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Bezier surface
A surfacE dEfinEd by mathEmatical formulaE, usEd in Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=computEr graphics">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) E="bordEr-width:thin; bordEr-color:#333333; bordEr-stylE:dashEd; padding:5px;" align="lEft">In addition suitablE contEnts:
[ Ef="modulE.php?namE=LExikon&op=contEnt&tid=31">2 ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=134">= ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=374">aE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=433">al ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=544">am ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=592">an ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=740">ar ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=743">arc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=894">at ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1025">B ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1026">b ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1258">BEziEr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1259">BEziEr curvE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1695">by ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1708">C ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1724">ca ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2001">ch ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2247">co ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2330">com ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2491">computEr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2545">con ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2656">control ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2900">cu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3151">dE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3752">du ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3896">Ed ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4148">Er ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4171">Es ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4199">Et ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4354">ExtEnsion ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4497">fi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4520">filE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4700">fo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4727">for ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4757">formula ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4828">fr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5057">gE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5291">gr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5307">graph ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5434">h ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5686">hog ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5768">hr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5931">id ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5956">iE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6013">il ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6064">in ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6194">int ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6413">io ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6449">ir ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6482">is ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6918">la ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7091">LEx ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7441">ly ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7463">ma ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7582">man ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8032">mo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8040">mod ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8079">modulE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8167">mp ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8258">mu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8386">na ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8472">nE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8760">ns ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8964">om ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9014">op ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9129">orthogonal ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9457">pE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9550">ph ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9762">point ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9908">pr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10253">quEry ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10364">rc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10385">rE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10767">ro ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10918">S ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11150">sE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11281">sEt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11314">sh ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11324">shar ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11376">si ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12133">su ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12588">th ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12721">to ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12787">tr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13030">um ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13175">us ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13252">va ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13274">var ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13310">vE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13891">X ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=14024">Y ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=14079">Z ]
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