Cream of the Crop 1

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GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 1 TO PRINT THIS FILE, TYPE "COPY GR.DOC PRN" AT THE DOS PROMPT. OVERVIEW -------- GRAPHITI is a mathematical function plotter, capable of displaying user-defined two-dimensional, three-dimensional, and polar functions, with the option of saving the output as a GIF file. GRAPHITI will work with any MS-DOS compatible computer with a CGA, Hercules, MCGA, EGA, VGA, or SVGA graphics adapter, and will take advantage of a math coprocessor if available. DISCLAIMER ---------- GRAPHITI is distributed on an "AS IS" basis without warranty, expressed or implied. Considerable testing effort has been expended, but the user is advised to check the program's suitability before relying on it. The user assumes full risk as to the results of using this program. Any liability of the author will be limited exclusively to product replacement. In no event shall the author be liable for any consequential damages arising from the use, or inability to use this program. REGISTRATION ------------ The unregistered version of GRAPHITI is freely distributable and fully functional, and may be used for a 30-day trial period. If you plan to continue using GRAPHITI after the trial period, you are obligated to pay the modest registration fee of $20. Registered users will receive the latest version of GRAPHITI with the "nag" messages removed, one free upgrade upon request, and half-priced subsequent upgrades. All registration information is contained in the REGISTER.TXT file. If that file is missing, register by sending a check or money order for $20 in U.S. dollars, drawn on a U.S. bank, to: Copy Con Incorporated PO Box 23255 Baltimore MD 21203-5255 We thank you for your support. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 2 OPERATION --------- GRAPHITI is activated from the command line, using the format GR expression [options] To stop a plot in progress, press any key, and the plotting will stop; another keypress will exit the program. Ctrl-Break will stop and exit immediately. EXPRESSIONS ----------- Expressions are mathematical formulas built with the supported functions, operators, constants and variables. Expressions must be in one of the following forms: x=f(y) 2-dimensional vertical Angles specified in radians y=f(x) 2-dimensional horizontal " " " " z=f(x,y) 3-dimensional " " " " r=f(p) Polar " " " degrees FUNCTIONS --------- Following are the functions that GRAPHITI supports: Function Description -------- ----------- abs Absolute value acos Arc cosine asin Arc sine atan Arc tangent ceil Smallest integer not less than input value (rounds up) cos Cosine cosh Hyperbolic cosine csc Cosecant ctn Cotangent cub Cube root exp E to the power of input value flr Largest integer not more than input value (rounds down) frac Fractional part of input value int Integer part of input value ln Natural logarithm log Natural logarithm (same as LN) logt Base 10 logarithm rand Random integer between 1 and input value (max 32767) sec Secant sgn Sign of input value (positive=1, negative=-1, zero=0) sin Sine sinh Hyperbolic sine sqr Square (x^2) sqrt Square root tan Tangent tanh Hyperbolic tangent GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 3 FUNCTIONS (continued) --------------------- Parentheses are optional when using functions; if they are not used, only the first value following the function will be considered the argument. For example: y=sin x is equivalent to y=sin(x) y=sin x/2 is equivalent to y=sin(x)/2 y=sin(x/2) is equivalent to y=sin(x/2) Use of functions without parentheses is potentially erroneous, and it is generally preferable to use parens to indicate function arguments. OPERATORS --------- Each operator has a precedence, and operators with higher precedence are evaluated before operators with lower precedence. Operators with equal precedence are handled from left to right within a function. Precedence is indicated by order in the following table (the first line has the highest precedence): Operators Description --------- ----------- ( ) Left parenthesis,Right parenthesis ! Unary factorial + - Unary sign ^ Exponential * / % Multiplication,Division,Modulus + - Addition,Subtraction Where it is not ambiguous, multiplication can be indicated by adjacency: 8(6-4) = 8*(6-4) = 16. Implicit multiplication is potentially erroneous, and it is generally preferable to use the '*' symbol to indicate multiplication. CONSTANTS --------- GRAPHITI supports numeric constants, as well as two alphabetic constants, PI and E. Alphabetic constants cannot directly follow functions; use "y=sin x" or "y=sin(x)", not "y=sinx". Numeric constants need not be separated from functions with spaces; "y=sin3" is okay. Numerical constants are entered just as you would ordinarily write them. They can be preceeded with optional + or - signs. The following are all valid numerical entries: 6.78 0.678 .678 -678 Blanks are not permitted in numbers; the expression "7 8" would be evaluated as 7 times 8, not 78. