Curve subdivision is a technique for generating smooth curves from initial control polygons by repeated refinement. The most common subdivision schemes are based on linear refinement rules, which are applied separately to each coordinate of the control points, and the analysis of these schemes is well understood. Since the resulting limit curves are not sufficiently sensitive to the geometry of...

Our main result is that two point interpolatory subdivision schemes using C nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also C. The significance of this result is the following consequence: Suppose that S is a subdivision algorithm operating on sequences of real numbers using linear binary averaging that generates C real-valued functions and S is t...

In this paper we discuss a natural way to deene barycentric coordinates on general sphere-like surfaces. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar planar case. Our constructions are based on a study of homogeneous polynomials on trihedra in IR 3. The special case of Bernstein-B ezier polynomials on a sphere is considered in detail.

Subdivision schemes are widely used in numerical mathematics such as signal/image approximation, analysis and control of data or analysis. However, to develop their full power, subdivision should be incorporated into a multiresolution that, mimicking wavelet analyses, provides multi-scale decomposition function, curve, surface. The ingredients needed define associated scheme decimation detail o...

In this paper, we present a new paradigm that allows dynamically changing the topology of 2-manifold polygonal meshes. Our new paradigm always guarantees topological consistency of polygonal meshes. Based on our paradigm, by simply adding and deleting edges, handles can be created and deleted, holes can be opened or closed, polygonal meshes can be connected or disconnected. These edge insertion...

This paper uses the symmetry properties of circles and Bernstein polynomials to establish a series of interesting barycentric properties of rational biquadratic Bézier patches. A robust algorithm is presented, based on these properties, for the conversion of Dupin cyclide patches into Bézier form. A set of conversion examples illustrates the use of this algorithm.

This paper presents the relationship between the Recursive Arbitrary Topology Splines (RATS) method, derived by the authors, and the Catmull and Clark recursive B-Spline method. Both methods are capable of defining surfaces of any arbitrary topology of control points. They "fill-in" n-sided regions with foursided patches. The Catmull & Clark method is derived from the midpoint subdivision of B-...

OBJECTIVE To evaluate and compare the depth of curve of Spee in class I, class II div 1 class II div 2, class II subdivision and class III malocclusion. METHODS A Cross sectional study was done at Dr Irshat-UI-Ebad Khan Institute of Oral Health Sciences, Karachi, Pakistan (DIKIOHS) from Oct 2009 to March 2010. The sample of 100 adolescent patients selected according to the inclusion criteria ...

In this paper we derive an approximation property of 4-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth ord...

In this paper, an algorithm has been introduced to produce ternary 2m-point (for any integer m≥ 1) approximating non-stationary subdivision schemes which can generate the linear spaces spanned by {1; cos(α.); sin(α.)}. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the schemes. The proposed algorithm can be consider as the non-stationary counter ...