3 edition of **Visualization of 3-D tensor fields** found in the catalog.

Visualization of 3-D tensor fields

- 312 Want to read
- 10 Currently reading

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 |

Bi, C, Takahashi, S & Fujishiro, I , Degeneracy-aware interpolation of 3D diffusion tensor fields. in Proceedings of SPIE-IS and T Electronic Imaging - Visualization and Data Analysis , , Proceedings of SPIE - The International Society for Optical Engineering, vol. , Visualization and Data Analysis , Burlingame, CA Cited by: 2. General purpose, cross-platform tool for 3-D scientific data visualization Visualization of scalar, vector and tensor data in 2 and 3 dimensions Easy scriptability using Python Mayavi is easy-to-use tool for 3D visualization Surfaces, iso-surfaces, vector fields.

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. It also examines the more general issues of visualizing a continuum volume field and animating the dimensions of time and motion in a state of behavior. The full text of this article hosted at is unavailable due to technical by:

behavior in 3-D, as static, interactive or animated imagery. This section begins with a discussion of the mathematics of engineering data for visualization, and then covers the current methods used for the display of scalar, vector and tensor fields. Another chapter examines the more general issues of visualizing a continuumFile Size: 6MB. dimensional arrays of coefﬁcients. For 3-D solids, a fourth-order tensor is a 3 3 3 3 array, a second-order tensor is a 3 3 array, etc. The order of a tensor is the same as the num-ber of subscripts needed to write a typical element. Thus, if E is a fourth-order tensor, a typical element is denoted by Eijk‘. Scalars, vectors, and matrices.

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Get this from a library. Visualization of 3-D tensor fields. [Lambertus Hesselink; United States. National Aeronautics and Space Administration.]. Topology of 3-D Tensor Fields We choose the elastic stress tensor induced by two compressive forces on the top of a semi-infinite plane to illustrate the advantages of using topolog-ical skeletons in visualizing 3-D tensor fields.

In principle, hyperstreamline trajectories of the stress tensor show the transmission of forces inside the material. 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.

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. 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.

Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging.

This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields.

Dynamic 3D Visualization of Stress Tensors Abstract further enhancing the understandi ng of the state-of-stress at a si ngle point through visualization. Regarding fields, Jermic, et al.6 present three different approaches to visualizing tensors (such as 3 d: ® ® ® ®. A scalar field is a tensor field composed of rank 0 tensors, a vector field is a tensor field composed of rank 1 tensors, and a rank k tensor field stores a k-dimensional matrix of values at each sample point.

Tensor fields require sophisticated visualization techniques to convey all of the information present at each sample. The book combines a basic overview of the fundamentals of computer graphics with a practitioner-oriented review of the latest 3-D graphics display and visualization techniques.

Each chapter is written by well-known experts in the : $ Tensor fields frequently occur in engineering and physical science computations. For example, rank 2 (second-order) tensors are used to describe velocity gradients, stress, and strain. Tensor fields present a difficult visualization problem since it is difficult to map even a second order tensor onto a set of visual cues.

Recently, matrix-valued data sets (so-called tensor fields) have gained significant importance in the fields of scientific visualization and image processing. This has been triggered by the following developments: Novel medical imaging techniques such as diffusion tensor magnetic resonance imaging (DT-MRI) have been introduced.

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 : Hardcover.Scientific visualization (also spelled scientific visualisation) is an interdisciplinary branch of science concerned with the visualization of scientific phenomena.

It is also considered a subset of computer graphics, a branch of computer purpose of scientific visualization is to graphically illustrate scientific data to enable scientists to understand, illustrate, and glean.

Imagine a circular disc made of a flexible material as shown below. Suppose this disk is stretched along one direction and compressed along another (shown with dotted lines) without twisting, thus converting the circle into an ellipse.

Further, le.