A boundary conforming grid generation system for interface tracking

Saunders, Bonita V.

doi:10.1016/0898-1221(95)00040-6

Cited by 7 publications

(7 citation statements)

References 14 publications

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“…We have experimented with both structured and unstructured grids, but we have found that structured grids allow us to write more efficient code to implement the interactive features for the visualizations. One of the primary grid generation techniques we have used is based on a tensor product mapping and smoothing functional developed by one of the authors to solve partial differential equations (pdes) related to aerodynamics and solidification theory [2,3]. The grid generation technique uses a tensor product mapping T from the unit square / 2 to the physical domain defined by…”

Section: The Grid Generation Mappingmentioning

confidence: 99%

“…We will first examine the problems that can arise when trying to display dynamic 3D graphics on the Web. Then we will discuss the grid generation technique we have used, examining an updated version of a tensor product B-spline grid generation algorithm designed by one of the authors [2], Finally, we will discuss our results and look at some possibilities for improvements.…”

Section: Introductionmentioning

confidence: 99%

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Boundarycontour fitted grid generation for effective visualizations in a digital library of mathematical functions

Saunders¹,

Wang²

2005

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Effective visualizations can help researchers obtain a more complete understanding of high level mathematical functions that arise in mathematics, statistics, physics, fluid dynamics and other fields of the mathematical and physical sciences. Accordingly, dynamic interactive 3D graphs of function surfaces will be a key feature of the National Institute of Standards and Technology Digital Library of Mathematical Functions, a new Web-based compendium of mathematical functions that will replace a popular but dated resource, the National Bureau of Standards Handbook of Mathematical Functions, published by Abramowitz and Stegun in 1964. As developers of commercial packages are well aware, creating software to accurately plot complicated 3D surfaces can be a challenging task. This paper looks at the effectiveness of modifying an algebraic tensor product spline grid generation technique, whose design was originally motivated by problems in aerodynamics and solidification theory, to create computational grids for accurate visualizations of 3D surfaces that capture key function features such as poles, branch cuts and other singularities.

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Section: The Grid Generation Mappingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boundarycontour fitted grid generation for effective visualizations in a digital library of mathematical functions

Saunders¹,

Wang²

2005

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“…To date two techniques have been used to create the grids used to develop the surface plots: simple transfinite interpolation and a tensor product spline algorithm developed by one of the authors [2] …”

Section: Grid Generation Techniquesmentioning

confidence: 99%

From 2D to 3D:

Saunders¹,

Wang²

2000

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“…While many researchers now prefer unstructured triangular and tetrahedral meshes typically used with finite element codes, there are still many structured codes being developed or maintained today. One of the authors modified a structured code she previously designed for modeling Bridgman growth of binary alloys in materials science [Saunders 1995;Saunders and Wang 2010] to develop boundary/contour fitted grids to create accurate plots of function graphs. An even trickier problem was determining the type of file formats to use, while considering the availability of graphics plugins that might be needed by the user.…”

Section: Introductionmentioning

confidence: 99%

Dynamic 3D visualizations of complex function surfaces using X3DOM and WebGL

Saunders

Antonishek

Wang

et al. 2015

Proceedings of the 20th International Conference on 3D Web Technology

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In 1997 the National Institute of Standards and Technology (NIST) embarked on a huge project to replace one of the most cited resources for mathematical, physical and engineering scientists, the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [Abramowitz and Stegun 1964], originally released by the National Bureau of Standards (NBS) in 1964. The 1997 project, designed to update and modernize the handbook, culminated in May 2010 with the launch of a freely available website, the NIST Digital Library of Mathematical Functions [DLMF ] (http://dlmf.nist.gov/), and its print companion, the NIST Handbook of Mathematical Functions [Olver et al. 2010].While the presence of graphics was sparse in the original handbook, the new resource contains more than 600 illustrations of high level mathematical functions, including close to 200 interactive 3D visualizations on the website. We provide the motivation for the visualization work through the context of the project and discuss our current implementation using X3DOM and WebGL.

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A boundary conforming grid generation system for interface tracking

Cited by 7 publications

References 14 publications

Boundarycontour fitted grid generation for effective visualizations in a digital library of mathematical functions

Boundarycontour fitted grid generation for effective visualizations in a digital library of mathematical functions

From 2D to 3D:

Dynamic 3D visualizations of complex function surfaces using X3DOM and WebGL

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