Words starting with beziersurf
Maybe these words will be useful:
- beziers — a city in S France: scene of a massacre (1209) during the Albigensian Crusade. It is a centre of the wine trade. Pop: 71 672 (2008)
- bezier — (graphics) (After Frenchman Pierre Bézier from Regie Renault) A collection of formulae for describing curved lines (Bezier curve) and surfaces (Bezier surface), first used in 1972 to model automobile surfaces. Curves and surfaces are defined by a set of "control points" which can be moved interactively making Bezier curves and surfaces convenient for interactive graphic design.
- bezier curve — (graphics) 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 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 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 Hermite or B-spline. Other important properties are multiple values, global and local control, versatility, and order of continuity.
- 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.