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Was (wer) ist Bezier surface - definition
SPECIES OF MATHEMATICAL SPLINE USED IN COMPUTER GRAPHICS, COMPUTER-AIDED DESIGN, AND FINITE ELEMENT MODELING, IS DEFINED BY A SET OF CONTROL POINTS
Bicubic patch; Bezier surface; Bezier surfaces; Bezier patch; Bézier patch
Bézier surface
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling.
Bezier surface
<graphics> A surface defined by mathematical formulae, used in
computer graphics. A surface P(u, v), where u and v vary
orthogonally from 0 to 1 from one edge of the surface to the
other, is defined by a set of (n+1)*(m+1) "control points"
(X(i, j), Y(i, j), Z(i, j)) for i = 0 to n, j = 0 to m.
P(u, v) = Sum i=0..n {Sum j=0..m [
(X(i, j), Y(i, j), Z(i, j))
* B(i, n, u) * B(j, m, v) ]}
B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i)
C(n, i) = n!/i!/(n-i)!
Bezier surfaces are an extension of the idea of {Bezier
curves}, and share many of their properties.
(1996-06-12)
Biharmonic Bézier surface
Biharmonic Bezier surface
A biharmonic Bézier surface is a smooth polynomial surface which conforms to the biharmonic equation and has the same formulations as a Bézier surface. This formulation for Bézier surfaces was developed by Juan Monterde and Hassan Ugail.
Wikipedia
Bézier surface
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central control points; rather, it is "stretched" toward them as though each were an attractive force. They are visually intuitive, and for many applications, mathematically convenient.
