# 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

Source Image Vertical Segment Horizontal Coordinate Bivariate Function Orthographic Projection
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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