Interval Bezier curve are new representation forms of parametric curves. Using this new representation, the problem of lack of robustness in all state-of-the art CAD systems can be largely overcome. In this paper this concept has been discussed to form a new curve over rectangular domain such that its parameter varies in an arbitrary range , instead of standard parameter , -. Where and are real...

Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform r...

In this paper, it is shown how the Discrete Smooth Interpolation method (D.S.I.) may be used as a new framework for creating, fairing and editing triangulated surfaces. Given an arbitrary mesh with an arbitrary set of vertices fixed by the user, D.S.I. assigns coordinates to the other nodes of the mesh, enabling the fixed vertices to be interpolated smoothly. The squared discrete Laplacian crit...

A sufficient condition for C1-continuity of subdivision surfaces was proposed by Reif [Comput. Aided Geom. Design, 12 (1995), pp. 153–174.] and extended to a more general setting in [D. Zorin, Constr. Approx., accepted for publication]. In both cases, the analysis of C1-continuity is reduced to establishing injectivity and regularity of a characteristic map. In all known proofs of C1-continuity...

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...

Subdivision schemes are equipped with some rules that take a polygon as an input and produce smooth curves or surfaces output. This presents the issue of how accurately approximates limit curve surface. What number iterations/levels would be necessary to achieve required shape at user-specified error tolerance? In fact, several methods have been introduced in case stationary address terms bound...