This paper describes a simple and efficient non-stationary subdivision scheme of order 4. This curve scheme unifies known subdivision rules for cubic B-splines, splines-in-tension and a certain class of trigonometric splines capable of reproducing circles. The curves generated by this unified subdivision scheme are C2 splines whose segments are either polynomial, hyperbolic or trigonometric fun...

A progressive curve representation based on reverse subdivision is introduced. Multiresolution structures for common subdivision rules that have both banded reconstruction and decomposition filters are produced. Multiresolution filters are usually applied to the whole curve uniformly, while progressive curves are based on collapse and split operations that can be applied locally on any portion ...

Subdivision started as a tool for eecient computation of spline functions, and is now an independent subject with many applications. It is used for developing new methods for curve and surface design, for approximation, for generating wavelets and mul-tiresolution analysis and also for solving some classes of functional equations. This paper reviews recent new directions and new developments in...

A new method is presented for computing the minimum distance between a point and a NURBS curve. It utilizes a circular clipping technique to eliminate the curve parts outside a circle with the test point as its center point. The radius of the elimination circle becomes smaller and smaller during the subdivision process. A simple condition for terminating the subdivision process is provided, whi...

A ternary 4-point interpolating subdivision scheme is proposed that generates the limiting curve of C1 continuity. Performance of the proposed subdivision scheme is improved using a tension parameter. The improved subdivision scheme generates a family of C1 limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the derivative continuity of the s...

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing ...