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A NURBS curve is defined by its order, a set of weighted control points, and a knot vector. [6] NURBS curves and surfaces are generalizations of both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points, which makes NURBS curves rational.
Leading-order terms; NURBS order, a number one greater than the degree of the polynomial representation of a non-uniform rational B-spline; Order of convergence, a measurement of convergence; Order of derivation; Order of an entire function; Order of a power series, the lowest degree of its terms; Ordered list, a sequence or tuple
Spline curve drawn as a weighted sum of B-splines with control points/control polygon, and marked component curves. In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.
In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
The following is a useful property to calculate low-integer-order polylogarithms recursively in closed form: ... (mathematics) List of integrals; Summation § Identities;
They had a limited understanding of mathematics, but they were very aware of the need to communicate geometric data between systems. Hence, Boeing very quickly prepared to propose NURBS to the August '81 IGES meetings. There are two reasons why IGES so quickly accepted NURBS. The first was that IGES was in great need of a way to represent ...
In mathematics, and more specifically in order theory, several different types of ordered set have been studied. They include: Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise; Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound.
The set of integers and the set of even integers have the same order type, because the mapping is a bijection that preserves the order. But the set of integers and the set of rational numbers (with the standard ordering) do not have the same order type, because even though the sets are of the same size (they are both countably infinite ), there ...