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In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, ... The choices made for representing the spline, 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]
The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Splines. B-spline; Nonuniform rational B-spline; Fractal curves
In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid.
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 ...
The most familiar example is the cubic smoothing spline, but there are many other possibilities, including for the case where is a vector quantity. Cubic spline definition [ edit ]