Book ChapterDOI
Mesh-Independent Surface Interpolation
David Levin
- pp 37-49
Reads0
Chats0
TLDR
In this article, a basic mesh-independent projection strategy for general surface interpolation is proposed, based upon the moving-least-squares (MLS) approach, and the resulting surface is C ∞ smooth.Abstract:
Smooth interpolation of unstructured surface data is usually achieved by joining local patches, where each patch is an approximation (usually parametric) defined on a local reference domain. A basic mesh-independent projection strategy for general surface interpolation is proposed here. The projection is based upon the ’Moving-Least-Squares’ (MLS) approach, and the resulting surface is C ∞ smooth. The projection involves a first stage of defining a local reference domain and a second stage of constructing an MLS approximation with respect to the reference domain. The approach is presented for the general problem of approximating a (d − 1)-dimensional manifold in ℝ d , d ≥ 2. The approach is applicable for interpolating or smoothing curve and surface data, as demonstrated here by some graphical examples.read more
Citations
More filters
Journal ArticleDOI
Computing and rendering point set surfaces
TL;DR: It is shown that the approximation error is bounded and present tools to increase or decrease the density of the points, thus allowing an adjustment of the spacing among the points to control the error.
Proceedings ArticleDOI
Efficient simplification of point-sampled surfaces
TL;DR: This work has implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of point-based models with lower sampling density, and shows how local variation estimation and quadric error metrics can be employed to diminish the approximation error.
Journal ArticleDOI
Semantic 3D Object Maps for Everyday Manipulation in Human Living Environments
TL;DR: The dissertation presented in this article proposes Semantic 3D Object Models as a novel representation of the robot’s operating environment that satisfies these requirements and shows how these models can be automatically acquired from dense 3D range data.
Journal ArticleDOI
Robust moving least-squares fitting with sharp features
TL;DR: A robust moving least-squares technique for reconstructing a piecewise smooth surface from a potentially noisy point cloud is introduced, based on a new robust statistics method for outlier detection: the forward-search paradigm.
Proceedings ArticleDOI
Non-iterative, feature-preserving mesh smoothing
TL;DR: The robustness of the local estimates allows this work to derive a non-iterative feature-preserving filtering technique applicable to arbitrary "triangle soups", which make it an excellent solution for smoothing large, noisy, and non-manifold meshes.
References
More filters
Journal ArticleDOI
Scattered data interpolation: tests of some methods
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.
Proceedings ArticleDOI
Efficient simplification of point-sampled surfaces
TL;DR: This work has implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of point-based models with lower sampling density, and shows how local variation estimation and quadric error metrics can be employed to diminish the approximation error.
Journal ArticleDOI
A survey of curve and surface methods in CAGD
TL;DR: It is suggested that B6zier curves should be considered as a single type of curve, but the design of these curves should not be confused with other types of curves, which are known to have different properties.
Journal ArticleDOI
The approximation power of moving least-squares
TL;DR: The interpolation approximation in R d is shown to be a C∞ function, and an approximation order result is proven for quasi-uniform sets of data points.
Proceedings ArticleDOI
Point set surfaces
TL;DR: To display the point set surface, a novel point rendering technique is introduced to evaluate the local maps according to the image resolution, which results in high quality shading effects and smooth silhouettes at interactive frame rates.