This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C²-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high-fidelity reconstruction is possible from a selected set of sparse and irregular samples.

In this paper we describe an approach to the construction of curvature-continuous surfaces with arbitrary control meshes using subdivision. Using a simple modification of the widely used Loop subdivision algorithm we obtain perturbed surfaces which retain the overall shape and appearance of Loop subdivision surfaces but no longer have flat spots or curvature singularities at extraordinary vertices. Our method is computationally efficient and can be easily added to any existing subdivision code.

xcmodel is a CAD system realized and usable in an academic environment. It integrates four packages: a 2D and a 3D modeller, an object composer and a realistic scene renderer; these subsystems can be regarded as being in constant evolution i.e. a continuous work in progress. The system summarises our knowledge and experience in geometric modelling and NURBS curves and surfaces acquired over ten years of research. xcmodel and its subsystems were designed to represent a research and teaching laboratory to experiment and learn; it is an ideal environment to develop, perfect and compare methods and algorithms in geometric modelling and graphic visualization.

this paper that we are given a set of normal fluid fluxes defined across the face centers of some tensor product cartesian mesh. Other velocity data may require pre-processing to obtain the desired format. x i\Gamma1 x i

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We present a manifold-based surface construction extending the C ∞ construction of Ying and Zorin (2004a). Our surfaces allow for pircewise-smooth boundaries, have user-controlled arbitrary degree of smoothness and improved derivative and visual behavior. 2-flexibility of our surface construction is confirmed numerically for a range of local mesh configurations. Key words: Geometric modeling, manifolds, high-order surfaces

Abstract not found