computer-aided design
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1: 7.21 Physical Applications
§7.21 Physical Applications
… ►More recently, Cornu’s spiral appears in the design of highways and railroad tracks, robot trajectory planning, and computer-aided design; see Meek and Walton (1992). …2: 26.19 Mathematical Applications
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►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)).
►Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs.
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3: 27.17 Other Applications
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►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.
4: Bonita V. Saunders
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►She is the Visualization Editor and principal designer of graphs and visualizations for the DLMF.
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5: About MathML
6: DLMF Project News
error generating summary7: Publications
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D. W. Lozier, B. R. Miller and B. V. Saunders (1999)
Design of a Digital Mathematical Library for Science, Technology and Education,
Proceedings of the
IEEE Forum on Research and Technology Advances in Digital Libraries (IEEE ADL ’99,
Baltimore, Maryland, May 19, 1999).
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B. V. Saunders and Q. Wang (2006)
From B-Spline Mesh Generation to Effective Visualizations for the
NIST Digital Library of Mathematical Functions,
in Curve and Surface Design, Proceedings of the Sixth International
Conference on Curves and Surfaces,
Avignon, France June 29–July 5, 2006,
pp. 235–243.
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8: Philip J. Davis
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►After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined.
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►Davis’s comments about our uninspired graphs sparked the research and design of techniques for creating interactive 3D visualizations of function surfaces, which grew in sophistication as our knowledge and the technology for developing 3D graphics on the web advanced over the years.
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9: Bibliography F
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Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions.
In Progress in Optics, E. Wolf (Ed.),
Vol. 9, pp. 311–407.
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10: Bibliography D
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A combinatorial interpretation of the Seidel generation of Genocchi numbers.
Ann. Discrete Math. 6, pp. 77–87.
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