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Published **1996**
by Stanford University, National Aeronautics and Space Administration, National Technical Information Service, distributor in Stanford, Calif, [Washington, DC, Springfield, Va .

Written in English

- Tensors.,
- Tensor analysis.,
- Eigenvectors.,
- Singularity (Mathematics),
- Multivariate statistical analysis.,
- Scalars.,
- Three dimensional models.,
- Scientific visualization.

**Edition Notes**

Other titles | Visualization of three-D tensor fields. |

Statement | principal investigator, Lambertus Hesselink. |

Series | [NASA contractor report] -- NASA CR-201805. |

Contributions | United States. National Aeronautics and Space Administration. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL18121539M |

The second section presents a detailed discussion of the algorithms and techniques used to visualize behavior in 3-D, as static, interactive, or animated imagery. It discusses the mathematics of engineering data for visualization, as well as providing the current methods used for the display of scalar, vector, and tensor fields. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. Visualization of 2-D and 3-D Tensor Fields Principal Investigator: Lambertus Hesselink* Stanford University, Stanford, California Phone: () Email: [email protected] Introduction In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point. 5 Visualization of Tensor Fields The major sources of material failure in structural mechanics are stresses and strains. For an idealized isotropic and homogeneous material failure will occur if.

Visualization and processing of tensor fields: advances and perspectives David H. Laidlaw, Joachim Weickert Visualisation and Processing of Tensor Fields provides researchers an inspirational look at how to process and visualize complicated . Visualization involves constructing graphical interfaces that enable humans to understand complex data sets; it helps humans overcome their natural limitations in terms of extracting knowledge from the massive volumes of data that are now routinely best argument for scientific visualization is that today's researchers must consume ever higher volumes of /5(3). Rapid advances in 3-D scientific visualization have made a major impact on the display of behavior. The use of 3-D has become a key component of both academic research and commercial product development in the field of engineering design. Computer Visualization presents a unified collection of computer graphics techniques for the scientific visualization of . The visualization of 3D stress and strain tensor ﬁelds 5 Visualization of Tensor Fields The aim of tensor ﬁeld visualization is therefore to transform these large amount of data into a single image which can be easily understood and interpreted by the user.

The stress tensor and strain tensor are both second-order tensor fields, and are related in a general linear elastic material by a fourth-order elasticity tensor field. In detail, the tensor quantifying stress in a 3-dimensional solid object has components that can be conveniently represented as a 3 × 3 array. Topology was introduced in the visualization literature some 15 years ago as a mathematical language to describe and capture the salient structures of symmetric second-order tensor fields. Yet, despite significant theoretical and algorithmic advances, this approach has failed to gain wide acceptance in visualization practice over the last by: 3. G. Kindlmann, D. Weinstein, and D.A. Hart. Strategies for direct volume rendering of diffusion tensor fields. IEEE Trans. on Visualization and Computer Graphics, 6(2)–, CrossRef Google ScholarCited by: 3D Symmetric, Traceless Tensor Field Analysis and Visualization Roy G. Biv, Ed Grimley, Member, IEEE, and Martha Stewart Fig. 1. In the Clouds: Vancouver from Cypress Mountain Abstract—Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui .

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