We describe a detailed computational procedure which, given data values at arbitrarily distributed points in the plane, determines if the data are convex and, if so, constructs a smooth convex surface that interpolates the data. The method consists of constructing a triangulation of the nodes (data abscissae) for which the triangle-based piecewise linear interpolant is convex, computing a set o...

Tom Lyche, a Trygve K. Nilssen, b and Ragnar Winther c,∗ a Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway E-mail: [email protected] b Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, 5007 Bergen, Norway E-mail: [email protected] c Department of Informatics and Department of Mathematics, University of Oslo, P.O. Box 1080 Blinder...

In this paper, we present algorithms to reconstruct surfaces generated by kinematic motions, such as the rotation about an axis or the rolling of a plane on a developlable surface. They share the property that a two-dimensional set of scattered data can be transformed into a one-dimensional one when we are able to detect the kinematics behind the data. We also present a technique to reconstruct...

Scattered data interpolation and approximation techniques allow for the reconstruction of a scalar field based upon a finite number of scattered samples of the field. In general, the fidelity of the reconstruction with respect to the original scalar field tends to deteriorate as the number of samples decreases. For the situation of very sparse sampling, the results may not be acceptable at all....

This paper deals with some basic aspects of scattered data problems. In particular, the following topics are discussed: Self-adjoint scattered data interpolation, sampling sets and interpolation sets, and irregular sampling of shift-invariant spline spaces. Results on band-limited functions are presented as well as results on univariate splines on the real line. x0. Introduction Scattered data ...

With the advent of contemporary GPUs, it has been possible to perform volume deformation at interactive rates. In particular, it has been shown that deformation can be important for the purposes of illustration. In such cases, rather than being the result of a physically-based simulation, volume deformation is often goal-oriented and user-guided. For this purpose, it is important to provide the...

Abstract. We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. Starting with a triangulated set of scattered data with associated function values, our scheme applies linear, stationary subdivision rules resulting in a hierarchy of triangulations that converge rapidly to a smooth limit surface. The novelty of our scheme is that it applies su...

Recent progress in acquisition technology has increased the availability and quality of measured appearance data. Although representations based on dimensionality reduction provide the greatest fidelity to measured data, they require assembling a high-resolution and regularly sampled matrix from sparse and non-uniformly scattered input. Constructing and processing this immense matrix becomes a ...

With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limite d degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In additi...