Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
gptkb:mathematical_concept |
| gptkbp:application |
gptkb:probability_theory
numerical analysis curve modeling surface modeling |
| gptkbp:author |
gptkb:Sergei_Natanovich_Bernstein
|
| gptkbp:definedIn |
non-negative integers n and k
|
| gptkbp:defines |
B_{k,n}(x) = C(n,k) x^k (1-x)^{n-k}
|
| gptkbp:field |
gptkb:mathematics
computer graphics approximation theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Bernstein basis polynomials
|
| gptkbp:introducedIn |
1912
|
| gptkbp:namedAfter |
gptkb:Sergei_Natanovich_Bernstein
|
| gptkbp:property |
non-negative on [0,1]
partition of unity form a basis for the vector space of polynomials of degree at most n sum to 1 for all x in [0,1] |
| gptkbp:relatedTo |
gptkb:Bezier_curve
gptkb:Bernstein's_theorem gptkb:Bernstein_polynomial |
| gptkbp:usedIn |
gptkb:Bezier_surfaces
gptkb:Bezier_curves polynomial approximation |
| gptkbp:bfsParent |
gptkb:Bernstein_polynomials
|
| gptkbp:bfsLayer |
7
|