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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.
Quarterly of Applied Mathematics. 4 (2): 45– 99. doi: 10.1090/qam/15914. Schoenberg, Isaac J. (1946). "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions:Part B.—On the Problem of Osculatory Interpolation. A Second Class of Analytic Approximation Formulae". Quarterly of Applied Mathematics. 4 (2): 112 ...
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Splines. B-spline; Nonuniform rational B-spline; Fractal curves
B-splines play the role of basis functions for the spline function space, hence the name. This property follows from the fact that all pieces have the same continuity properties, within their individual range of support, at the knots. [6] Expressions for the polynomial pieces can be derived by means of the Cox–de Boor recursion formula [7]
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 ...
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
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.
In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. [1] The Akima spline was published by Hiroshi Akima in 1970 from Akima's pursuit of a cubic spline curve that would appear more natural and smooth, akin to an intuitively hand-drawn curve.