Robert Preece Burton 3326 TMCB Brigham Young University Provo, UT 84602 (801) 378-6467 rpburton@cs.byu.edu December 9, 1998
2D cross section of a 5D Julia set		3D cross section of an 8D Mandelbrot set

Robert Preece Burton is a Professor of Computer Science at Brigham Young University. Prior to his affiliation with the BYU faculty in 1974, he was employed as an experimental systems engineer at Bell Laboratories. He received a Ph.D. in Computer Science from the University of Utah in 1973 under the tutelage of Ivan E. Sutherland. His dissertation is entitled Real-time Measurement of Multiple Three-dimensional Positions. He received an Honors Degree of Bachelor of Arts in Physics from the University of Utah in 1969. His bachelor's thesis is entitled Computerized Identification of X-ray Diffraction and Infrared Patterns. He terminated his high school studies in Europe in 1964 to accept Early Admissions with Honors at Entrance to the University of Utah.

Shortly after his affiliation with the BYU faculty, Professor Burton established the Hyperspace Research Group , the Computer Science Department's oldest, continuous research project. He has been a Senior Scientist and Principal Investigator for Hyperspace Research at the Eyring Research Institute. Professor Burton has authored or co-authored 29 publications related to hyperspace graphics , and has made numerous presentations at conferences, universities, and research institutions in the United States, Europe, and the Middle East. He has produced holograms and motion pictures depicting hyperdimensional phenomena. He has authored or co-authored 23 additional publications related to computer graphics.

Between 1978 and 1981, Professor Burton attended the J. Reuben Clark Law School emphasizing Information Privacy and Transborder Data Flows. He has authored or co-authored 7 publications related to these subjects, and had made presentations at conferences and universities in the United States, Europe, and the Middle East. In 1983, he was an invited guest (and Ex-officio Member, US State Department Delegation) to the OECD International Symposium on Information, Computer and Communications Policy, held in London, England. In 1984, he was an invited participant (and the only representative from the United States) at the Council of Europe International Conference on Problems in Data Protection Legislation, held in Madrid, Spain.

Professor Burton has authored or co-authored an additional 10 publications on other computer science topics.

Professor Burton regularly teaches a course in computer graphics at Brigham Young University. He has developed and taught similar course for IBM Corporation, Evans & Sutherland Computer Corporation, and Unisys. Over the past quarter century, he has taught courses in several computer science subject areas.

He has been a consultant for Ford Motor Company, IBM Corporation, Smith Kline & French International Company, The Church of Jesus Christ of Latter-day Saints (where he was the Executive Consultant for Data Protection and Transborder Data Flows), and has been retained by prominent law firms as an expert witness.

He has supervised 30 completed master's theses.

In 1998 he received a Computer Science Department Teacher of the Year award. In 1989 he received the Karl G. Maeser Distinguished Teaching Award. In 1985 he received the Karl G. Maeser Research and Creative Arts Award. He is a member of six honor societies.

He and his wife Lara reside in the Sundance recreational and arts community. Family activities are recreational (including downhill and cross-country skiing, snowshoeing, dogsledding, canoeing, kayaking, SCUBA diving, technical climbing, biking, and motorcycling) and culinary (including cheese making, grilling, smoking, and brick oven cooking).

Hyperspace Research

The objective of the Hyperspace Research Group is the meaningful pictorial presentation of more than three simultaneous variables. Often more than three simultaneous variables must be considered in situations which range from science and engineering through defense and business. Consider presenting, for example, the number of shoes sold in each geographic region of the United States during each month of 1998 - a situation involving four variables. Two- and even three-dimensional graphs or charts are useful when only two or three variables need to be considered, but are insufficient even for this simple situation. If the adage that "a picture is worth a thousand words" can be extended to higher dimensions, a multitude of higher-dimensional problems can be addressed and potentially solved using pictures. Unfortunately, there have been no satisfactory analogs of graphs and charts in higher dimensions. As a result, higher-dimensional presentations usually consist of tables of numbers or lower-dimensional partial presentations. Such tables of numbers and partial presentations make it difficult or impossible to grasp situations as wholes or to think creatively about solutions.

