Graph It On The Atari
John Malcolm Neil
Portland, OR
One application for which the Atari is suitable is drawing accurate plots and graphs. With a minimum of programming effort, one can create graphs of any function — a handy aid for algebra and trigonometry homework.
The following listing is a 2K program to plot functions in graphics mode eight. It will run on either the Atari 400 or 800, providing that you have at least 16K of memory. A major feature of the program is that the user can look at any part of the Cartesian plane. One is not limited to the range of the graphics mode (320×160) when making graphs.
Line 500 sets the default limits for the range and domain of the function:
-20 < x < 20, -10 < y < l0
This region is the user's window on the coordinate plane. To change these values, enter your own window when the computer prints "WINDOW?" in the form:
x1, x2, y1, y2
Where x1 and x2 are the minimum and maximum range, and y1 and y2 are the minimum and maximum domain.
To use the default values, just press RETURN.
The prompt "INTERVAL?" asks you to enter the interval at which to draw the tic marks. The default values are set in line 500 to one.
Enter the interval in the form:
x1, y1
Where x1 is the interval on the x-axis, and y1 on the y-axis.
Press RETURN to use the default values.
The relative positions of the x and y axes are drawn in lines 600-700; lines 800-890 draw the tic marks. The actual plotting of the function (lines 1000-1080) is rather unimpressive. The total range (Y2-Y1) is divided into 320 points, and the value at each is plotted. Should an error occur (divide by zero, cursor out of range), the program skips over that point.
Line 1030 contains the function to be graphed.
To graph another, simply change it to read:
FUNCTION = (your function)
Any variables in it must be "X".
Now you are ready to graph! Try the functions in Appendix E for starters, and this one:
1030 FUNCTION = PEEK(53279)
Press some of the console keys (START, SELECT, OPTION). Wow!
A few words of warning — functions like f(x) = 0 will not be visible because the x-axis is drawn on zero. Also, if it is essential that your graph not be distorted, make sure that the range is twice the domain.
One idea I have for improvement is to couple this program with a machine language routine to dump the screen to a printer. I'm working on that one right now. In the meantime, happy graphing!
400 GRAPHICS 0 410 REM *** INITIAL CONSTANTS *** 500 X1 = -20 : X2 = 20 : Y1 = 10 : Y2 = 10 : XIN = 1 : YIN = 1 510 LIST 1030 520 PRINT "WINDOW (X1, X2, Y1, Y2)"; 530 TRAP 550 540 INPUT X1, X2, Y1, Y2 545 IF X2 - X1 = 0 OR Y2 - Y1 = 0 THEN 520 550 PRINT CHR$(125) ; "INTERVAL (X AXIS, Y AXIS)"; 560 TRAP 590 570 INPUT XIN, YIN 580 IF XIN < = 0 OR YIN <= 0 THEN 550 590 GRAPHICS 8 : SETCOLOR 2, 0, 0 : SETCOLOR 1, 0, 10 : COLOR 1 : POKE 752, 1 595 REM *** DRAW AXES *** 600 XTOP = Y2/(Y2 - Y1) * 159 610 IF Y2 < 0 THEN XTOP = 0 620 IF Y1 > 0 THEN XTOP = 159 630 YSIDE = ABS(X1)/(X2 - X1) * 319 640 IF X1 > 0 THEN YSIDE = 0 650 IF X2 < 0 THEN YSIDE = 319 700 PLOT 0, XTOP : DRAWTO 319, XTOP : PLOT YSIDE, 0: DRAWTO YSIDE, 159 710 REM *** DRAW TIC MARKS *** 800 TIC1 = XTOP - 1 * (XTOP > 0) : TIC2 = XTOP + 1 * (XTOP < 159) 810 FX = INT(X2/XIN) * XIN 820 XV = (FX - X1)/(X2 - X1) * 319 : IF XV < 0 THEN 850 830 PLOT XV, TIC1 : DRAWTO XV, TIC2 840 FX = FX - XIN : GOTO 820 850 TIC1 = YSIDE - 1 * (YSIDE > 0) : TIC2 = YSIDE + 1 * (YSIDE < 319) 860 FY = INT(Y2/YIN) * YIN 870 YV = (Y2 - FY)/(Y2 - Y1) * 159 : IF YV > 159 THEN 1000 880 PLOT TIC1, YV : DRAWTO TIC2, YV 890 FY = FY - YIN : GOTO 870 900 REM *** GRAPH FUNCTION *** 1000 PRINT CHR$(125) : LIST 1030 1005 TRAP 2000 1010 C = 0 : FLAG = 1 1020 FOR X = X1 TO X2 STEP (X2 - X1)/319 1030 FUNCTION = SIN(X) 1040 IF FLAG THEN PLOT C, (Y2 - FUNCTI0N)/(Y2 - Y1) * 159 : FLAG = 0 : GOTO 1060 1050 DRAWTO C, (Y2 - FUNCTION)/( Y2 - Y1) * 159 1060 C = C + 1 1070 NEXT X 1080 POKE 752, 0 : GOTO 520 1090 REM *** ERROR HANDLER *** 2000 TRAP 2000 : FLAG = 1 2010 GOTO 1060