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In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...
English: A uniform cubic B-spline (yellow), a cubic Hermite spline (dashed), and a spline based on successive over-relaxation (orange). Plotted is the distribution of civil weddings in Tilburg (954 in total) over the year 1997. The data charted here was collected in the course of my doctoral research; (c) Tijs Michels, 2004.
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.
The method is termed active spline model. [5] The model is devised on the basis of active shape model, but uses centripetal Catmull-Rom spline to join two successive points (active shape model uses simple straight line), so that the total number of points necessary to depict a shape is less. The use of centripetal Catmull-Rom spline makes the ...
In the mathematical subfield of numerical analysis, an M-spline [1] [2] is a non-negative spline function. An M-spline family of order three with four interior knots. Definition
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 ...