# Efficient Raster-Graphing of Bivariate Functions by Incremental Methods

• Wolfgang G. Kramarczyk
Conference paper
Part of the NATO ASI Series book series (volume 40)

## Abstract

The graph of a bivariate function z=f(x,y) is a surface in a three-dimensional space. Suppose that we have ascribed discrete intensities or pseudo-colors i=1,2,..,ncolors to the graph in such a manner that
$$i(x,y) = l + \left[ {\frac{{f(x,y) - b}}{{\Delta z}}} \right],$$
where [ ] means the nearest integer function, Δz is a positive discretization step and b is a lower bound of f(x,y) on a rectangle with opposite corners at (xmin,Ymin) and (xmax,Ymax). i=0 is reserved for the background color. Suppose further that we have sampled these intensities on a grid (xk,y1), where
$$\begin{array}{*{20}{c}} {{x_k} = {x_{\min }} + k\Delta x{\text{ }},k = o,1, \ldots ,{n_{cols}} - 1,{\text{ }}\Delta x = \frac{{{x_{\max }} - {x_{\min }}}}{{{n_{cols}} - 1}},} \\ {{y_1} = {y_{\min }} + 1\Delta y{\text{ }},1 = o,1, \ldots ,{n_{rows}} - 1,\Delta y = \frac{{{y_{\max }} - {y_{\min }}}}{{{n_{rows}} - 1}},} \end{array}$$
and stored them in a two-dimensional array. Such an array may be considered to be a raster-image of the graph viewed from the top. Let us call it the source image.

### Keywords

Dinates Spectrophotometry Cond Photography Verse

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### References

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