the expected largest range of motion should be calculated first in the sequence. (
  • It's important to realize that the order of sequence can effect rotations. (
  • Think of this as specifying the rotation from the object's point of view, that is, relative to the direction it is currently facing. (
  • The vector should be the difference between the object's current position and the desired "center-point" of rotation. (
  • class encapsulates an object's rotation. (
  • This method solves the problem of FOV deviation from the target scope during the zooming process, since the optical axis was not taken as the zooming center of the FOV. (
  • Phase measurements provide high accuracy optical path length measurements across the specimen along the optical axis. (
  • The angle between the beam axis and the optical axis is θ. (
  • 4. Apparatus according to claim 1, wherein the pattern of discrete separated point light sources lie along an invertible function of distance from the optical axis of the objective lens. (
  • 6. Apparatus according to claim 1, wherein the ophthalmic diagnostic instrument includes means for folding the pattern of discrete separated point light sources onto the optical axis of the instrument, toward the cornea, with the means for projecting the pattern including a source of the pattern off-axis from the optical axis and from the path of the returned, distorted pattern image. (
  • For example, the elevation and azimuth angles of e suffice to locate it in any particular Cartesian coordinate frame. (
  • Using 3D laser vibrometry to measure tympanum deflection, we show that female lesser waxmoths ( Achroia grisella ) can orient toward the 100-kHz male song, because each ear functions independently as an asymmetric pressure gradient receiver that responds sharply to high-frequency sound arriving from an azimuth angle 30° contralateral to the animal's midline. (
  • Where body size is diminutive and interear distance is short, as is generally the case in acoustic insects and anurans, it is improbable that an animal can rely on interaural intensity difference (IID) or interaural time difference (ITD) mechanisms to resolve the azimuth angle toward the source ( 2 ). (
  • Helical axis descriptions are handy for user interaction but do not provide a unique way to combine rotations into a single desired rotation. (
  • For example, in two dimensions rotating a body clockwise about a point keeping the axes fixed is equivalent to rotating the axes counterclockwise about the same point while the body is kept fixed. (
  • Successive rotations are also reviewed in this context as well as the attitude kinematic equations. (
  • Composition of rotations sums their angles modulo 1 turn , which implies that all two-dimensional rotations about the same point commute . (
  • Rotations in three-dimensional space differ from those in two dimensions in a number of important ways. (
  • Also, unlike the two-dimensional case, a three-dimensional direct motion, in general position , is not a rotation but a screw operation . (
  • In general a rotation occurs in a plane, that is a two dimensional space, which may be embedded in 3D space. (
  • But it can be easily verified that only two dimensional representations of SO(3) satisfy this property. (
  • Or is there a more general result which relates all representations of SO(3) to rotation in three dimensions (like the one two-dimensional representations have, that is more than just having the same commutation relation for the generator). (
  • Like any linear transformation of finite-dimensional vector spaces, a rotation can always be represented by a matrix . (
  • Each such rotation acts as an ordinary 2-dimensional rotation in the plane orthogonal to this axis. (
  • The software coordinates motor movement of all 3 axes (anterior-posterior, medial-lateral, and dorsal-ventral) probe placement in relation to 3-dimensional visual representation of a rat (Paxinos & Watson, 6th Edition) or mouse (Watson, 3rd edition) Brain Atlas. (
  • Detectors record information about the intensity of the rays transmitted through the head at each angle, which is sort of like taking a series of two-dimensional snapshots. (
  • By allowing doctors and researchers to view the full volume of the head, CT Stands for 'computerized tomography'. This imaging technique uses x-rays to generate detailed pictures of structures inside the body. " target="_blank" >CT scans can provide much more information about the brain than traditional X-ray scans, which only offer a two-dimensional representation of the brain. (
  • Gimbals are typically nested one within another to accommodate rotation about multiple axes. (
  • A display apparatus includes a scanning assembly that scans about two or more axes, typically in a raster pattern. (
  • Simplifying the complicated locomotion kinematics to a sinusoidal wing rotation about two axes, the main features of dynamic avian flight were approximated. (
