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