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  2. B-spline - Wikipedia

    en.wikipedia.org/wiki/B-spline

    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]

  3. Spline interpolation - Wikipedia

    en.wikipedia.org/wiki/Spline_interpolation

    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 ...

  4. De Boor's algorithm - Wikipedia

    en.wikipedia.org/wiki/De_Boor's_algorithm

    In the mathematical subfield of numerical analysis, de Boor's algorithm [1] is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves. The algorithm was devised by German-American mathematician Carl R. de Boor. Simplified ...

  5. Spline (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Spline_(mathematics)

    The choices made for representing the spline, for example: using basis functions for the entire spline (giving us the name B-splines) using Bernstein polynomials as employed by Pierre Bézier to represent each polynomial piece (giving us the name Bézier splines) The choices made in forming the extended knot vector, for example:

  6. Spline wavelet - Wikipedia

    en.wikipedia.org/wiki/Spline_wavelet

    The cardinal B-splines are defined recursively starting from the B-spline of order 1, namely (), which takes the value 1 in the interval [0, 1) and 0 elsewhere. Computer algebra systems may have to be employed to obtain concrete expressions for higher order cardinal B-splines.

  7. Category:Interpolation - Wikipedia

    en.wikipedia.org/wiki/Category:Interpolation

    Discrete spline interpolation; G. Gal's accurate tables; H. Hermite interpolation; ... Non-uniform rational B-spline; Numerical smoothing and differentiation; P ...

  8. Interpolation (computer graphics) - Wikipedia

    en.wikipedia.org/wiki/Interpolation_(computer...

    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 ...

  9. Polyharmonic spline - Wikipedia

    en.wikipedia.org/wiki/Polyharmonic_spline

    Interpolation with different polyharmonic splines that shall pass the 4 predefined points marked by a circle (the interpolation with phi = r 2 is not useful, since the linear equation system of the interpolation problem has no solution; it is solved in a least squares sense, but then does not pass the centers)