Rotation formalisms in three dimensionsIn geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.
Faraday effectThe Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the magnetic field along the direction of the light propagation. Formally, it is a special case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal. This effect occurs in most optically transparent dielectric materials (including liquids) under the influence of magnetic fields.
Rotation (mathematics)Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire (n − 1)-dimensional flat of fixed points in a n-dimensional space.
Coherent sheafIn mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an , and so they are closed under operations such as taking , , and cokernels.
Coherent sheaf cohomologyIn mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties. Many geometric questions can be formulated as questions about the existence of sections of line bundles or of more general coherent sheaves; such sections can be viewed as generalized functions. Cohomology provides computable tools for producing sections, or explaining why they do not exist. It also provides invariants to distinguish one algebraic variety from another.
AnimationAnimation is the method by which are manipulated to create moving images. In traditional animation, images are drawn or painted by hand on transparent celluloid sheets to be photographed and exhibited on film. Today, many animations are computer animations made with (CGI). Stop motion animation, in particular claymation, has continued to exist alongside these other forms. Animation is contrasted with live-action film, although the two do not exist in isolation. Many moviemakers have produced films that are a hybrid of the two.
Quaternions and spatial rotationUnit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis.
Animeis hand-drawn and computer-generated animation originating from Japan. Outside Japan and in English, anime refers specifically to animation produced in Japan. However, in Japan and in Japanese, anime (a term derived from a shortening of the English word animation) describes all animated works, regardless of style or origin. Animation produced outside Japan with similar style to Japanese animation is commonly referred to as anime-influenced animation. The earliest commercial Japanese animations date to 1917.
DreamWorks AnimationDreamWorks Animation LLC (DWA, also known as DreamWorks Animation Studios and simply known as DreamWorks) is an American animation studio that produces animated films and television programs and is a subsidiary of Universal Pictures, a division of NBCUniversal, which is itself a division of Comcast. The studio has released a total of 46 feature films as of June 2023, 44 of which were theatrically released. Their catalogue includes several of the highest-grossing animated films of all time, with Shrek 2 (2004) having been the highest at the time of its release.
Computer animationComputer animation is the process used for digitally generating animations. The more general term (CGI) encompasses both static scenes (s) and dynamic images (s), while computer animation refers to moving images. Modern computer animation usually uses 3D computer graphics to generate a three-dimensional picture. The target of the animation is sometimes the computer itself, while other times it is film. Computer animation is essentially a digital successor to stop motion techniques, but using 3D models, and traditional animation techniques using frame-by-frame animation of 2D illustrations.
TaskbarThe Taskbar is a graphical user interface element that has been part of Microsoft Windows since Windows 95, displaying and facilitating switching between running programs. The Taskbar and the associated Start Menu were created and named in 1993 by Daniel Oran, a program manager at Microsoft who had previously collaborated on Great ape language research with the behavioral psychologist B.F. Skinner at Harvard. The Taskbar is an exemplar of a category of always-visible graphical user interface elements that provide access to fundamental operating system functions and information.
Traditional animationTraditional animation (or classical animation, cel animation, or hand-drawn animation) is an animation technique in which each frame is drawn by hand. The technique was the dominant form of animation in cinema until the end of the 20th century, when there was a shift to computer animation in the industry, specifically 3D computer animation. Animation production usually begins after a story is converted into an animation film script, from which a storyboard is derived.
