Improved Display Methods of Single-valued Functions of Two Variables

[+] Author and Article Information
P. A. Simionescu

Auburn University, Department of Mechanical Engineering, 202 Ross Hall, Auburn University, AL 36849e-mail: pasimi@eng.auburn.edu

J. Comput. Inf. Sci. Eng 3(2), 136-143 (Jun 30, 2003) (8 pages) doi:10.1115/1.1576809 History: Received August 01, 2002; Revised March 01, 2003; Online June 30, 2003
Copyright © 2003 by ASME
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Grahic Jump Location
Family of curves seen as vertical projections of a waterfall diagram
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Construction lines for an oblique-projection diagram, defined inside a viewport OC4OC2
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Wireframe (a) and crosshatch (b) representations of Sf in oblique projection
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Two methods of drawing the function surface as lines of constant u: as band polygons (a) and as successive 4-side patches followed by the erasure of certain borderlines of the current patch (b)
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Sf drawn (a) as constant v polylines and (b) as raised level curves with the hidden-lines removed
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Truncated z-domain representations produced (a) with MATHEMATICA 4 (July 1999 release) and (b) with MATLAB 5.3.1 (October 1999 release)
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An accurate solution to the intersection problem also applicable to producing level curve diagrams
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Schematics for solving the intersection variant (1001)down (the meaning of the 1–8 numbers in the corners of the initial and secondary patch will be explained later in the text in connection with Fig. 10)
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Schematics for solving the intersection variant (0011)down
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Intersection variants of an initial four-sided patch (shown in white) with one of the cutting planes (secondary patches shown in black). The numbers in the corners show how the initially-coincident-vertex polygons change configuration by expanding or merging vertices.
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Combined intersections (0011)down+(0100)up (a) and (0011)down+(1100)up (b)—in the latter case the initial four-sided patch changes into a pentagon
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Combinations of the variants in which the upper and the lower cutting planes can intersect simultaneously the same initial patch P1P2P3P4 (the x-marks signify a possible double intersection with the upper and the lower cutting planes).
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Errors appearing (a) when ignoring the intersection variants (1010)* and (0101)* and (b) corrected representation obtained by deleting the segments shown in dashed-thick lines and drawing the transverse segments shown in thin lines in detail above
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Level curve diagrams produced (a) with SigmaPlot 2001 and (b) with MATLAB 6
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Same representation as in Fig. 14 with the bridge-like defects corrected, produced with a program that implements the theory presented in the paper
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The variant (1010)up occurring for a local minima of Sf
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Variant (1010)up* occurring for a local maxima of Sf
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Other projections obtained (a) by shearing an initial parallel oblique projection in the vertical direction, and (b) by generalization of the construction lines in Fig. 2
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A number of representations generated with the D_3D program that implements the theory presented in the paper  



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