1. A machine for producing a rendering of a line graph onto a display medium comprising: (a) a display medium for displaying a rendering of the graph for viewing by user; (b) a data storage device which is able to store information describing the location in graph space of various graph points, axis domains, tick axes, tick values, bounding rectangles; and (c) a controller capable of rendering images onto said display medium; (d) a plurality of tick value spacings stored in said data storage device; (e) means for mapping from locations in graph space to corresponding locations upon said display medium; (f) means for collecting a first coordinate value and a second coordinate values of each of a plurality of graph points and storing the coordinate values into said data storage device; (g) means for determining the locations in graph space of a first boundary line and a second boundary line of each of a plurality of nonoverlapping axis domains and storing data describing said locations into said data storage device; (h) means for calculating a position of each of a plurality of tick axes and storing into said data storage device data associating each of said positions in one to one relation with said axis domains such that said tick axes are parallel to the boundary lines of said axis domains; (i) means for partitioning said graph points into subsets comprising: (1) means for retrieving said first coordinate value for each of said graph points from said data storage device; (2) means for determining within which of said axis domains said graph point is located by comparing said first coordinate with said locations of said first boundary line and said second boundary line of one or more of said axis domains; (3) means for storing data into said data storage device indicating which of said axis domains said graph point lies within; (j) means for selecting a font size suited to rendering tick labels on said display medium; (k) means for selecting a tick spacing conducive to legible rendering of adjacent tick labels; (l) means for composing a set of tick values for each of said axis domains whereby for each of said graph points within each of said axis domains, the smallest multiple of said tick spacing larger than said second coordinate value of such graph points and the largest multiple of said tick spacing smaller than said second coordinate value of such graph points is placed into said set of tick values, as well as said second coordinate value of such graph points, if said second coordinate value is a multiple of said tick spacing; (m) means for computing a plurality of exclusion rectangles, each of said exclusion rectangles being associated with one of said axis domains; (n) means for determining which of said set of tick values should not be rendered onto said display medium; and (o) means for rendering comprising: (1) means for communicating information from memory; (2) means for mapping from information to display positions; and (3) means for rendering images representing values, lines, etc onto said display medium, whereby said rendering of said line graph is rendered onto said display medium in such a way that a person viewing said rendering can readily perceive the contour of said line graph and estimate the x and y values of said graph points.