Gregory Nielson

Scientific Visualization, Geometric Modeling, 

を組合せた曖昧さのないマーチング・キューブ法の整数化Asymptotic Deciderを組合せた曖昧さのないマーチング・キューブ法の整数化AN00349328

Nielson's paper "The side-vertex method for interpolating in triangles" published in 1979 is amongst the top 20 most highly cited papers of the Journal of Approximation Theory, which has been in publication for over 40 years with more than 3500 papers published.

Nielson's paper with his student, Bernd Hamann, "The asymptotic decider: resolving the ambiguity in marching cubes" published in 1991, is the overall 3rd most highly cited paper of the IEEE Visualization Conference Series which began in 1990.  Nielson has said that he thinks this is one of his most clever and useful ideas for volume visualization!

http://en.wikipedia.org/wiki/Asymptotic_decider

Nielson's paper "On Marching Cubes" which appeared in IEEE Transactions on Visualization and Computer Graphics in 2003 is among the top 20 most highly cited papers for this journal over the past 10 years.

Nielson's paper "Multivariate smoothing and interpolating splines" SIAM Journal of Numerical Analysis 1974 was published nearly 40 years ago, yet they it continues to be currently cited.

One of Nielson's most notable (and maybe the most innovative) paper was never published as a refereed journal article.  This is the TR 40 technical report of the Mathematics Department at ASU "Some piecewise polynomical alterrnatives to splines under tension".  It has been continuously cited every year since it was written in the early 70s (nearly half a century ago!)  Extremely few research papers have this longevity or influence!  These curves (which are sometimes referred to as nu-splines) exploided for design purposes a disconnect between the continuity and smoothness properties of the graphs of component functions and the graphs of the resulting parametric curves.  Parmetric curves with component functions which have very smooth graphs (no corners e. g.) can conveniently lead to parametric curve graphs with sharp features!  (E. g. corners, Go figure! How can this happen??? Rather amazing and very useful!)  This feature allows these curves and surfaces to be used for modeling buildings and other artifacts.   If you are interested and can't easily find a copy, please contact: nielson@asu.edu

Most Cited Publications

• Techniques for extracting and modeling geometric features from point cloud data sets, Intelligent Computer Graphics, 2012, Springer.
• Dual Marching Cubes, Visualization Conference Proceedings 2004
• Interval Volume Tetrahedrization , with J. Sung, Visualization Conference Proceedings  1997
• Scattered Data Modeling, IEEE Computer Graphics and Applications, 1993
• Terrain Simulation using a Model of Stream Erosion, with A Kelley & M Malin, SIGGRAPH 1988
• Direct Manipulation Techniques for 3D Objects using 2D Locators, with D Olsen, Computer Graphics 1986
• Method for interpolating scattered data based upon minimum norm network, Mathematics of Computation, 1983
• Smooth interpolation of large sets of scattered data, with R Franke, International Journal of Numerical Analysis, 1980
• Some piecewise polynomial alternatives to splines under tension, Computer Aided Geometric Design, 1974

It is one thing to have citations to your research but a whole different level of recognition is to have your research referred to in the title of a research publication.  Some examples are:

 Publications with Professor Nielson's name in the title:

"A Novel 3D Mesh Blind Watermarking Algorithm Based on Nielson Affine Invariant Norm", Jin Jianqiu, Wang Xun, Computer-Aided Design and Computer Graphics, 2007 10th IEEE International Conference, ISBN 978-1-4244-1579-3, pp 294-297

Nielson-type Transfinite triangular interpolants by means of quadratic enery functional optimization", Agoston Roth, arXiv:1604.01910v1 [math.NA] 7 Apr 2016

"A Modified Nielson's Side-Vertex Triangular Mesh Interpolation Scheme", Zhihong Mao

"The Geometric Meaning of Nielson's Affine Invariant Norm", by: Wendelin L., F. Degen and Volker Milbrandt, Computer Aided Geometric Design, Volume 15, Issue 1, December 1997, Pages 19-25.

Based upon citation counts (ref. Google Scholar) Prof. Nielson is in the top 5% in the areas of Visualization, Computer Graphics & Numerical Analysis and in the top 10% in Geometric Modeling.  Overall, based upon research statistics, he is in the top 5% of ASU faculty.

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">Nielson, Gregory M.; Hamann, Bernd (1991). Nielson, Gregory M.; Rosenblum, Larry, eds. The asymptotic decider: resolving the ambiguity in marching cubes. Proceedings of the 2nd conference on Visualization '91 (VIS '91). Los Alamitos, CA: IEEE Computer Society. pp. 83–91. ISBN 978-0-8186-2245-8.

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">Here is a list of some research papers with titles making reference to Prof. Nielson's research:

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">"A Modified Nielson's Side-Vertex Triangular Mesh Interpolation Scheme"

by: Zhihong Mao, Lizhuang Ma, and Wuzheng Tan;

in: O.Gervasi et al (Eds.) :ICCSA 2005, LNCS, 3480, pp. 776-785, 2005

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">"A Novel 3D Mesh Blind Watermarking Algorithm Based on Nielson Affine Invariant Norm,

by: Jin jianqiu, Wang Xun, Zhejiang Gongshang Univ. Hangzhou; in: Computer-Aided

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">Design and Computer Graphics, 2007 10th IEEE International Conference on:,

 ISBN: 978-1-4244-1579-3

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">

"Nielson-type transfinite triangular interpolants

by means of quadratic energy functional optimizations"

by: Agoston Roth, arXiv:1604.01910v1 [math.NA] 7 Apr 2016

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">"The Geometric Meaning of Nielson's Affine Invariant Norm"

by: Wendelin L., F. Degen and Volker Milbrandt, Computer Aided Geometric Desing,

 Volume 15, Issue 1, December 1997, Pages 19-25

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">] [PDF] Real-time simulation of elastic objects in Virtual Environments using finite element method and precomputed Green's functions

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px">…, M Göbel, S Klimenko, GM Nielson - … Workshop on Virtual …, 2002

text-align:start;widows: 2;-webkit-text-stroke-width: 0px;text-decoration-style: initial;
text-decoration-color: initial;word-spacing:0px"> "Nielson-type transfinite triangular interpolants

by means of quadratic energy functional optimizations"

by: Agoston Roth, arXiv:1604.01910v1 [math.NA] 7 Apr 2016