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Visualization of irregular multivariate data

Authors:

Thomas A. Foley,

David A. LaneAuthors Info & Claims

VIS '90: Proceedings of the 1st conference on Visualization '90

Pages 247 - 254

Published: 23 October 1990 Publication History

Abstract

Scientific data is often sampled at irregular spatial locations because of physical constraints, yet most visualization software applies only to gridded or regular data. We will discuss effective techniques for representing scalar and vector valued functions that interpolate to irregularly located data. Special attention will be given to the situations where the sampling domain is a 2D plane, a 3D volume, or a closed 3D surface. The globally defined interpolants can be evaluated on a fine regular grid and they can then be visualized using conventional techniques. Triangular and tetrahedral based visualization techniques are also presented.

References

[1]

Barnhill, R. E. (1985), Surfaces in computer aided geometric design: A survey with new results, Computer Aided Geometric Design 2, 1--17.

Digital Library

[2]

Barnhill, R. E., Makatura, G. T. and Stead, S. E. (1987), A new look at higher dimensional surfaces through computer graphics, in: G. E. Farin, ed., 'Geometric Modeling', SIAM, Philadelphia, 123--129.

[3]

Barnhill, R. E. and Ou, H. S. (1990), Surfaces defined on surfaces, Computer Aided Geometric Design 7, 323--336.

Digital Library

[4]

Barnhill, R. E., Piper, B. R. and Rescorla, K.(1987), Interpolation to arbitrary data on a surface, in: G. E. Farin, ed., 'Geometric Modeling', SIAM, Philadelphia, 281--289.

[5]

Carlson, R. E. and Foley, T. A. (1990), The parameter R2 and multiquadric interpolation, Technical Report, Lawrence Livermore National Laboratory.

[6]

Drebin, R., Carpenter, L. and Hanrahan, P. (1988), Volume rendering, Computer Graphics 22, no.4, 65--74.

Digital Library

[7]

Duchon, J. (1975), Splines minimizing rotation-invariant semi-norms in Sobolev spaces, in: Schempp, W. and Zeller, K., eds., Multivariate Approximation Theory, Birkhauser, Basel, 85--100.

[8]

Foley, T. A. (1987), Interpolation and approximation of three and four-dimensional scattered data, Comp. Math. Appls. 13, 711--740.

[9]

Foley, T. A.(1990), Interpolation to scattered data on a spherical domain, in: M. Cox and J. Mason, eds., 'Algorithms for Approximation II', Chapman and Hall, London, 303--310.

[10]

Foley, T. A., Lane, D. A. and Nielson, G. M. (1990), Towards animating ray-traced volume visualization, Visualization and Computer Animation Journal 1.

[11]

Foley, T. A., Lane, D. A., Nielson, G. M., Franke, R. and Hagen H. (1990), Interpolation of scattered data on closed surfaces, Computer Aided Geometric Design 7, 303--312.

Digital Library

[12]

Foley, T. A., Lane, D. A., Nielson, G. M. and Ramaraj, R. (1990), Visualizing functions over a sphere, IEEE Computer Graphics & Applications 10, no. 1, 32--40.

Digital Library

[13]

Franke, R. (1982), Smooth interpolation of scattered data by local thin plate splines, Comp. Math. Appls. 8, 273--281.

[14]

Franke, R. (1982), Scattered data interpolation: Tests of some methods, Math. Comp. 38, 181--200.

[15]

Franke, R. and Nielson, G. M. (1980), Smooth interpolation to large sets of scattered data, Intern. J. Numer Meth. Engrg. 15, 1691--1704.

[16]

Franke, R. and Nielson, G. M. (1990), Scattered data interpolation and applications: a tutorial and survey, in Geometric Modeling: Methods and Their Applications, Springer.

[17]

Hardy, R. L. (1971), Multiquadratic equation of topography and other irregular surfaces, J. Geophys. Res. 76, 1905--1915.

[18]

Hardy, R. L. (1990), Theory and applications of the multiquadric-biharmonic method, Comp. Math. Appls. 19, no. 8, 163--208.

[19]

Hardy, R. L. and Goepfert, W. M. (1975), Least squares prediction of gravity anomalies, geoidal undulations, and deflections of the vertical with multiquadric harmonic functions, Geophys. Research Letters 2, 423--426.

[20]

Lawson, C. L. (1984), C1 Surface interpolation for scattered data on a sphere, Rocky Mountain J. Math. 14, 177--202.

[21]

Levoy, M. (1988), Display of surfaces from volume data, IEEE Computer Graphics & Applications 8, no. 5, 29--37.

Digital Library

[22]

Lorensen, W. E. and Cline, H.(1987), Marching cubes: a high resolution 3D surface construction algorithm, Computer Graphics 21, no. 4, 163--169.

