Bezier surface

Bezier surface

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 [

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.
Mentioned in ?
References in periodicals archive ?
An example of the Bezier surface, which is calculated based on the measured data in the SCA research [5], for successful attacks is presented in Figure 5.
Bezier surface presentations are utilized to support both decision-making and to integrate the results of several design or reasoning stages, e.
When evaluating the reliability aspects of the surface modeling, two main points were checked: How the selected Bezier surface calculation differed from other possible modeling techniques in relation to pattern recognition and what the difference is in grading.
A Bezier surface, defined by several bulb geometrical parameters, has been used to model the forebody and to allow the modifications.
In order to allow the modifications of the bulbous bow defined by several parameters, the fore part has been modeled with a Bezier surface because of its possibility to create a grid of desired density from a relatively low number of points.
Guo, "Quartic generalized Bezier surfaces with multiple shape parameters and its continuity conditions," Transactions of the Chinese Society for Agricultural Machinery, vol.
FreeDimension is based on patented N-sided surfacing (NSS) technology, which frees users from quadrilateral surfacing technologies like NURBS and Bezier surfaces.
FreeDimension is based on the patent-pending N-Sided Surfacing (NSS) technology, which frees users from quadrilateral surfacing technologies like NURBS and Bezier surfaces.
Bernard said Dassault had held off on implementing NURBS in Catia because Bezier surfaces have better continuity for complex curves.
In this paper we introduce a class of surface patch representations, called S-patches, that unify and generalize triangular and tensor product Bezier surfaces by allowing patches to be defined over any convex polygonal domain; hence, S-patches may have any number of boundary curves.
The 3-D capability will allow the analysis to handle the contact of deformable bodies idealized as curved shells and brick elements, and of rigid bodies modeled as flat patches, ruled surfaces, surfaces of revolution, or Bezier surfaces.