  • In kinematics, we use a 'moving coordinate system' instead of fixed axes. (
  • Because of their tendency to intersect the V1/V2 border at right angles, the trajectories of columns near the border tend to follow trajectories that can be predicted from the border. (
  • This paper surveys the two fundamental possible choices in representing the attitude of an aerospace vehicle: active and passive rotations. (
  • Also, your last question has a trivial answer: The identity map on SO(3), defined by I(R)=R for all R in SO(3), satisfies the definition of a representation. (
  • and the identity map satisfies the definition of a rotation. (
  • This equivalence described above is like mapping 3D rotations to the axis-angle representation. (
  • The first three elements specify the axis of rotation and the fourth element specifies the angle. (
  • In LSL this can be represented using the vector type, where the x element specifies the roll (angle of rotation around the x-axis), the y element specifies the pitch (angle of rotation around the y-axis), and the z element specifies the yaw (angle of rotation around the z-axis). (
  • The rotation occurs in the sense prescribed by the right-hand rule. (
  • This motion occurs about the X-axis (pointing anteriorly). (
  • To rotate a point around an axis, you cannot just pointwise multiply it by another vector. (
  • So after applying cosine you multiply cos()*(1,0) the x-axis. (
  • It does not matter whether we add or subtract the angle - we always multiply by the same factor! (
  • What would the recommended way be to achieve the desired rotations in OpenGL, other than manually building the matrix as I'm doing now? (
  • The plane of rotation is a plane that is invariant under the rotation. (
  • These three independent quantities are directly related to target shape and dimensions and are invariant with respect to rotation about the sensor-to-target axis. (
  • A representation of \(\Gamma\) is irreducible if the only proper subspace of \(\Bbb F^n\) left invariant by all elements of \(\Gamma\) is the origin. (
  • In addition, a rotation-invariant identification remains an unsolved problem, even with the use of 2D images. (
  • The objective of the current study was to design a rotation-invariant recognition process while using a 3D signature for classifying hand postures. (
  • This study has demonstrated the efficiency of the proposed rotation invariant 3D hand posture signature which leads to 93.88% recognition rate after testing 14,732 samples of 12 postures taken from the alphabet of the American Sign Language. (
  • He imagined three reference frames that could rotate one around the other, and realized that by starting with a fixed reference frame and performing three rotations, he could get any other reference frame in the space (using two rotations to fix the vertical axis and another to fix the other two axes). (
  • Perhaps a better way to look at this is to let the solid body be the sphere itself, then the surface of the sphere is automatically the same as rotation in 3D space. (
  • A representation of rotations is a particular formalism, either algebraic or geometric, used to parametrize a rotation map. (
  • The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. (
  • Rotation in mathematics is a concept originating in geometry . (
  • For the rotation of a single vector it may be more efficient than converting e and θ into a rotation matrix to rotate the vector. (
  • So if you want to define a '''rotation''' about an axis at 45 degrees in the x-y plane (North East in region coordinates), you'd need to point the axis with the same amount of x and y, but with no z. (
  • Think about how to get from, a way to describe rotation which is intuitive, such as a set of angles and to turn that into a way to map the coordinates of an object before rotation to its coordinates after rotation. (
  • To take advantage of this potential symmetry element, we decided to represent RSPs using cylindrical coordinates, (ρ,θ,z), with the z-axis as the main axis and one 'tip' of the protein at the origin, with 'tip' being defined as one of two points lying along the protein axis and defining its longest dimension. (
  • a rotation matrix - a real 3-by-3 matrix with and the time derivative of the rotation, Validity of Rotation matrix calculations from angular R is the rotation matrix. (
  • 4. The system of claim 3 , wherein the plurality of dental position appliances further includes at least one appliance with cavities shaped to apply force to at least partially intrude the tooth during or subsequent to rotation of the tooth to its upright position. (
  • You are already thinking about the problem area, because you carefully described your desired subsequent rotations as about the 'original' axes. (
  • Subsequent 'rotations about y' will be about this rotated y axis, not the original y axis. (