In 1975 Robert P. Burton, Professor of Computer Science at Brigham Young University, began to attack the problems of graphically representing higher-dimensional phenomena. Efforts under his direction have resulted in an unsurpassed repository of Cartesian hyperspace graphics capabilities and a sophisticated graphics software system for parallel (as opposed to perpendicular) axes, planes, and volumes graphics.

Hyperspace Graphics Papers

• Ning Xie and Robert P. Burton, "Conic Sections and other Bezier Curves in Parallel Planes Coordinates," Journal of Imaging Science and Technology, Vol. 42, No. 6, November/December 1998, pp. 541-549.
  
  
• Ping J. Xun and Robert P. Burton, "Parallel Volumes Coordinates for Hyperdimensional Computer Graphics," Journal of Imaging Science and Technology, Vol. 41, No. 1, January/February, 1997, pp 59-70.
  
  
• John D. Melville and Robert P. Burton, "Piles for Hyperdimensional Graphics," Computers & Graphics, Vol. 21, No. 1, Vol 21., No. 1, 1997, pp. 51-60.
  
  
• Stephen L. Dixon, Kevin L. Steele, and Robert P. Burton, "Generation and Graphical Analysis of Mandelbrot and Julia Sets in More than Four Dimensions," Computers & Graphics, Vol. 20, No. 3, 1996.
  
  
• John D. Melville and Robert P. Burton, "Point-Line Intersection in Parallel Axes," Journal of Imaging Science and Technology, Vol. 39, No. 2, March/April 1995, pp. 162-166.
  
  
• Tan Xiaoxi and Robert P. Burton, "Parallel Planes Coordinates for Hyperdimensional Computer Graphics," Journal of Imaging Science and Technology, Vol. 36, No. 6, November/December 1992, pp 591-595.
  
  
• Glendon R. Whiteley, Robert P. Burton and Bill Hays, "Representing n-Dimensional Hyperplanes Using Parallel Axes Computer Graphics, with a Linear Programming Demonstration," Journal of Imaging Technology, Vol. 17, No. 5, December 1991, pp. 274-278.
  
  
• G. Gregg Smith and Robert P. Burton, "The Effective Presentation of n-Dimensional Data Using Parallel Axes Graphics, Journal of Imaging Technology, Vol. 17, No. 5, December 1991, pp. 259-268.
  
  
• Eric Jon Magleby, Robert P. Burton and Del T. Scott, "Parallel Axes Graphics Techniques for the Analysis of Multivariate Data," Journal of Imaging Science, Vol. 35, No. 6, November/December 1991, pp. 394-397.
  
  
• Elizabeth Cluff, Robert P. Burton and William A. Barrett, "A Survey and Characterization of Multidimensional Presentation Techniques," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 142-153.
  
  
• Donald B. Curtis and Robert P. Burton, "A Comparison of Parallel Axes Graphics and Binocular Parallax Graphics," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 154-156.
  
  
• Scott A. Carey and Robert P. Burton, "Shading the Fourth and Higher Dimensions," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 157-164.
  
  
• Gary L. Bringhurst and Robert P. Burton, "Raytracing in Four-dimensional Space," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 165-167.
  
  
• Donald B. Curtis, Robert P. Burton and Douglas M. Campbell, "Parallel Axes Geometry for n-Dimensional Computer Graphics," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 168-175.
  
  
• Donald B. Curtis, Robert P. Burton and Douglas M. Campbell, "An n-Dimensional Line Intersection Algorithm," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 175-177.
  
  
• Paul L. Isaacson and Robert P. Burton, "An n-Dimensional Object Intersection Algorithm," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 177-181.
  
  
• Elizabeth Cluff, Robert P. Burton and William A. Barrett, "Characterization and Categorization of Higher Dimensional Presentation Techniques," Proceedings, 1990 SPIE/SPSE Symposium on Electronic Imaging Science and Technology, pp. 83-96.
  
  
• Donald B. Curtis and Robert P. Burton, "Parallel Axes Graphics Using Lincoln's Log Method as an Alternative to Binocular Parallax Graphics," Proceedings, 1990 SPIE/SPSE Symposium on Electronic Imaging Science and Technology, pp. 172-181.
  
