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# 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 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)

Tagged:

• Beziers

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 […]

• Bewept

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 […]

• Bezoar

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 […]

• Bezonian

an indigent rascal; scoundrel. Historical Examples ‘That Very Mab’ May Kendall and Andrew Lang noun (archaic) a knave or rascal

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