Search results
Results from the WOW.Com Content Network
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:
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.
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]
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.
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.
Smoothing splines are function estimates, ^ () ... The most familiar example is the cubic smoothing spline, but there are many other possibilities, ...
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 ...
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.