  
• William P. Armstrong and Robert P. Burton, "Perspective and Stereo for Projection from and Presentation of Higher Dimensional Information," Proceedings, 1990 SPIE/SPSE Symposium on Electronic Imaging Science and Technology, pp. 54-61.
  
  
• Robert P. Burton, "Raster Algorithms for Cartesian Hyperspace Graphics," Journal of Imaging Technology, XV, 2, April 1989, pp. 89-95.
  
  
• Robert P. Burton, "Algorithms and Display Techniques for Four-dimensional Cartesian Graphics," Proceedings, SPSE's International Symposium and Exposition on Electronic Imaging Devices and Systems '88, pp. 95-102.
  
  
• Scott A. Carey, Robert P. Burton and Douglas M. Campbell, "Shades of a Higher Dimension," Computer Graphics World, X, 10, October 1987, pp. 93-94.
  
  
• Donald B. Curtis, Robert P. Burton and Douglas M. Campbell, "An Alternative to Cartesian Graphics," Computer Graphics World, X, 6, June 1987, pp. 95-98.
  
  
• K. Victor Steiner and Robert P. Burton, "Hidden Volume Removal in Four Dimensions," Computer Graphics World, X, 2, February 1987, pp. 71-74.
  
  
• William P. Armstrong and Robert P. Burton, "Perception Cues for n Dimensions," Computer Graphics World, VIII, 3, March 1985, pp. 11-28.
  
  
• Paul L. Isaacson, Robert P. Burton and Douglas M. Campbell, "Presentation of Hypothesized 4-D Phenomena," Computer Graphics World, VII, 8, August 1984, pp. 48-63.
  
  
• Mei-chi Liu, Robert P. Burton and Douglas M. Campbell, "A Shadow Algorithm for Hyperspace," Computer Graphics World, VII, 7, July 1984, pp. 51-59.
  
  
• Robert P. Burton and David R. Smith, "A Hidden-Line Algorithm for Hyperspace," SIAM Journal on Computing, XI, February 1, 1982, pp. 71-80.
  
  
• Robert P. Burton and Bruce F. Webster, "Some Thoughts on Higher-dimensional Realms," Brigham Young University Studies, XX, 3, Spring 1980, pp. 281-296.
  
  
  

Other Computer Graphics Papers

• Barton T. Stander, Thomas W. Sederberg, Robert P. Burton and Guojin Wang, "Approximating Rational Surfaces Using Polynomial Surfaces, " CADDM, Computer Aided Drafting, Design and Manufacturing, Vol. 3, No. 2, December 1993, pp. 1-7.
  
  
• Geoffrey S. Slinker and Robert P. Burton, "The Generation and Animation of Random Dot Autostereograms," Journal of Imaging Science and Technology, Vol. 36, No. 3, May/June 1992, pp. 260-267.
  
  
• Brent J. Hale, Robert P. Burton, Dan R. Olsen and W. Douglas Stout, "A Three-Dimensional Sketching Environment Using Two-Dimensional Perspective Input," Journal of Imaging Science and Technology, Vol. 36, No. 2, March/April 1992, pp. 188-195.
  
  
• Jerome A. Broekhuijsen, Robert P. Burton and William A. Barrett, "Interactive Editing of Volumetric Objects with 3D Input and Output Devices," Journal of Imaging Technology, Vol. 17, No. 5, December 1991, pp. 269-274.
  
  
• Rodney O. Davis and Robert P. Burton, "Free-Form Deformation as an Interactive Modeling Tool," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 181-187.
  
  
• Alan E. Richardson, Robert P. Burton and William A. Barrett, "A Volumetric System for Interactive Three-Dimensional Design," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 188-194.
  
  
• Sidney M. Petersen, William A. Barrett and Robert P. Burton, "A System for Automated Interpolation and Visualization of Height Grids from Contour Images," Journal of Imaging Technology, Vol. 17, No. 4, August/September 1991, pp. 195-200.
  
  
• Robert P. Burton, "Graphics system software - a scholarly approach," Computer-Aided Design, Vol. 22, No. 4, May 1990, p. 253.
  
