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Another type of spline that is much used in graphics, for example in drawing programs such as Adobe Illustrator from Adobe Systems, has pieces that are cubic but has continuity only at most [,]. This spline type is also used in PostScript as well as in the definition of some computer typographic fonts.
In this example, multiplicity four knots resided at either end of the curve and ensures that the curve is defined over the entire parametric range of u and that the curve interpolates its end points. This is not a general case; intervals can be partitioned by single multiplicity knots over the entire parametric range.
Hand-drawn technical drawings for shipbuilding are a historical example of spline interpolation; drawings were constructed using flexible rulers that were bent to follow pre-defined points. Originally, spline was a term for elastic rulers that were bent to pass through a number of predefined points, or knots.
IIllustration of spline interpolation of a data set. The same data set is used for other interpolation algorithms in the Interpolation. Date: 26 June 2007: Source: self-made in Gnuplot: Author: Berland
The interpolated surface (meaning the kernel shape, not the image) is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm.
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Splines. B-spline; Nonuniform rational B-spline; Fractal 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. For a typical example of 2-D interpolation through key points see cardinal spline. For examples which go near key points see nonuniform rational B-spline, or Bézier curve. This is extended to the forming of ...
See also Subdivision surfaces, which is an emerging alternative to spline-based surfaces. Pages in category "Splines (mathematics)" The following 30 pages are in this category, out of 30 total.