In this paper we show that the best constrained degree reduction of a given Bézier curve f of degree from n to m with C α−1-continuity at the boundary in L 2-norm is equivalent to the best weighted Euclidean approximation of the vector of Bernstein–Bézier (BB) coefficients of f from the vector of degree raised BB coefficients of polynomials of degree m with… (More)
We give a recipe for deriving local spline approximation methods which reproduce the whole spline space. The methods are obtained by solving a series of local approximation problems. Examples of specific quadratic and cubic approximation methods are given. §1. Introduction Many applications of splines make use of some approximation method to produce a… (More)
In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and… (More)
In recent years high quality interaction devices have become very popular in our environment. The industries are also currently undergoing rapid change and various technologies have been explored to enable these capabilities. Projection systems using beam projectors and laser pointer became the ubiquitous infrastructure for command technology. Group… (More)
A new class of subdivision schemes is presented. Each scheme in this class is a quasi-interpolatory scheme with a tension parameter , which reproduces polynomials up to a certain degree. We find that these schemes extend and unify not only the well-known Deslauriers–Dubuc interpolatory schemes but the quadratic and cubic B-spline schemes. This paper… (More)
We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L 2-norm for the interval [0, 1], using the weight… (More)
In the work, we rebuild the masks of well-known interpolatory symmetric subdivision schemes-binary 2n-point inter-polatory schemes, the ternary 4-point interpolatory scheme using only the symmetry and the necessary condition for smoothness and the butterfly scheme, and the modified butterfly scheme using the factorization property.
Human-Computer Interaction (HCI) exists ubiquitously in our daily lives. It is usually achieved by using a physical controller such as a mouse, keyboard or touch screen. It hinders Natural User Interface (NUI) as there is a strong barrier between the user and computer. There are various hand tracking systems available on the market, but they are complex and… (More)