  
• Sidney M. Petersen, William A. Barrett and Robert P. Burton, "A New Morphological Algorithm for Automated Interpolation of Height Grids from Contour Images," Proceedings, 1990 SPIE/SPSE Symposium on Electronic Imaging Science and Technology, pp. 62-72.
  
  
• Alan E. Richardson, Robert P. Burton and William A. Barrett, "Sculptbox - a Volumetric Environment for Interactive Design of 3D Objects," Proceedings, 1990 SPIE/SPSE Symposium on Electronic Imaging Science and Technology, pp. 198-209.
  
  
• Robert P. Burton, "Advanced University Courses in Computer Graphics," Computer-aided Design, XXI, 2, March 1989, pp. 116-119.
  
  
• Dan R. Olsen Jr. and Robert P. Burton, "Structured Files for Interactive Graphics Programs," Proceedings, Seventh Annual Information Systems Education Conference, October 29-30, 1988, pp. 194-197.
  
  
• Robert P. Burton, "First University Course in Computer Graphics," Computer-aided Design, XX, 9, November 1988, pp. 566-568.
  
  
• Brent J. Hale and Robert P. Burton, "Extending 2D to 3D," Computer Graphics World, XI, 5, May 1988, pp. 75-78.
  
  
• Bennett W. Anderson and Robert P. Burton, "Computer Graphics Curricula: A Survey of Ph.D. Granting Departments," Computer Graphics, April 1988, pp. 94-98.
  
  
• Judith R. Brown, Robert P. Burton, Steve Cunningham and Mark Ohlson, "Varieties of Computer Graphics Courses in Computer Science," SIGCSE Bulletin, XX, 1, February 1988, p. 313.
  
  
• Robert P. Burton, Shawn C. Becker, Jerome A. Broekhuijsen, Brent J. Hale and Alan E. Richardson, "Advanced Concepts in Device Input for 3D Display," Proceedings, SPSE's International Symposium and Exposition on Electronic Imaging Devices and Systems '88, pp. 59-63.
  
  
• Bennett W. Anderson and Robert P. Burton, "Changing Curricula - on Computer Science," Computer Graphics World, X, 9, September 1987, pp. 72-78.
  
  
• Thomas H. Taylor and Robert P. Burton, "An Icon-based Graphical Editor," Computer Graphics World, IX, 10, October 1986, pp. 77-82.
  
  
• K. Brook Richan and Robert P. Burton, "A Voice-driven Graphics System," Computer Graphics World, VII, 4, April 1984, pp. 89-90.
  
  
• Robert P. Burton and Ivan E. Sutherland, "TWINKLEBOX:  A Three-dimensional Computer Input Device," AFIPS Conference Proceedings, 1974 National Computer Conference, July 1974, XLIII, pp. 513-520.  Also Bell Laboratories Technical Memorandum TM-74-5161-3, July 1974.
  
  
• Robert P. Burton, Real-time Measurement of Multiple Three-dimensional Positions, University of Utah Computer Science Technical Report UTEC-CSc-72-122, June 1973.
  
  
• Robert P. Burton, Real-time Measurement of Multiple Three-dimensional Positions Technical Manual, University of Utah Computer Science Technical Manual TMAN-73-01, June 1973.
  
  
• Robert E. Stephenson and Robert P. Burton, "Computer Animation of Halftone Images for the Display of Calculated Molecular Motion and Structure," Proceedings of the Purdue 1971 Symposium on Applications of Computers to Electrical Engineering Education, April 26-28, 1971, pp. 118-120.
  
  
  

Information Primary and Transborder Data Flow Papers

• Robert P. Burton and Roger D. Malmrose, "Impact of Privacy Laws on Religious Bodies," Transnational Data and Communications Report, X, 6, June 1987, pp. 5-9.
  
  
• Robert P. Burton and Roger D. Malmrose, "The Effects of Recent Privacy Laws on the Rights of Deceased Persons," Transnational Data Report, VII, 4, July/August 1984, pp. 237-242.
  
  
• Robert P. Burton, "Two Pieces of the Puzzle:  Religious and Racial Information in Safe Contexts for International Cooperation with Regard to TDF," Intergovernmental Bureau for Informatics Second World Conference on Transborder Data Flow Policies, Conference Publication, June 26-29, 1984.
  
