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Give the Bernstein polynomials! What are their properties?
Partition of unity:
Define the Bernstein polynomial
Bezier curve
Properties
Define the Bernstein polynomial
Bezier curve
Properties
- Partition of unity
- Non-negativity
- Maximum
- Endpoint interpolation
- Symmetry
- Recursion
(by definition)Because of this, the affine combination of coefficients is geometrically meaningful.
for 
Points of the curve are actually convex combinations of the coefficients. Thus, the curve will lie inside the convex hull of the control points.
has its maximum at 
This ensures local influence of the control points.
, thus 
, thus 
where 
and 
Karteninfo:
Autor: janisborn
Oberthema: Informatik
Thema: Computergrafik
Schule / Uni: RWTH Aachen
Ort: Aachen
Veröffentlicht: 18.05.2022