Bezier curves
E155915
Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
All labels observed (8)
| Label | Occurrences |
|---|---|
| Bezier curves canonical | 5 |
| Bezier curve | 1 |
| Bezier paths | 1 |
| Bezier surfaces | 1 |
| Bézier curves and surfaces | 1 |
| Bézier spline | 1 |
| Bézier surface | 1 |
| De Casteljau algorithm | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1368156 — 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.
Target entity: Bezier curves Context triple: [PostScript, hasFeature, Bezier curves]
-
A.
Page curve
The Page curve is a theoretical prediction in black hole physics that describes how the entanglement entropy of Hawking radiation should rise and then fall over time if black hole evaporation is ultimately unitary.
-
B.
Fermat curve
A Fermat curve is an algebraic curve defined by an equation of the form \(x^n + y^n = 1\), studied in number theory and algebraic geometry for its rich arithmetic and geometric properties.
-
C.
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.
-
D.
Circle line
The Circle line is a central London Underground route forming a loop through key districts and interchanges in the city’s transport network.
-
E.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Bezier curves Target entity description: Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
-
A.
Page curve
The Page curve is a theoretical prediction in black hole physics that describes how the entanglement entropy of Hawking radiation should rise and then fall over time if black hole evaporation is ultimately unitary.
-
B.
Fermat curve
A Fermat curve is an algebraic curve defined by an equation of the form \(x^n + y^n = 1\), studied in number theory and algebraic geometry for its rich arithmetic and geometric properties.
-
C.
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.
-
D.
Circle line
The Circle line is a central London Underground route forming a loop through key districts and interchanges in the city’s transport network.
-
E.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
geometric primitive
ⓘ
mathematical curve ⓘ parametric curve ⓘ |
| componentOf |
Bezier curves
self-linksurface differs
ⓘ
surface form:
Bézier spline
Bezier curves self-linksurface differs ⓘ
surface form:
Bézier surface
|
| definedBy |
Bernstein polynomials
ⓘ
Bezier curves self-linksurface differs ⓘ
surface form:
De Casteljau algorithm
|
| developedAt | Renault ⓘ |
| developedBy | Pierre Bézier ⓘ |
| field |
computer graphics
ⓘ
computer-aided design ⓘ computer-aided geometric design ⓘ vector graphics ⓘ |
| hasAdvantage |
compact representation of complex shapes
ⓘ
scale invariance ⓘ smooth interpolation between points ⓘ |
| hasProperty |
C0 continuity at endpoints
ⓘ
affine invariance ⓘ defined by control points ⓘ lies within convex hull of control points ⓘ polynomial representation ⓘ variation diminishing property ⓘ |
| mathematicalDomain |
approximation theory
ⓘ
computational geometry ⓘ numerical analysis ⓘ |
| namedAfter | Pierre Bézier ⓘ |
| parameter | t in [0,1] ⓘ |
| relatedTo |
B-splines
ⓘ
surface form:
B-spline
B-splines ⓘ
surface form:
NURBS
|
| subtype |
cubic Bézier curve
ⓘ
higher-order Bézier curve ⓘ linear Bézier curve ⓘ quadratic Bézier curve ⓘ |
| timePeriod | 1960s ⓘ |
| usedFor |
curve fitting
ⓘ
digital typography ⓘ font outlines ⓘ modeling smooth curves ⓘ motion paths ⓘ path animation ⓘ scalable icons ⓘ shape design ⓘ |
| usedIn |
CAD systems
ⓘ
OpenType font technology ⓘ
surface form:
OpenType fonts
Portable Document Format ⓘ
surface form:
PDF
PostScript ⓘ SVG ⓘ TrueType ⓘ
surface form:
TrueType fonts
vector drawing software ⓘ |
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.
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.
Subject: Bezier curves Description of subject: Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
Referenced by (12)
Full triples — surface form annotated when it differs from this entity's canonical label.