Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
The visualization of second-order tensor fields
The visualization of second-order tensor fields
The Topology of Symmetric, Second-Order 3D Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
Feature Extraction of Separation and Attachment Lines *
IEEE Transactions on Visualization and Computer Graphics
Surface representations of two- and three-dimensional fluid flow topology
VIS '90 Proceedings of the 1st conference on Visualization '90
The topology of symmetric, second-order tensor fields
VIS '94 Proceedings of the conference on Visualization '94
Topological Lines in 3D Tensor Fields
VIS '04 Proceedings of the conference on Visualization '04
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Interactive Tensor Field Design and Visualization on Surfaces
IEEE Transactions on Visualization and Computer Graphics
Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces
IEEE Transactions on Visualization and Computer Graphics
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices
IEEE Transactions on Visualization and Computer Graphics
Data Visualization
Asymmetric Tensor Analysis for Flow Visualization
IEEE Transactions on Visualization and Computer Graphics
Invariant Crease Lines for Topological and Structural Analysis of Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
PACIFICVIS '09 Proceedings of the 2009 IEEE Pacific Visualization Symposium
Visualization and Processing of Tensor Fields: Advances and Perspectives
Visualization and Processing of Tensor Fields: Advances and Perspectives
Vector and tensor field topology simplification on irregular grids
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
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This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifolds embedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of a given dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extraction methods result in an incomplete topological skeleton. In particular with regard to the high computational costs of the extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields that leads to complete results. The core idea is to include the locations of discontinuity into the topological analysis. For this purpose the model of continuous transition bridges is introduced, which allows to capture the entire topology on the discontinuous field. The proposed method is applied to piecewise linear three-dimensional tensor fields defined on the vertices of the triangulation and for piecewise constant two or three-dimensional tensor fields given per triangle, e.g. rate of strain tensors of piecewise linear flow fields.