related topics
{math, number, function}
{@card@, make, design}

In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky from Kazan State University, Russia. A fundamental theorem states that every spline function of a given degree, smoothness, and domain partition, can be represented as a linear combination of B-splines of that same degree and smoothness, and over that same partition.[1] The term B-spline was coined by Isaac Jacob Schoenberg and is short for basis spline.[2] B-splines can be evaluated in a numerically stable way by the de Boor algorithm. Simplified, potentially faster variants of the de Boor algorithm have been created but they suffer from comparatively lower stability.[3][4]

In the computer science subfields of computer-aided design and computer graphics, the term B-spline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of B-splines (in the mathematical sense above). A B-spline is simply a generalisation of a Bézier curve, and it can avoid the Runge phenomenon without increasing the degree of the B-spline.


Full article ▸

related documents
Topological vector space
A* search algorithm
Banach space
Normal space
Partially ordered set
Universal quantification
Ordered pair
Optimization (mathematics)
Document Type Definition
Free group
Associative array
Graph theory
Stokes' theorem
Algebraically closed field
Direct product
NP (complexity)
Henri Lebesgue
Sheffer stroke
LL parser
Expander graph
Empty set
Net (mathematics)
Greatest common divisor
Polish notation
Minimum spanning tree
Integer factorization
Grover's algorithm
Affine transformation