We present a method for constructing tensor product Bezier surfaces from contour (cross-section) data. Minimal area triangulations are used to guide the surface construction, and the final surface reflects the optimality of the triangulation. The resulting surface differs from the initial triangulation in two important ways: it is smooth (as opposed to the piecewise planar triangulation), and i...

In this paper we approximate a cylindrical helix by biconic and bi-quadratic Bezier curves. Each approximation method is G end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. A...

The description of the steganographic method for embedding digital watermark into image vector files SVG format is given. Vector images in can include elements based on Bezier curves. proposed splitting cubic Embedding hidden information involves curves according to given as numerical sequence. Algorithms direct and reverse transformation are considered proving authenticity integrity a image. S...

Ghandmjit L. Bajaj t Department of Computer Science, Purdue University, West Lafayette, IN 47907 In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained by different characterizations of the zero contours of the Bernstein-Bezier (BB) form of bivariate po...

. Parametric curves are represented using these modified Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We get Bézier curve defined on [0, 1] when we set the parameter α, β to the value 0. We also present a de Casteljau algorithm to compute Bernstein Bézier curves and surfaces with shifted knots. The new curves have some properti...

Using the matrix representation form, first, second, third, fourth, and fifth derivatives of 5th order Bezier curves are examined based on control points in E 3 E3 . In addition to this, each derivative is given by their points. Further, a simple way has been find its using notations. An example also provided corresponding figures which drawn Geogebra v5 have presented end.