Isometric embedding by surface reconstruction from distances

Authors:
Ingrid Hotz
Affiliations:
University of Kaiserslautern, D-67653 Kaiserslautern, Germany
Venue:
Proceedings of the conference on Visualization '02
Year:
2002

Citing 5
Cited 2

Numerical recipes in C (2nd ed.): the art of scientific computing

Numerical recipes in C (2nd ed.): the art of scientific computing
Interactive deformations from tensor fields

Proceedings of the conference on Visualization '98
A new approach to the visualization of tensor fields

Graphical Models and Image Processing
The Topology of Symmetric, Second-Order 3D Tensor Fields

IEEE Transactions on Visualization and Computer Graphics
Visualization of second order tensor fields and matrix data

VIS '92 Proceedings of the 3rd conference on Visualization '92

Physically Based Methods for Tensor Field Visualization

VIS '04 Proceedings of the conference on Visualization '04
Radial Hermite Operators for Scattered Point Cloud Data with Normal Vectors and Applications to Implicitizing Polygon Mesh Surfaces for Generalized CSG Operations and Smoothing

VIS '04 Proceedings of the conference on Visualization '04

Quantified Score

Hi-index	0.00

Visualization

Abstract

To display the intuitive meaning of an abstract metric it is helpful to look on an embedded surface with the same inner geometry as the given metric. The resulting partial differential equations have no standard solution. Only for some special cases satisfactory methods are known. I present a new algorithmic approach which is not based on differential equations. In contrast to other methods this technique also works if the embedding exists only locally. The fundamental idea is to estimate Euclidean distances, from which the surface is built up. In this paper I focus on the reconstruction of a surface from these estimated distances. Particular the influence of a perturbation of the distances on the shape of the resulting surface is investigated.