  
• Roger D. Malmrose and Robert P. Burton, "The Geostationary Orbit and Radio Spectrum Allocation:  A Priori vs. A Posteriori," Transnational Data Report, VI, 7, October/November 1983, pp. 401-404.
  
  
• Robert P. Burton and Roger D. Malmrose, "International Information Regulation," Proceedings, IEEE International Conference on Computer Design, October 31 - November 3, 1983, pp. 6-9.
  
  
• Robert P. Burton, "Nonregulation of the Private, Noncommercial Sector," Intergovernmental Bureau for Informatics World Conference on Transborder Data Flow Policies, June 23-27, 1980, summarized in the Final Proceedings, Red Series, Conference Documents, Conf./02.1 October 1980, p. 63.
  
  
• Robert P. Burton, "Transnational Data Flows:  International Status, Impact, and Accommodation," Data Management, XVIII, 6, June 1980, pp. 27-34.
  
  

Other Computer Science Papers

• Gary L. Bringhurst, Robert P. Burton and Ira E. Heiney, "A Corporate University Level Computer Science Program," Proceedings, Sixth Annual Information Systems Education Conference, October 31 - November 1, 1987, pp. 297-300.
  
  
• Kevin T. Cragun, Robert P. Burton and Val S. Judd, "A First Course for Retraining Corporate Employees for Careers in Computer Programming," Proceedings, Sixth Annual Information Systems Education Conference, October 31 - November 1, 1987, pp. 301-304.
  
  
• Michelle M. Pfister, Robert P. Burton, Douglas M. Campbell and Larry C. Christensen, "A University Computer Science Course for Advanced High School Students," Proceedings, Sixth Annual Information Systems Education Conference, October 31 - November 1, 1987, pp. 361-364.
  
  
• Dan R. Olsen Jr. and Robert P. Burton, "A Command-based User Interface Management System," Proceedings, Second International Conference on Computers and Applications, June 23-27, 1987, pp. 344-349.
• Kirk L. Malmrose and Robert P. Burton, "File Processing and the Undergraduate Computer Science Curriculum," Proceedings, Eighteenth Annual SIGCSE Technical Symposium, February 19-20, 1987, pp. 330-335.
  
  
• Kirk L. Malmrose and Robert P. Burton, "'Data Files and Databases' and the Undergraduate Computer Information Systems Curriculum," Proceedings, Fifth Annual Information Systems Education Conference, October 25-26, 1986, pp. 65-68.
  
  
• Thomas H. Miller and Robert P. Burton, "Dynamics in the Evolution of a Standard for Reusable Elementary Function Programs," Proceedings, Computer Standard Conference 1986, May 13-15, 1986, pp. 50-53.
  
  
• Robert P. Burton and Douglas M. Campbell, "A Curious Recursive Function," International Journal of Computer Mathematics, XIX, 3/4.
  
  
• Cheryl M. Black, Robert P. Burton and Thomas H. Miller, "The Need for an Industry Standard of Accuracy for Elementary Function Programs," ACM Transactions on Mathematical Software, X, 4, December 1984, pp. 361-366.
  
  
• Robert O. French, Robert P. Burton and Armin P. Langheinrich, Computerized Identification of X-ray Diffraction Patterns, Kennecott Copper Corporation WMD Research Department Report No. 69-15, December 31, 1969.
  
  
  

Teaching Experience

• Introduction to Computer Programming
  
  
• Computer Programming
  
  
• Prolog and Expert Systems
  
  
• Discrete Mathematics
  
  
• Digital Logic Design
  
  
• Control Structures
  
  
• Data Abstraction
  
  
• Information Structures
  
  
• Algorithms and Data Structures
  
  
• Algorithmic Analysis
  
  
• File Processing
  
  
• Computer Architecture
  
  
• Seminar in Computer Science Topics
  
  
• List and String Processing
  
  
• Computer Graphics
  
  
• Advanced Computer Graphics
  
  
• Security and Privacy
  
  
  

Master's Theses

• John D. Melville, "A Description of the Mandelbrot Set as an Infinite Set of Geometric Objects, April 1998
  
  
• Val G. Cook, "Simultaneous Rendering and Collision Detection of Autonomous Objects in a Distributed Architecture," August 1995.
  
