Added to Favorites

Computing Dictionary

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?]

(1996-06-12)

Explore Dictionary.com

More from Thesaurus.com

Synonyms and Antonyms for Bezier curve

More from Reference.com

Search for articles containing Bezier curve

More from Dictionary.com Translator

Translate Bezier curve into French

Translate Bezier curve into German

Translate Bezier curve into Italian

Translate Bezier curve into another language

Dictionary.com Word FAQs

Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.

Nearby Words

Copyright © 2014 Dictionary.com, LLC. All rights reserved.