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Euler Filter
In computer graphics, an Euler filter is a filter intended to prevent gimbal lock and related discontinuities in animation data sets in which rotation is expressed in terms of Euler angles. These discontinuities are caused by the existence of many-to-one mappings between the Euler angle parameterization of the set of 3D rotations. This allows the data set to flip between different Euler angle combinations which correspond to a single 3D rotation, which, although remaining continuous in the space of rotation, are discontinuous in the Euler angle parameter space. The Euler filter chooses on a sample-by-sample basis between the possible Euler angle representations of each 3D rotation in the data set in such a way as to preserve the continuity of the Euler angle time series, without changing the actual 3D rotations. Euler filtering is available in a number of 3D animation packages. See also * Charts on SO(3) * Rotation formalisms in three dimensions In geometry, various formalism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by graphics hardware, computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as Computer-generated imagery, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, sprite (graphics), sprite graphics, Rendering (computer graphics), rendering, ray tracing (graphics) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filter (software)
A filter is a computer program or subroutine to process a stream, producing another stream. While a single filter can be used individually, they are frequently strung together to form a pipeline. Some operating systems such as Unix are rich with filter programs. Windows 7 and later are also rich with filters, as they include Windows PowerShell. In comparison, however, few filters are built into cmd.exe (the original command-line interface of Windows), most of which have significant enhancements relative to the similar filter commands that were available in MS-DOS. OS X includes filters from its underlying Unix base but also has Automator, which allows filters (known as "Actions") to be strung together to form a pipeline. Unix In Unix and Unix-like operating systems, a filter is a program that gets most of its data from its standard input (the main input stream) and writes its main results to its standard output (the main output stream). Auxiliary input may come from command lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gimbal Lock
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. The term gimbal-''lock'' can be misleading in the sense that none of the individual gimbals are actually restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbals' axes there is no gimbal available to accommodate rotation about one axis, leaving the suspended object effectively locked (i.e. unable to rotate) around that axis. Gimbals A gimbal is a ring that is suspended so it can rotate about an axis. Gimbals are typically nested one within another to accommodate rotation about multiple axes. They appear in gyroscopes and in inertial measurement units to allow the inner gimbal's orientation to remain fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Angle
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478PDF/ref> They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations. The geometrical definition demonstrates that three composed '' elemental rotations'' (rotations about the axes of a coordinate system) are always sufficient to reach any target frame. The three elemental rotations may be extrinsic (rotations about the axes ''xyz'' of the original coordinate system, which is assumed to remain motionless), or intrin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameterization
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. "To parameterize" by itself means "to express in terms of parameters". Parametrization is a mathematical process consisting of expressing the state of a system, process or model as a function of some independent quantities called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrization thus consists of one function of several real variables for each coordinate. The number of parameters is the number of degrees of freedom of the system. For example, the position of a point that moves on a curve in three-dimensional space is determined by the time needed to reach the point when starting from a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Of 3D Rotations
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space \R^3 under the operation of composition. By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry), and orientation (i.e., ''handedness'' of space). Composing two rotations results in another rotation, every rotation has a unique inverse rotation, and the identity map satisfies the definition of a rotation. Owing to the above properties (along composite rotations' associative property), the set of all rotations is a group under composition. Every non-trivial rotation is determined by its axis of rotation (a line through the origin) and its angle of rotation. Rotations are not commutative (for example, rotating ''R'' 90° in the x-y plane followed by ''S'' 90° in the y-z plane is not the same as ''S'' followed by ''R''), making the 3D rotation group a nona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charts On SO(3)
In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold. The various charts on SO(3) set up rival coordinate systems: in this case there cannot be said to be a preferred set of parameters describing a rotation. There are three degrees of freedom, so that the dimension of SO(3) is three. In numerous applications one or other coordinate system is used, and the question arises how to convert from a given system to another. The space of rotations In geometry the rotation group is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.Jacobson (2009), p. 34, Ex. 14. 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. A length-preserving transformation which reverses orientation is called an i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Formalisms In Three Dimensions
In 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. According to Euler's rotation theorem the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. However, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
