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FCurve
An FCurve (also written f-curve) is a function curve or the graph of a function. An example of a FCurve is a spline. In the field of computer animation and especially in animation editors, e.g. Maya, an FCurve is an animation curve with a set of keyframes, which are represented as points, curve segments between keys, and tangents that control how curve segments enter and exit a key. These keys are laid out on a graph that displays their position relative to zero. One can have keys that are either positive or negative values. This visual graph of keyframes allows one to see the value of the key and its interpolation In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ... to the next key, which shows the animation "ease ins" and "ease outs". Computer animation {{animation-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Of A Function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x) = y. In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane. In the case of functions of two variables, that is functions whose domain consists of pairs (x, y), the graph usually refers to the set of ordered triples (x, y, z) where f(x,y) = z, instead of the pairs ((x, y), z) as in the definition above. This set is a subset of three-dimensional space; for a continuous real-valued function of two real variables, it is a surface. In science, engineering, technology, finance, and other areas, graphs are tools used for many purposes. In the simplest case one variable is plotted as a function of another, typically using rectangular axes; see '' Plot (graphics)'' for details. A graph of a function is a special case of a relation. In the modern foundations of mathematics, and, typicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline Curve
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term ''spline'' more frequently refers to a piecewise polynomial ( parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. Introduction The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Animation
Computer animation is the process used for digitally generating animations. The more general term computer-generated imagery (CGI) encompasses both static scenes (still images) and dynamic images (moving images), 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. Computer-generated animations can also allow a single graphic artist to produce such content without the use of actors, expensive set pieces, or props. To create the illusion of movement, an image is displayed on the computer monitor and repeatedly replaced by a new image that is similar to it but advanced slightly in time (usually at a ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maya (software)
Autodesk Maya, commonly shortened to just Maya ( ), is a 3D computer graphics application that runs on Windows, macOS and Linux, originally developed by Alias and currently owned and developed by Autodesk. It is used to create assets for interactive 3D applications (including video games), animated films, TV series, and visual effects. History Maya was originally an animation product based on code from The Advanced Visualizer by Wavefront Technologies, Thomson Digital Image (TDI) Explore, PowerAnimator by Alias, and ''Alias Sketch!''. The IRIX-based projects were combined and animation features were added; the project codename was Maya. Walt Disney Feature Animation collaborated closely with Maya's development during its production of ''Dinosaur''. Disney requested that the user interface of the application be customizable so that a personalized workflow could be created. This was a particular influence in the open architecture of Maya, and partly responsible for it becoming popul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keyframe
In animation and filmmaking, a key frame (or keyframe) is a drawing or shot that defines the starting and ending points of a smooth transition. These are called ''frames'' because their position in time is measured in frames on a strip of film or on a digital video editing timeline. A sequence of key frames defines which movement the viewer will see, whereas the position of the key frames on the film, video, or animation defines the timing of the movement. Because only two or three key frames over the span of a second do not create the illusion of movement, the remaining frames are filled with " inbetweens". Use of key frames as a means to change parameters In software packages that support animation, especially 3D graphics, there are many parameters that can be changed for any one object. One example of such an object is a light (In 3D graphics, lights function similarly to real-world lights. They cause illumination, cast shadows, and create specular highlights). Lights have m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve at a point if the line passes through the point on the curve and has slope , where ''f'' is the derivative of ''f''. A similar definition applies to space curves and curves in ''n''-dimensional Euclidean space. As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a '' tangent line approximation'', the graph of the affine function that best approximates the original function at the given point. Similarly, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Of A Function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x) = y. In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane. In the case of functions of two variables, that is functions whose domain consists of pairs (x, y), the graph usually refers to the set of ordered triples (x, y, z) where f(x,y) = z, instead of the pairs ((x, y), z) as in the definition above. This set is a subset of three-dimensional space; for a continuous real-valued function of two real variables, it is a surface. In science, engineering, technology, finance, and other areas, graphs are tools used for many purposes. In the simplest case one variable is plotted as a function of another, typically using rectangular axes; see '' Plot (graphics)'' for details. A graph of a function is a special case of a relation. In the modern foundations of mathematics, and, typicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolation
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
