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Properties. 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 ...
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.
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 ...
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.
Spline (mathematics) For the drafting tool, see Flat spline. Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with C2 parametric continuity. Triple knots at both ends of the interval ensure that the curve interpolates the end points. In mathematics, a spline is a function defined piecewise by polynomials.
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 ...
In metaphysics, the A series and the B series are two different descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between events and the resulting ontological implications regarding time. John McTaggart introduced these terms in 1908, in an ...
Multivariate interpolation. In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of ...