D. Doo

Bio: D. Doo is an academic researcher from Brunel University London. The author has contributed to research in topics: Division (mathematics) & Eigenvalues and eigenvectors. The author has an hindex of 2, co-authored 2 publications receiving 1393 citations.

Behaviour of recursive division surfaces near extraordinary points

Abstract: The behaviour of the limits surface defined by a recursive division construction can be analysed in terms of the eigenvalues of a set of matrices. This analysis predicts effects actually observed, and leads to suggestions for the further improvement of the method.

Behaviour of recursive division surfaces near extraordinary points

Abstract: The behaviour of the limits surface defined by a recursive division construction can be analysed in terms of the eigenvalues of a set of matrices. This analysis predicts effects actually observed, and leads to suggestions for the further improvement of the method.

Recursively generated B-spline surfaces on arbitrary topological meshes

Abstract: This paper describes a method for recursively generating surfaces that approximate points lying-on a mesh of arbitrary topology. The method is presented as a generalization of a recursive bicubic B-spline patch subdivision algorithm. For rectangular control-point meshes, the method generates a standard B-spline surface. For non-rectangular meshes, it generates surfaces that are shown to reduce to a standard B-spline surface except at a small number of points, called extraordinary points. Therefore, everywhere except at these points the surface is continuous in tangent and curvature. At the extraordinary points, the pictures of the surface indicate that the surface is at least continuous in tangent, but no proof of continuity is given. A similar algorithm for biquadratic B-splines is also presented.

A signal processing approach to fair surface design

Abstract: In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals – functions defined on polyhedral surfaces of arbitrary topology –, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique. CR

A butterfly subdivision scheme for surface interpolation with tension control

Abstract: A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is C1 for a specified range of the tension parameter, with a few exceptions. Application of the butterfly scheme and the role of the tension parameter are demonstrated by several examples.

Multiresolution analysis for surfaces of arbitrary topological type

Abstract: Multiresolution analysis and wavelets provide useful and efficient tools for representing functions at multiple levels of detail. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation, and numerical analysis. In this article, we present a new class of wavelets, based on subdivision surfaces, that radically extends the class of representable functions. Whereas previous two-dimensional methods were restricted to functions difined on R2, the subdivision wavelets developed here may be applied to functions defined on compact surfaces of arbitrary topological type. We envision many applications of this work, including continuous level-of-detail control for graphics rendering, compression of geometric models, and acceleration of global illumination algorithms. Level-of-detail control for spherical domains is illustrated using two examples: shape approximation of a polyhedral model, and color approximation of global terrain data.