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.
[What do these properties mean?]
- Bezier surface
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 […]
a city in S France, SW of Montpellier. Historical Examples Travels in France during the years 1814-1815 Archibald Alison The Itinerary of Benjamin of Tudela Benjamin of Tudela The Itinerary of Benjamin of Tudela Benjamin of Tudela A Popular History of France From The Earliest Times Francois Pierre Guillaume Guizot Memoir, Correspondence, And Miscellanies, From […]
to weep over (something): to beweep one’s foolish mistakes. Historical Examples The Classic Myths in English Literature and in Art (2nd ed.) (1911) Charles Mills Gayley Sketches New and Old, Complete Mark Twain (Samuel Clemens) Wolf’s Head Charles Egbert Craddock (AKA Mary Noailles Murfree) The Nibelungenlied Unknown Ulysses James Joyce Les Misrables Victor Hugo The […]
a calculus or concretion found in the stomach or intestines of certain animals, especially ruminants, formerly reputed to be an effective remedy for poison. Obsolete. a counterpoison or antidote. Historical Examples A Decade of Italian Women, v. II (of 2) T. Adolphus Trollope A Journal of the First Voyage of Vasco da Gama 1497-1499 Unknown […]