BEZIER CURVE
\bˈɛzɪə kˈɜːv], \bˈɛzɪə kˈɜːv], \b_ˈɛ_z_ɪ__ə k_ˈɜː_v]\
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A type of curve defined by mathematical formulae,used in computer graphics. A curve with coordinates P(u),where u varies from 0 at one end of the curve to 1 at theother, is defined by a set of n+1 "control points" (X(i),Y(i), Z(i)) for i = 0 to n.P(u) = Sum i=0..n [ (X(i), Y(i), Z(i)) * B(i, n, u)]B(i, n, u) = C(n, i) * u^i * (1u)^ (ni)C(n, i) = n!/i!/ (ni)!A Bezier curve (or surface) is defined by its control points,which makes it invariant under any affine mapping(translation, rotation, parallel projection), and thus evenunder a change in the axis system. You need only to transformthe control points and then compute the new curve. Thecontrol polygon defined by the points is itself affineinvariant.Bezier curves also have the variationdiminishing property.This makes them easier to split compared to other types ofcurve such as Hermite or Bspline.Other important properties are multiple values, global andlocal control, versatility, and order of continuity.[What do these properties mean?]
By Denis Howe
Word of the day
Cynarrhodium
 fruit like that rose, consisting a cup formed of the calyx tube receptacle, and containing achenes. [Greek] An etaerio with achenes placed on concave thalamus.
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