Digital Library

[23]

Nielson, G. M. (1983), A method for interpolation of scattered data based upon a minimum norm network, Math. Comp. 40, 253--271.

[24]

Nielson, G. M. and Foley, T. A. (1989), A survey of applications of an affine invariant norm, in: Lyche, T., Schumaker, L. L., eds., Mathematical Methods in CAGD, Academic Press, New York.

Digital Library

[25]

Nielson, G. M. and Hamann, B. (1990), Techniques for interactive visualization of volumetric data, this issue.

Digital Library

[26]

Nielson, G. M. and Ramaraj, R. (1987), Interpolation over a sphere based upon a minimum norm network, Computer Aided Geometric Design 4, 41--57.

Digital Library

[27]

Pottmann, H. and Eck, M. (1990), Modified multiquadric methods for scattered data interpolation over a sphere, Computer Aided Geometric Design 7, 313--322.

Digital Library

[28]

Renka, R. L. (1984), Interpolation of data on the surface of a sphere, ACM Trans. Math. Software, 417--436.

Digital Library

[29]

Renka R. L. (1988), Algorithm 660: QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data, ACM TOMS 14, 149--150.

Digital Library

[30]

Sabella, P. (1988), A rendering algorithm for visualizing 3D scalar fields, Computer Graphics 22, no. 4, 51--58.

Digital Library

[31]

Upson, C. and Keeler, M. (1988), V-BUFFER: visible volume rendering, Computer Graphics 22, no. 4, 59--64.

Digital Library

Cited By

Vemuri RWolfe G(2004)Adaptive sampling and modeling of analog circuit performance parameters with pseudo-cubic splinesProceedings of the 2004 IEEE/ACM International conference on Computer-aided design10.1109/ICCAD.2004.1382709(931-938)Online publication date: 7-Nov-2004
https://dl.acm.org/doi/10.1109/ICCAD.2004.1382709
Foley TLane DAthay RBrown BGrinstein GKaufman A(1991)Multi-valued volumetric visualizationProceedings of the 2nd conference on Visualization '9110.5555/949607.949643(218-225)Online publication date: 22-Oct-1991
https://dl.acm.org/doi/10.5555/949607.949643
Nielson GFoley THamann BLane D(1991)Visualizing and Modeling Scattered Multivariate DataIEEE Computer Graphics and Applications10.1109/38.7945311:3(47-55)Online publication date: 1-May-1991
https://dl.acm.org/doi/10.1109/38.79453
Show More Cited By

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Information & Contributors

Information

Published In

cover image ACM Conferences

VIS '90: Proceedings of the 1st conference on Visualization '90

October 1990

501 pages

ISBN:0818620838

Conference Chairs:
Bruce Eric Brown
Oracle Corporation, Belmont, CA
,
Gary Laguna
Lawerence Livermore National Laboratory, Livermore, CA
,
Editor:
Arie Kaufman
State University of New York, Stony Brook, New York
,
Program Chairs:
Larry Rosenblum
Naval Research Laboratory, Washington, DC
,
Gregory M. Nielson
Arizona State University, Tempe, AZ

Sponsors

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
IEEE Computer Society Technical Committee on Computer Graphics

Publisher

IEEE Computer Society Press

Washington, DC, United States

Publication History

Published: 23 October 1990

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Conference

VIS90

Sponsor:

SIGGRAPH

VIS90: Visualization '90

October 23 - 26, 1990

California, San Francisco

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Citations

Cited By

Vemuri RWolfe G(2004)Adaptive sampling and modeling of analog circuit performance parameters with pseudo-cubic splinesProceedings of the 2004 IEEE/ACM International conference on Computer-aided design10.1109/ICCAD.2004.1382709(931-938)Online publication date: 7-Nov-2004
https://dl.acm.org/doi/10.1109/ICCAD.2004.1382709
Foley TLane DAthay RBrown BGrinstein GKaufman A(1991)Multi-valued volumetric visualizationProceedings of the 2nd conference on Visualization '9110.5555/949607.949643(218-225)Online publication date: 22-Oct-1991
https://dl.acm.org/doi/10.5555/949607.949643
Nielson GFoley THamann BLane D(1991)Visualizing and Modeling Scattered Multivariate DataIEEE Computer Graphics and Applications10.1109/38.7945311:3(47-55)Online publication date: 1-May-1991
https://dl.acm.org/doi/10.1109/38.79453
Nielson GHamann BBrown BLaguna GRosenblum LNielson G(1990)Techniques for the interactive visualization of volumetric dataProceedings of the 1st conference on Visualization '9010.5555/949531.949538(45-50)Online publication date: 23-Oct-1990
https://dl.acm.org/doi/10.5555/949531.949538

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