This paper shows how to construct a rational Bezier model of a swept surface that interpolates N frames (i.e., N position/orientation pairs) of a fixed rational space curve c(s) and maintains the shape of the curve at all intermediate points of the sweep. Thus, the surface models an exact sweep of the curve, consistent with the given data. The primary novelty of the method is that this exact mo...

A strategy to obtain sets of initial configuration to design freeform reflector surfaces is presented. This strategy brings the initial configuration of the reflector surface using a collection of elemental facets defined by Bezier surfaces and able to face the optimization process of the illumination system. The purpose of this communication is to provide initial configurations to obtain a set...

The problem of styling surfaces modeling is tackled. An approach based on section curves fairing is chosen. The concept of template curves is developed for approximating profiles with a monotone curvature variation. Constrained Bezier curves called typical curves are used for that. A curve growing process based on a G typical curve fitting method, is investigated. It consists first in determini...

There are many studies to approximate sine curve or wave. In this study, it has been examined the way how wave can be written as any order Bezier curve. First, 5th and 7th degree Maclaurin series expansion of parametric form Also, they paths, based on control points with matrix in E2. Hence given coefficients curves three steps. Further too.

B-spline methods have several advantages over Bezier techniques. B-splines are piecewise polynomials that meet smoothly at their common boundaries independent of the location of the control points. This guaranteed smoothness allows designers to use low degree polynomial pieces to construct complicated freeform shapes. In addition, a control point of a B-spline curve or surface has no influence ...

Despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continue to be the standard motions of modern CNC machines. However, the increasing industrial demand for parts with intricate shapes cannot be satisfied with only these standard motions. The proportion of parts which are not covered by the standard CNC motions is certain...

The matrix forms for curves and surfaces were largely promoted in CAD. These formulations are very compact to write, simple to program, and clear to understand. They manifest the desired basis as a matrix transformation of the common power basis. Furthermore, this implementation can be made extremely fast if appropriate matrix facilities are available in either hardware or software. Derivatives...