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 4 CONSTANTS (continued) --------------------- Alphabetic constants can be used as easily as real numbers; just be careful not to string them together with functions, variables, and other alphabetic constants; instead of "z=lnx+ypi", use "z=ln x + y pi", or "z=ln(x)+y*pi". "y=3pi/x" and "x=3e" are valid, as GRAPHITI can tell where one constant ends and another begins. Following are the approximate values of the alphabetic constants: PI = 3.14159265 E = 2.71828183 VARIABLES --------- The three variables (X, Y, and P) change value from their lower range to their higher range (with increments determined by the D and L options), and the function's value is plotted accordingly. Variables can be used in the following functions: Variable Functions -------- --------- X y=f(x), z=f(x,y) Y x=f(y), z=f(x,y) P r=f(p) The variables are plotted according to the functions they are used in: x=f(y), y=f(x) | z=f(x,y) | r=f(p) ---------------------|------------------------|-------------------- y | z -y(back) | r | | | / | | | | |/ | | -x ------+------ x | -x ------+------ x | r ------+------ r | | /| | | | | / | | | -y | (fore)y -z | r OPTIONS ------- Options must be in the form "OPTION:value[,value...]", as in "u:2" or "rx:-3,5". Case is not important. Separate options with spaces. Option Description ------ ----------- A Axis lines - determines whether the X- Y- and/or Z-axes will be drawn. Default is Y. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 5 OPTIONS (continued) ------------------- Option Description ------ ----------- C Color - the color of the plotted graph. Range is 0 thru the maximum amount of colors for the video screen. Default is 1 for a monochrome screen, 13 for a color screen. Colors are as follows: COLOR MONOCHROME Num Color Num Color --- ----- --- ---- 0 Black 0 Black 1 Blue 1 White 2 Green 3 Cyan 4 Red 5 Magenta 6 Brown 7 Light Grey 8 Dark Grey 9 Light Blue 10 Light Green 11 Light Cyan 12 Light Red 13 Light Magenta 14 Yellow 15 White For 3D graphs, the fill color and fill style can also be specified. Use the above chart for the fill colors (default is 0). Fill styles are as follows (default is 1): Num Style --- ----- 0 No fill (for see-thru graphs; plots faster) 1 Solid fill 2 Fill with --- 3 Fill with /// 4 Fill with ///, thick lines 5 Fill with \\\, thick lines 6 Fill with \\\ 7 Light hatch fill 8 Heavy crosshatch fill 9 Interleaving line fill 10 Widely spaced dot fill 11 Closely spaced dot fill D Dot resolution - number of pixels per scan line for 2D and polar graphs. Range is 1 thru 10; the amount of pixels will be 2^(D-1). Default is 1. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 6 OPTIONS (continued) ------------------- Option Description ------ ----------- FS GIF file save - GIF filename to save screen to after plotting. A pixel will appear on the right side of the current line being processed. When the pixel reaches the bottom, the screen has been saved; if any key is pressed before that time, the incomplete GIF file will be deleted. Default is none. L Line resolution - number of lines per unit for 3D graphs. Range is 1 thru 5; number of lines will be 2^(L-1). Default is 2. RP Range of P - low and high range of variable P in r=f(p). Ranges are any two numbers, as long as the low range is less than the high range. If only one number is entered, the range will be the negative value of the number to the positive value. Defaults are 0,360. RX Range of X - low and high range of variable X in y=f(x) and z=f(x,y). Low range is -15 times the unit value (see option U) to the high range. High range is the low range to 15 times the unit value. That can be expressed as: -15*U <= low range < high range <= 15*U If only one number is entered, the range will be the negative value of the number to the positive value. Defaults are -15,15. RY Range of Y - low and high range of variable Y in x=f(y) and z=f(x,y). Ranges and defaults: Graph Range (See option U) Defaults -------- --------------------------------------- -------- x=f(y) -10*U <= low range < high range <= 10*U -10,10 z=f(x,y) -15*U <= low range < high range <= 15*U -15,15 If only one number is entered, the range will be the negative value of the number to the positive value. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 7 OPTIONS (continued) ------------------- Option Description ------ ----------- S SVGA mode - type of Super VGA card in your system. Range is 0 thru 6, where: Num SVGA Card --- --------- 0 None 1 ATI 2 Orchid 3 Paradise 4 VEGA 5 Compro 6 SOTA This option does nothing unless VGA/SVGA is detected, but GRAPHITI cannot tell what type of SVGA card is present, so do not use the S option without the proper card. If you are not sure what type of video card you have, don't mess with the S option - you may do harm to your video system. Default is 0. T True graph - whether 2D and polar graphs will just display the plotted points (Y), or also attempt to draw connecting lines between them (N). Default is N. U Unit value - value of one unit (used for scaling). There are ten units from the center of the screen to the top, and the units are marked on the axis lines. Range is .0001 to 10000. Default is 1. ERROR MESSAGES -------------- Following are error messages you may come across, along with their descriptions and corresponding DOS errorlevels: Level Message & Description ----- --------------------- 1 Invalid command line options - GRAPHITI cannot understand your input. Functions must start with "X=", "Y=", "Z=", or "R=". Options must be in the form "OPTION:value[,value...]", as in "u:2" or "rx:-3,5". Don't type the quotes! Case is not important. 