Bezier curve
A type of curve defined by mathematical formulae, used in href="module.php?name=Lexikon&file=search&eid=1&query=computer graphics">computer graphics. A curve with coordinates P(u), where u varies from 0 at one end of the curve to 1 at the other, 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 * (1-u)^(n-i) C(n, i) = n!/i!/(n-i)! A Bezier curve (or surface) is defined by its control points, which makes it invariant under any href="module.php?name=Lexikon&file=search&eid=1&query=affine mapping">affine mapping (translation, rotation, parallel projection), and thus even under a change in the axis system. You need only to transform the control points and then compute the new curve. The control polygon defined by the points is itself affine invariant. Bezier curves also have the variation-diminishing property. This makes them easier to split compared to other types of curve such as href="module.php?name=Lexikon&file=search&eid=1&query=Hermite">Hermite or href="module.php?name=Lexikon&file=search&eid=1&query=B-spline">B-spline. Other important properties are multiple values, global and local control, versatility, and order of continuity. [What do these properties mean?] (1996-06-12) In addition suitable contents: [ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=374">ae ] [ href="module.php?name=Lexikon&op=content&tid=383">af ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=683">app ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=996">av ] [ href="module.php?name=Lexikon&op=content&tid=1025">B ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1034">ba ] [ href="module.php?name=Lexikon&op=content&tid=1258">Bezier ] [ href="module.php?name=Lexikon&op=content&tid=1695">by ] [ href="module.php?name=Lexikon&op=content&tid=1708">C ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2330">com ] [ href="module.php?name=Lexikon&op=content&tid=2491">computer ] [ href="module.php?name=Lexikon&op=content&tid=2545">con ] [ href="module.php?name=Lexikon&op=content&tid=2656">control ] [ href="module.php?name=Lexikon&op=content&tid=2702">coordinate ] [ href="module.php?name=Lexikon&op=content&tid=2900">cu ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3565">do ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=3929">ee ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4700">fo ] [ href="module.php?name=Lexikon&op=content&tid=4727">for ] [ href="module.php?name=Lexikon&op=content&tid=4757">formula ] [ href="module.php?name=Lexikon&op=content&tid=4828">fr ] [ href="module.php?name=Lexikon&op=content&tid=5057">ge ] [ href="module.php?name=Lexikon&op=content&tid=5171">gl ] [ href="module.php?name=Lexikon&op=content&tid=5185">glob ] [ href="module.php?name=Lexikon&op=content&tid=5291">gr ] [ href="module.php?name=Lexikon&op=content&tid=5307">graph ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5493">hang ] [ href="module.php?name=Lexikon&op=content&tid=5540">hat ] [ href="module.php?name=Lexikon&op=content&tid=5656">hing ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5791">hu ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=5956">ie ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6053">import ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6194">int ] [ href="module.php?name=Lexikon&op=content&tid=6406">invariant ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6789">ke ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7107">li ] [ href="module.php?name=Lexikon&op=content&tid=7151">line ] [ href="module.php?name=Lexikon&op=content&tid=7399">ls ] [ href="module.php?name=Lexikon&op=content&tid=7410">lt ] [ href="module.php?name=Lexikon&op=content&tid=7415">lu ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=7607">map ] [ href="module.php?name=Lexikon&op=content&tid=7610">mapping ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8167">mp ] [ href="module.php?name=Lexikon&op=content&tid=8258">mu ] [ href="module.php?name=Lexikon&op=content&tid=8303">multiple value ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8472">ne ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8630">ni ] [ href="module.php?name=Lexikon&op=content&tid=8660">nl ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=8787">nu ] [ href="module.php?name=Lexikon&op=content&tid=8820">O ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=9014">op ] [ href="module.php?name=Lexikon&op=content&tid=9117">ordinate ] [ href="module.php?name=Lexikon&op=content&tid=9204">pa ] [ href="module.php?name=Lexikon&op=content&tid=9457">pe ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9616">ping ] [ href="module.php?name=Lexikon&op=content&tid=9651">pl ] [ href="module.php?name=Lexikon&op=content&tid=9762">point ] [ href="module.php?name=Lexikon&op=content&tid=9821">port ] [ href="module.php?name=Lexikon&op=content&tid=9908">pr ] [ href="module.php?name=Lexikon&op=content&tid=10058">projection ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10767">ro ] [ href="module.php?name=Lexikon&op=content&tid=10918">S ] [ href="module.php?name=Lexikon&op=content&tid=10922">sa ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11281">set ] [ href="module.php?name=Lexikon&op=content&tid=11314">sh ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11525">sl ] [ href="module.php?name=Lexikon&op=content&tid=11651">so ] [ href="module.php?name=Lexikon&op=content&tid=11851">split ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12246">sy ] [ href="module.php?name=Lexikon&op=content&tid=12312">system ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12787">tr ] [ href="module.php?name=Lexikon&op=content&tid=12970">type ] [ href="module.php?name=Lexikon&op=content&tid=13030">um ] [ href="module.php?name=Lexikon&op=content&tid=13175">us ] [ href="module.php?name=Lexikon&op=content&tid=13252">va ] [ href="module.php?name=Lexikon&op=content&tid=13260">value ] [ href="module.php?name=Lexikon&op=content&tid=13274">var ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ] [ href="module.php?name=Lexikon&op=content&tid=13891">X ] [ href="module.php?name=Lexikon&op=content&tid=14024">Y ] [ href="module.php?name=Lexikon&op=content&tid=14079">Z ]
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