The distance between two objects is an important problem in CAGD, CAD and CG etc. It will be presented in this paper that a simple and quick method to estimate the distance between a point and a Bezier curve on a Bezier surface. Keywords—Geodesic-like curve, distance, projection, Bezier.

We present an approach for representing digital image by using B-spline curve fittings to the segmented digital image. The image is first segmented to form isolated contours and regions. Each region’s boundary (contour) is thereafter approximated by a B-spline curve. A cubic B-spline curve is used instead of a far higher degree Bezier curve to approximate the boundary because it has a local con...

This paper presents a simple matrix form for degree elevation of interval Bezier curve using LegendreBernstein basis transformations. The four fixed Kharitonov's polynomials (four fixed Bezier curves) associated with the original interval Bezier curve are obtained. These four fixed Bezier curves are expressed in terms of the Legendre polynomials. The process of degree elevations r times are app...

Displaying objects with high accuracy is important in CAGD and for the synthesis of photo-realistic images. The representation of free-form surfaces can be classified into two: parametric surfaces such as Bezier patches, and implicit surfaces like metaballs. We discuss display methods for both Bezier patches and metaballs by using Bezier Clipping. Traditionally, polygonal approximation methods ...

In this paper, we develop a new hybrid curve fitting model using fuzzy set and rough set theory. The developed method differs from classical curve fitting techniques and algorithms. For produced rule sets of model to create by using fuzzy logic technique and the membership functions of input and output functions, the range of membership functions and the relations between membership functions i...

We develop an efficient algorithm for the construction of common tangents between a set of Bezier curves. Common tangents are important in visibility, lighting, robot motion, and convex hulls. Common tangency is reduced to the intersection of parametric curves in a dual space, rather than the traditional intersection of implicit curves. We show how to represent the tangent space of a plane Bezi...

Approximation of helices has been studied by using in many ways. In this study, it examined how a circular helix can be written as Bezier curve and the 3th degree, 5th 7th degree Maclaurin series expansions for polynomial forms. Hence, they cubic, order, order curves, based on control points with matrix form we have already given E3. Further coefficients expansion helix.