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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.
Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with C 2 parametric continuity. Triple knots at both ends of the interval ensure that the curve interpolates the end points. In mathematics, a spline is a function defined piecewise by polynomials.
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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 ...
Download QR code; Print/export ... This is a list of Wikipedia articles about curves used in different fields: mathematics (including ... Splines. B-spline;
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.
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.
Smoothing splines are related to, but distinct from: Regression splines. In this method, the data is fitted to a set of spline basis functions with a reduced set of knots, typically by least squares. No roughness penalty is used. (See also multivariate adaptive regression splines.) Penalized splines. This combines the reduced knots of ...