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  2. 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:

  3. Spline interpolation - Wikipedia

    en.wikipedia.org/wiki/Spline_interpolation

    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.

  4. 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]

  5. Non-uniform rational B-spline - Wikipedia

    en.wikipedia.org/wiki/Non-uniform_rational_B-spline

    Within those intervals, the weight changes according to a polynomial function (basis functions) of degree d. At the boundaries of the intervals, the basis functions go smoothly to zero, the smoothness being determined by the degree of the polynomial. As an example, the basis function of degree one is a triangle function.

  6. Cubic Hermite spline - Wikipedia

    en.wikipedia.org/wiki/Cubic_Hermite_spline

    Cubic polynomial splines are extensively used in computer graphics and geometric modeling to obtain curves or motion trajectories that pass through specified points of the plane or three-dimensional space. In these applications, each coordinate of the plane or space is separately interpolated by a cubic spline function of a separate parameter t.

  7. Smoothing spline - Wikipedia

    en.wikipedia.org/wiki/Smoothing_spline

    Smoothing splines are function estimates, ^ () ... The most familiar example is the cubic smoothing spline, but there are many other possibilities, ...

  8. Thin plate spline - Wikipedia

    en.wikipedia.org/wiki/Thin_plate_spline

    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 ...

  9. Polyharmonic spline - Wikipedia

    en.wikipedia.org/wiki/Polyharmonic_spline

    Evaluating the computed polyharmonic spline function at data points requires () operations. In many applications (image processing is an example), M {\displaystyle M} is much larger than N , {\displaystyle N,} and if both numbers are large, this is not practical.