B-splines

E171244

B-splines are piecewise polynomial functions widely used in computer graphics and numerical analysis to create smooth, flexible curves and surfaces controlled by a set of control points.

All labels observed (7)

How this entity was disambiguated

Statements (51)

Predicate Object
instanceOf mathematical concept
piecewise polynomial function
spline
advantageOver Bezier curves for high degree
global polynomial interpolation
component B-spline basis functions
control polygon
curveType parametric curve
definedBy control points
degree
knot vector
field approximation theory
computer graphics
computer-aided geometric design
finite element analysis
numerical analysis
generalizationOf Bezier curves
Bezier surfaces
linked to: Bezier curves
hasProperty affine invariance
continuity up to degree minus one
local control
non-negativity
partition of unity
piecewise-defined
polynomial segments
smoothness
hasSubtype NURBS
linked to: B-splines

non-uniform B-splines
rational B-splines
uniform B-splines
introducedBy Isaac Jacob Schoenberg
introducedIn 1940s
mathematicallyDefinedBy Cox–de Boor recursion formula
linked to: B-splines
nameMeaning basis splines
supportsOperation degree elevation
knot insertion
knot refinement
local shape editing
surfaceType tensor-product surface
usedFor curve modeling
data approximation
data interpolation
geometric design
image processing
isogeometric analysis
signal processing
surface modeling
usesParameter knot multiplicity
non-uniform knot vector
open knot vector
uniform knot vector

How these facts were elicited

Referenced by (13)

Full triples — surface form annotated when it differs from this entity's canonical label.

Bézier curve relatedTo B-spline
subject linked to: Bezier curves
linked to: B-splines
Bézier curve relatedTo NURBS
subject linked to: Bezier curves
linked to: B-splines
B-splines hasSubtype NURBS
linked to: B-splines
B-splines mathematicallyDefinedBy Cox–de Boor recursion formula
linked to: B-splines
Catmull–Rom spline relatedTo B-spline
linked to: B-splines
Isaac Jacob Schoenberg notableConcept B-spline
linked to: B-splines
Coons patch relatedTo B-spline surface
linked to: B-splines
David F. Rogers wroteAbout NURBS (Non-Uniform Rational B-Splines)
linked to: B-splines
I. J. Schoenberg hasConceptNamedAfter Schoenberg spline
linked to: B-splines