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 (4)
| Label | Occurrences |
|---|---|
| B-spline | 2 |
| NURBS | 2 |
| B-splines canonical | 1 |
| Cox–de Boor recursion formula | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1490708 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: B-splines Context triple: [Computer Graphics: Principles and Practice, covers, B-splines]
-
A.
Bezier curves
Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
-
B.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
C.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
D.
Lagrange interpolation polynomial
The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
-
E.
BSP
BSP is the Bangko Sentral ng Pilipinas, the central bank of the Philippines responsible for monetary policy, financial stability, and currency issuance.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: B-splines Target entity description: 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.
-
A.
Bezier curves
Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
-
B.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
C.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
D.
Lagrange interpolation polynomial
The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
-
E.
BSP
BSP is the Bangko Sentral ng Pilipinas, the central bank of the Philippines responsible for monetary policy, financial stability, and currency issuance.
- F. None of above. chosen
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 curves ⓘ
surface form:
Bezier surfaces
|
| hasProperty |
affine invariance
ⓘ
continuity up to degree minus one ⓘ local control ⓘ non-negativity ⓘ partition of unity ⓘ piecewise-defined ⓘ polynomial segments ⓘ smoothness ⓘ |
| hasSubtype |
B-splines
self-linksurface differs
ⓘ
surface form:
NURBS
non-uniform B-splines ⓘ rational B-splines ⓘ uniform B-splines ⓘ |
| introducedBy | Isaac Jacob Schoenberg ⓘ |
| introducedIn | 1940s ⓘ |
| mathematicallyDefinedBy |
B-splines
self-linksurface differs
ⓘ
surface form:
Cox–de Boor recursion formula
|
| 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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: B-splines Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Bézier curve
this entity surface form:
B-spline
subject surface form:
Bézier curve
this entity surface form:
NURBS
this entity surface form:
NURBS
this entity surface form:
Cox–de Boor recursion formula
this entity surface form:
B-spline