Texas Instruments TI89 Developer Guide - Page 236

194 Chapter 17: Graphing 17.5. as described above. The only difference is that the backup screen and the graph reference flags in the variables are not cleared first. During graphing, each function is evaluated at every point that the trace cursor will fall on naturally to insure that the cursor will always be directly on the function when traced. To retain floating point accuracy when line clipping is necessary and when computing the values to use for the independent variable in each graph mode, the Window variables xmin, xmax, ymin, ymax, tmin, tmax, etc., are limited to 12 significant digits in the mantissa, while ∆x, ∆y, tstep, etc. use all 14 significant digits available in a floating-point number. VarStore automatically rounds values to 12 digits when storing to the min/max Window variables. The first x value plotted in function mode graphing is always xmin. The last x value will either be xmax or, if no trace point falls on xmax due to the value of xres, the first xres increment greater than xmax insuring that the graph of the function does not end before the edge of the screen. In the modes with an independent variable other than x, the first value is tmin, θmin, etc., and the final value is the last computed value for the independent variable that does not go beyond tmax, θmax, etc. Each segment of the graph is drawn as the functions are evaluated at every computed value of the independent variable. Either or both of the end-points of any segment may be outside the viewing window, so that line clipping is required. Line clipping involves interpolating using the given end-points and the viewing window variables. The system routine GrLineFlt performs all necessary clipping based on the Window variables, while drawing the line segment in the specified style. Most errors encountered while graphing will cause the graph to stop, leaving the dirty flag set so the graph will be regraphed the next time it is displayed. However, the errors FIRST_OVERFLOW, FIRST_ZERO_DIVIDE, FIRST_DOMAIN_ERR, ER_SINGULARMAT, and FIRST_UNREAL_ERR are ignored while graphing, merely causing the point where the error occurred to be skipped. The function is evaluated as usual at the next value of the independent variable and the dirty flag is not set. Graph Application Memory Usage In the RAM area set aside for system use, memory is permanently reserved for two GR_WIN_VARS structs, two sets of Window variables and graph format settings for all six graph modes, and two sets of table variables among other things, to insure that all data is available for two graph mode. During system initialization, the gr_active graph window is opened (although not displayed since the Home screen is shown at first) and its backup screen is created. The backup screen for this graph window is always large enough for a full screen graph, even if the calculator is later put into split screen mode. TI-89 / TI-92 Plus Developer Guide Not for Distribution Beta Version January 26, 2001