Based on the depth-sorting hidden-line removal algorithm, new methods of producing silhouette and raised level-curve diagrams with the hidden-lines removed of single-valued functions of two variables are presented. An algorithm of generating accurate truncated representations over the z-axis of the same types of functions is also described. These methods are particularly advantageous when plotting multimodal functions, noisy data or penalized objective functions encountered in optimization problems. Since all the graphic operations are performed entirely in the 2D image-space, the methods presented are suitable for implementation in low memory hardware like hand-held calculators and field instruments.
Issue Section:
Technical Papers
1.
Kubert
, B.
, Szabo
, J.
, and Giulieri
, S.
, 1968
, “The Perspective Representation of Functions of Two Variables
,” J. ACM
, 2
, pp. 193
–204
.2.
Williamson
, H.
, 1972
, “Algorithm 420, Hidden-Line Plotting Program
,” Commun. ACM
, 15
, pp. 100
–103
.3.
Wright
, T. J.
, 1973
, “Two-Space Solution to the Hide Line Problem for Plotting Functions of Two Variables
” IEEE Trans. Comput.
, C22
, pp. 28
–33
.4.
Watkins
, S. L.
, 1974
, “Algorithm 483, Masked Three-Dimensional Plot Program With Rotations
,” Commun. ACM
, 17
, pp. 520
–523
.5.
Butland
, J.
, 1979
, “Surface Drawing Made Simple
,” Comput.-Aided Des.
, 11
, pp. 19
–22
.6.
Boese
, F. G.
, 1988
, “Surface Drawing Made Simple But Not too Simple
,” Comput.-Aided Des.
, 20
, pp. 249
–258
.7.
Sowerbutts
, W. T. C.
, 1983
, “A Surface-Plotting Program Suitable for Microcomputers
,” Comput.-Aided Des.
, 15
, pp. 324
–327
.8.
Gordon
, D.
, 2002
, “The Floating Column Algorithm for Shaded, Parallel Display of Function Surfaces Without Patches
,” IEEE Trans. Vis. Comput. Graph.
, 8
, pp. 76
–91
.9.
Foley, J. D., van Dam, A., Feiner, S. K., and Hughes, J. F., 1996, Computer Graphics: Principles and Practice Addison-Wesley, 651–656.
10.
Dayhoff
, M. O.
, 1963
, “A Contour-Map Program for X-ray Crystallography
,” Commun. ACM
, 6
, pp. 620
–622
.11.
Bourke
, P. D.
, 1987
, “A Contouring Subroutine
,” BYTE
, pp.
143
–150
.12.
Encarnacao, J. L., Lindner, R., and Schlechtendahl, E. G., 1990, Computer Aided Design: Fundamentals and System Architecture, Springer-Verlag, pp. 335–342.
13.
Thomas, A. L., 1997, “Contouring Algorithms for Visualization and Shape Modeling Systems,” in Visualization and Modeling (R. Ernshaw et al., eds.) Academic Press, pp. 99–175.
14.
Newell, M. E., Newell, R. G., and Sancha, T. L., 1972, “A Solution to the Hidden Surface Problem,” Proceedings of the ACM National Meeting, pp. 443–450.
15.
Hern, D., and Baker, M. P., 1997, Computer Graphics: C Version, Prentice-Hall, pp. 478–481.
16.
Patrikalakis
, N. M.
, 1993
, “Surface-to-Surface Intersections
,” IEEE Comput. Graphics Appl.
, 13
, pp. 89
–95
.17.
Simionescu, P. A., and Beale D., 2001, “A Software for Graphical Representation of Objective Functions,” Artificial Neural Networks in Engineering Conference (ANNIE), St. Louis, MO, November 4–7.
18.
Rogers, D. F., 1985, Procedural Elements for Computer Graphics, McGraw-Hill, 191–205.
19.
Lorensen
, W.
, and Cline
, H.
, 1987
, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm
,” Comput. Graph.
, 21
, pp. 163
–170
.20.
Nielson, G. M., and Hamann, B., 1991, “The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes,” Proc. of the IEEE Visualization Conference, pp. 83–90.
21.
Van Gelder
, A.
, and Wilhelms
, J.
, 1994
, “Topological Considerations in Isosurface Generation
,” ACM Trans. Graphics
, 13
, pp. 337
–375
.22.
Natarajan
, B. K.
, 1994
, “On Generating Topologically Consistent Isosurfaces From Uniform Samples
,” Visual Comput.
, 11
, pp. 52
–62
.23.
Brent, R. P., 1973, Algorithms of Minimization Without Derivatives, Prentice-Hall, New York.
24.
Anderson
, D. P.
, 1982
, “Hidden-Line Elimination in Projected Grid Surfaces
,” ACM Trans. Graphics
, 1
, pp. 274
–288
.25.
Kohl
, H. W.
, 1996
, “Hidden-Curve Algorithm for Correct Grid Surface Representation of Functions of Two Variables
,” Comput. Graphics
, 20
, pp. 243
–261
.26.
Simionescu
, P. A.
, and Smith
, M. R.
, 2000
, “Single Valued Functions Graphical Representations in Linkage Mechanisms Design
,” Mech. Mach. Theory
, 35
, pp. 1709
–1726
.27.
Simionescu, P. A., and Beale, D., 2002, “New Concepts in Graphic Visualization of Objective Functions,” Proceedings of The ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal, September 29–October 2.
28.
Patnaik
, L. M.
, Shenoy
, R. S.
, and Krishnan
, D.
, 1986
, “Set Theoretic Operations on Polygons Using the Scan-Grid Approach
,” Comput.-Aided Des.
, 18
, pp. 275
–279
.Copyright © 2003
by ASME
You do not currently have access to this content.
