Open Access
8. A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants.
Stephen Mann,Charles Loop,Michael Lounsbery,David Meyers,James Painter,Tony DeRose,Kenneth R. Sloan +6 more
- pp 145-172
Reads0
Chats0
TLDR
A unifying survey of the published methods for solving variants of the problem of passing a surface through a set of data points to identify causes of shape defects, and suggestions for improving the aesthetic quality of the interpolants are presented.Abstract:
This paper has been published as a chapter in \Curve and Surface Design", H. Ha-gen, (ed), SIAM, 1992 Some of the gures from that paper are missing from this version, as are all of the black-and-white photographs. There are currently a number of methods for solving variants of the following problem: Given a triangulated polyhedron P in three space with or without boundary, construct a smooth surface that interpolates the vertices of P. In general, while the methods satisfy the continuity and interpolation requirements of the problem, they often fail to produce pleasing shapes. The purpose of this paper is to present a unifying survey of the published methods, to identify causes of shape defects, and to ooer suggestions for improving the aesthetic quality of the interpolants. The problem of passing a surface through a set of data points arises in numerous areas of application such as medical imaging, geological modeling, scientiic visualization, and geometric modeling. Variants of this problem have been approached from many directions. Tensor-product B-splines work well for modeling surfaces based on rectilinear control nets but are not suu-cient for more general topologies. Triangulated data, however, can represent 1read more
Citations
More filters
Journal ArticleDOI
Multiresolution analysis for surfaces of arbitrary topological type
TL;DR: 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.
Proceedings ArticleDOI
Surface reconstruction by Voronoi filtering
Nina Amenta,Marshall Bern +1 more
TL;DR: A simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points that uses Voronoi vertices to remove triangles from the Delaunay triangulation is given.
Proceedings ArticleDOI
Functional optimization for fair surface design
TL;DR: A simple-to-use mechanism for the creation of complex smoothly shaped surfaces of any genus or topology that allows the specification of a desired surface in the most natural way and produces very high quality surfaces with predictable, intuitive behavior.
Proceedings ArticleDOI
Free-form shape design using triangulated surfaces
William Welch,Andrew Witkin +1 more
TL;DR: This work presents an approach to modeling with truly mutable yet completely controllable free-form surfaces of arbitrary topology, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patch-based approaches.
Journal ArticleDOI
Surfaces from contours
TL;DR: A method that can handle sets of contours in which adjacent contours share a very contorted boundary is presented, and a new approach to solving the correspondence problem using a Minimum Spanning Tree generated from the contours is described.
References
More filters
Book
Differential geometry of curves and surfaces
TL;DR: This paper presents a meta-geometry of Surfaces: Isometrics Conformal Maps, which describes how the model derived from the Gauss Map changed over time to reflect the role of curvature in the model construction.
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.
Journal ArticleDOI
High accuracy geometric Hermite interpolation
TL;DR: A parametric cubic spline interpolation scheme for planar curves which is based on an idea of Sabin for the construction of C^1 bicubic parametric spline surfaces is described, a natural generalization of [standard] Hermite interpolation.
Proceedings ArticleDOI
Design of solids with free-form surfaces
TL;DR: A unified method of generating a wide range of three dimensional objects from polyhedra to solids with free-form surfaces by using local modifications is proposed and a geometric modeling system MODIF is made.