2 Graphics hardware not detected - either your computer is not equipped with a graphics adapter, or GRAPHITI cannot determine what type of adapter it is. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 8 ERROR MESSAGES (continued) -------------------------- Level Message & Description ----- --------------------- 3 Abnormal program termination - either we erred in trapping a math function, or the program has been corrupted somehow. (Please drop us a line describing everything that led up to this error, if you happen to come across it.) 4 Invalid function '(function)' - you have attempted to use an unsupported function. If it's a common function, let us know, and we will add it. 5 Invalid operator '(op)' - you have attempted to use an unsupported operator. If it's a common operator, let us know, and we will add it. 6 Mixmatched parentheses - either there were an uneven amount of parentheses, or a right paren was encountered before its matching left paren. 7 Invalid use of functions - functions cannot be directly followed by an operator (unless the operator is a "+" or "-" indicating the sign of the value that follows). 8 Invalid use of operators - operators cannot be directly followed by other operators (unless the second operator is a "+" or "-" indicating the sign of the value that follows). 9 Formula too complex - your function has 128 or more references to constants and variables. 10 Formula cannot reference itself - the function variable on the left side of the equals sign cannot be referred to on the right side (as in "y=sin y"). 11 Variable '(variable)' cannot be used in this function - function must be in the form "x=f(y)", "y=f(x)", "z=f(x,y)", or "r=f(p)". 12 Unable to open file '(file)' - the named GIF file cannot be opened for writing. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 9 EXAMPLES -------- GR y=sin x c:3 rx:0,10 displays a sine wave, using color #3 (cyan), and shows only the part of the graph where X falls between 0 and 10. GR x=tan(y) t:y d:4 displays a tangent wave using true graphing and a dot resolution of 4. If true graphing had been kept off, the asymptotes would have been displayed, and they are not an actual part of the tangent function. The resolution was increased so that more of the function points would be plotted. (The D option is generally not needed if true graphing is left off.) GR r=p u:360 rp:7200 a:n displays a polar graph with a unit value of 360 (meaning there are now 3600 units from the center of the screen to the top), showing all values where P >= -7200 and <= 7200 (since only one number was used for the range), and keeping the axis lines off. GR y=sqr abs cos x sgn cos x s:3 displays a 2D graph, using a Paradise SVGA card at 800x600. The function could also have been written as GR y=sqr(abs(cos(x)))*sgn(cos(x)) s:3 , either way is fine. BTW, the S option does nothing unless VGA/SVGA is detected, but GRAPHITI cannot tell what type of SVGA card is present, so do not use the S option without the proper card. If you are not sure what type of video card you have, don't mess with the S option - you may do harm to your video system. GR z=cos((x*x+y*y)/20) l:3 c:2,1,9 fs:3d_cos displays a 3D graph with a line resolution of 3 (l:3), in color #2 (green), with a fill color of 1 (blue), and fill style #9 (interleaving line fill). When finished, the screen will be saved to file 3D_COS.GIF (.GIF is appended by default). GR z=2sin(x*y/8) l:3 c:9,,0 displays a sine graph, with a fill style of 0 (no fill), which will produce a see-thru graph. A fill color was not specified, but it wouldn't have shown up anyway, due to the fill style. GRAPHITI V1.05 Copyright (c) 1991-1992 Copy Con Incorporated Page 10 CREDITS ------- GIF encoding routines based on code by David Rowley. SVGA driver written by John Sieraski. Much thankage to John "Catman" Lalmond and to Deborah Carey, the original beta-testers. CORRESPONDENCE -------------- If you have questions, comments, suggestions, bug reports, etc., feel free to contact us by one of the following methods: 1: By modem at The Programmer's Corner (301-596-7692 or 410-995-6873). Send a message to user number 3000, and check back in a couple of work days for a reply. 2: By U.S. Mail at the address given on the first page. If you would like a reply, please include a self-addressed, stamped envelope. We look forward to hearing from you.