For a wide class of stationary subdivision methods, we derive necessary and suucient conditions for these schemes to produce C k continuous limit curves. These stationary schemes include those arising from midpoint subdivision of irregularly-spaced knot sequences. We also describe a matrix method for computing various derivative schemes associated with such stationary schemes. x1. Introduction ...

This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and...

To remain an attractive model, skeleton-based implicit surfaces have to allow the design and display of shapes at interactive rates. This paper focuses on surfaces whose skeletons are graphs of interconnected curves. We present subdivision-curve primitives that rely on convolution for generating bulge-free and crease-free implicit surfaces. These surfaces are efficiently yet correctly displayed...

Recursive subdivision is receiving a great deal of attention in the deenition of B-spline surfaces over arbitrary topology. The technique has recently been extended to generate interpolating surfaces with given normal vectors at the interpolated vertices. This paper describes an algorithm to generate recursive subdivision surfaces that interpolate B-spline curves. The control polygon of each cu...

Semi-automatic segmentation approaches tend to overlook the problems caused by missing or incomplete image information. In such situations, powerful control mechanisms and intuitive modelling metaphors should be provided in order to make the methods practically applicable. Taking this problem into account, the usage of subdivision curves in combination with the simulation of edge attracted mass...

The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: (1) Hausdorff distance, and (2) a sum of total curvature and derivative. High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern...

By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.