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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]
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.
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae) and modeled shapes. It is a type of curve modeling, as ...
Visual difference between sphere (green) and Catmull-Clark subdivision surface (magenta) from a cube. The Catmull–Clark algorithm is a technique used in 3D computer graphics to create curved surfaces by using subdivision surface modeling. It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline ...
In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function. [1] There are different types of spline wavelets. The interpolatory spline wavelets introduced by C.K. Chui and J.Z. Wang are based on a certain spline interpolation formula. [2] Though these wavelets are orthogonal, they do not have ...
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A Bézier curve is defined by a set of control points P0 through Pn, where n is called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the curve; however, the intermediate control points generally do not lie on the curve.
B-spline From the plural form : This is a redirect from a plural noun to its singular form. This redirect link is used for convenience; it is often preferable to add the plural directly after the link (for example, [[link]]s ).