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Two classical techniques for series acceleration are Euler's transformation of series [1] and Kummer's transformation of series. [2] A variety of much more rapidly convergent and special-case tools have been developed in the 20th century, including Richardson extrapolation, introduced by Lewis Fry Richardson in the early 20th century but also known and used by Katahiro Takebe in 1722; the ...
Clipping, in the context of computer graphics, is a method to selectively enable or disable rendering operations within a defined region of interest.Mathematically, clipping can be described using the terminology of constructive geometry.
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
Comparison of a slow down video without interframe interpolation (left) and with motion interpolation (right) Motion interpolation or motion-compensated frame interpolation (MCFI) is a form of video processing in which intermediate film, video or animation frames are generated between existing ones by means of interpolation, in an attempt to make animation more fluid, to compensate for display ...
The computed interpolation process is then used to insert many new values in between these key points to give a "smoother" result. In its simplest form, this is the drawing of two-dimensional curves. The key points, placed by the artist, are used by the computer algorithm to form a smooth curve either through, or near these points.
In 3D computer graphics, a wire-frame model (also spelled wireframe model) is a visual representation of a three-dimensional (3D) physical object. It is based on a polygon mesh or a volumetric mesh, created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using (straight) lines or curves.
Now we do interpolation between and to find , and to find . Finally, we calculate the value c {\displaystyle c} via linear interpolation of c 0 {\displaystyle c_{0}} and c 1 {\displaystyle c_{1}} In practice, a trilinear interpolation is identical to two bilinear interpolation combined with a linear interpolation:
Slerp gives a straightest and shortest path between its quaternion end points, and maps to a rotation through an angle of 2Ω. However, because the covering is double ( q and − q map to the same rotation), the rotation path may turn either the "short way" (less than 180°) or the "long way" (more than 180°).