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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.
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.
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Splines. B-spline; Nonuniform rational B-spline; Fractal curves
Black and red / yellow / green / blue dots correspond to the interpolated point and neighbouring samples, respectively. Their heights above the ground correspond to their values. In mathematics , bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating data ...
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 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.
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 ...
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." [1] [2] They were introduced to geometric design by Duchon. [3] They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and ...