  
• Mark D. Stevens, "Computer Graphics Emulation of M.C. Escher Single Frame Migration Characteristics," November 1994.
  
  
• Ning Xie, "Bezier Curves in Parallel Planes Coordinates," August 1994.
  
  
• Ping J. Xun, " Parallel Volumes Coordinates for Hyperdimensional Computer Graphics," January 1993.
  
  
• Geoffrey Slinker, "Inbetweening Using a Physically Based Model and Nonlinear Path Interpolation," October 1992.
  
  
• Barton T. Stander, "An Examination of Hybrid Curves and Surfaces," August 1992.
  
  
• James N. Wadley, "Representation and Display of Hyperdimensional Objects Using Sphyxel Trees," April 1992.
  
  
• Xiaoxi Tan, "Parallel Planes Coordinates for Hyperdimensional Computer Graphics," November 1991.
  
  
• Eric Jon Magleby, "Parallel Axes Graphics Techniques for the Analysis of Multivariate Data," August 1990.
  
  
• Jerome A. Broekhuijsen, "Combining 3-D Input Tools with 3-D Output Tools to Create an Interactive Environment for Editing Primitive Volumetric Objects," April 1989.
  
  
• Glendon R. Whiteley, "Representing n-dimensional Hyperplanes Using Parallel Axes Computer Graphics: a Demonstration Using Linear Programming," April 1989.
  
  
• Alan E. Richardson, "Sculptbox: a Volumetric Environment for Interactive Design of Three-dimensional Objects," April 1989.
  
  
• Elizabeth Cluff, "A Characterization and Categorization of Higher Dimensional Presentation Techniques," June 1988.
  
  
• Gary L. Bringhurst, "Hyperdimensional Imagery: the Raytracing of Hyperobjects," December 1987.
  
  
• Brent J. Hale, "A Three-dimensional Sketching Environment Using Two-dimensional Perspective Input," December 1987.
  
  
• Scott A. Carey, "A Four-dimensional Shading Model," August 1987.
  
  
• Rodney O. Davis, "Free-form Deformation as a General Purpose Modeling Tool," December 1986.
  
  
• G. Gregg Smith, "The Effective Presentation of n-dimensional Data Using Parallel Axes Graphics," December 1986.
  
  
• K. Victor Steiner, "Hidden-volume Elimination in Four Dimensions," April 1986.
  
  
• Donald B. Curtis, "The Design of a Parallel Axes Graphics Software System," April 1986.
  
  
• Yih-Hang Han, "Complexity Analysis of Graph Coloring Algorithms," December 1985.
  
  
• Thomas H. Taylor, "An Icon-based Graphical Editor," August 1985.
  
  
• Paul L. Isaacson, "Computer Graphic Presentation of Hypothesized Four-dimensional Phenomena," August 1984.
  
  
• Mei-chi Liu, "A Four-dimensional Shadow Algorithm," August 1982.
  
  
• K. Brook Richan, "A Voice-driven Graphics System," December 1981.
  
  
• William P. Armstrong, "Hyperdimensional Graphics: The Computer Display of Objects in Hyperspace," December 1981.
  
  
• Robert D. Reeder, "The Presentation of Four-dimensional Scenes: A Visual Cue Approach," April 1980.
  
  
• Michael H. Forster, "A Method for Evaluating Graphical Instruction Sets," August 1979.
  
  
• Dan R. Olsen, Jr. "SKAPL: A Semantically Extendable Programming Language," April 1978.
  
  

Honor Societies

• Eta Kappa Nu (Electrical Engineering)
  
  
• Phi Kappa Phi (General Scholarship)
  
  
• Pi Mu Epsilon (Mathematics); former Vice-Director, Utah Alpha Chapter
  
  
• Sigma Xi (Research)
  
  
• Tau Beta Pi (Engineering)
  
  
• Upsilon Pi Epsilon (Computer Science); Charter Faculty Advisor, Utah Alpha Chapter