The goal of this paper is to characterize the evolute, involute and parallel curves a Bezier curve which applicable computer graphics related subjects. Especially, these couples are investigated at endpoints. Moreover, curvatures given.

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...

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...

This paper presents a new method to generate curves, which allows the designer to produce a curve in combinational way allowing him to get the shape that he had in his imagination with keeping the four control point for the curve design. Basing on the modified BEZIER curve, the upgraded algorithm used de Casteljau algorithm on interval [r, s] as a mathematical base to upgrade the suggested meth...

This paper presents a technique to convert surfaces, obtained through a Data Dependent Triangulation, in Bezier Curves by using a Scalable Vector Graphics File format. The method starts from a Data Dependent Triangulation, traces a map of the boundaries present into the triangulation, using the characteristics of the triangles, then the estimated barycenters are connected, and a final conversio...

This paper presents a scale method for developing high dimensional scale functions to blend implicitly defined objects. Scale functions are differentiable on the entire domain except the origin, provide blending range control, and behave like Min/Max operators everywhere, so even a successive composition of blending operations containing overlapped blending regions can be generated smoothly. Be...

A near-optimal midcourse trajectory shaping guidance algorithm is proposed for both air and ballistic target engagement mission attributes for generic long range interceptor missile. This guidance methodology is based on the maximum final velocity as the objective function and maximum permissible flight altitude as the in-flight state constraint as well as the head-on orientation as the termina...