Simtel MSDOS 1992 June

home *** CD-ROM | disk | FTP | other *** search

/ Simtel MSDOS 1992 June / SIMTEL_0692.cdr / msdos / plot / plot61.arc / PLOTTER.DOC next >

Wrap

Text File | 1990-02-14 | 33.4 KB | 614 lines

Plotter Version 6.10 by Adrian Mariano Shareware and Support If you have problems with PLOTTER, I will help you. I am very interested in hearing any comments or suggestions you should have about it, especially bugs. If you find out about bugs, tell me about them. They will be fixed. If you find this program useful, PLEASE support my effort in further developing this program and other similar programs by sending me $15 to register your copy. If you register, you will receive your own personal registration number (that in itself is worth $15), my undying gratitude, and my vote for president (if you decide to run). Feel free to distribute unmodified copies of PLOTTER with this documentation. Send money and comments to: Adrian Mariano 2729 72nd Ave. SE Mercer Island, WA 98040 Or send comments to me at: theorem@blake.u.washington.edu Introduction. This is a program which was written to plot functions on the infamous color graphics adapter on IBM's or compatibles. It requires at least a CGA and makes use of a VGA if detected. It requires 190k if run with a CGA and 260k if run with a VGA. Operations. Invoke the program by typing PLOTTER at the command line. It will immediately display the main function entry screen. [I never got around to designing a cute opening screen]. You may now enter the functions you wish to plot. Enter each function, pressing return when done. Hit return again when done. The status box, in the lower right corner, displays the domain and range of the plot in the form of intervals, and the stepsize. Status -------------------------------- |X [-20,20] | |Y [-20,20] | |Stepsize: 320 Steps | -------------------------------- When entering functions, the default interval for the type of function selected is printed on the right. To change this interval, press the backtab key. Then enter the start of the interval, and press comma. Type in the end of the interval, and press enter. Press the letter I to get an infinity symbol. In both cases, you may press return to keep the old value. You will be returned to the end of your function, and may continue entering it. Once all functions are entered, press the enter key again. Plotting will proceed. If you desire to interrupt the plotting of a specific funtion, press the ESC key. The program will attempt to deal with discontinuities. When plotting is completed, the computer will beep and wait for you to hit a key. If you hit the ESC key, or the RETURN key, then you will be returned to the main menu. If you press the * key, then the screen will be printed on an Okidata printer. Otherwise a set of cross hairs will appear. A box will appear on the right which will indicate the X and Y coordinates of the cross hairs. Pressing the cursor keys will move the cross hairs in the appropriate direction. If you wish to change the unit of movement, which is also printed in the box on the right, use the plus and minus keys to increase or reduce it by a factor of ten. To exit the cross hair mode, press ESC. If you wish to print the screen on an Okidata printer, press * at any time during the operation. If you wish to plot the same set of functions again, on a different scale, then the rescale option may be invoked. Locate the cross hairs at one corner of the desired window for the replot, and hit the Ins key. If you wish to relocate that point, then pressing the Del key will remove it. Once Ins has been pressed, move the other corner of the box to the desired location, and press Ins again (or return) to initiate the replot. The entire set of functions will immediately be plotted again, at the new window setting. If you wish to plot the same set of functions at a larger scale, invoke the upscale option with Ctrl-PgUp. The window will be set at an integer value 5 times larger on both sides. The downscale, invoked with Ctrl-PgDn will plot the same functions on a window that has sides 1/5 the current sides to the nearest integer, with the same center as the current window. (If values are close to zero, they are not rounded.) Ctrl-End will replot a smaller window centered around the cross hairs. If you wish to replot with the current window and stepsize, then press Ctrl-Right Arrow. This key should be used in conjunction with Ctrl-S, Ctrl-R, and Ctrl-W which alter the stepsize, and window without replotting. Ctrl-Right, Ctrl-PgUp, and Ctrl-PgDn may be pressed before plotting has concluded. The Grid Ordinarily, the functin is plotted on a bare rectangle, with only the x and y axis. However, if you wish, you may add hatch marks or a grid pattern. To turn on hatch marks, wait until the function has been plotted, and press G. Hatch marks will appear on the screen. If you press G a second time, the hatch marks will be erased and a grid will appear. If you press G a third time, the grid will be erased. The state of the grid is remembered from plot to plot. Advanced Editing features PLOTTER prohibits the entering of illegal functions. It beeps if you attempt to enter an illegal character. The Left Arrow and Right Arrow will move the cursor left or right. The program will allow you to have illegal expressions to the right of the cursor, but if you try to include illegal characters in the function by using the Right Arrow, the program will complain. The Ins key will toggle insert mode. When insert mode is on, the cursor is half hight, and characters typed will be inserted into the function. When insert mode is off, each character typed will replace the character the cursor is on. The Del key may be used to delete the character the cursor is on, and the backspace key to delete the character before the cursor. Ctrl-End will delete everything from the cursor to the right, and ESC will delete the entire function. Alt-N (Nuke) will delete all the functions. The Alt-B (Backup) key is similar to Alt-N. It will delete all functions and return you to the previous function plot. This is useful if you accidentally clear a function. The Home key will move the cursor to the first character of the function, and the End key will move it to the last, or to the first illegal character. Pressing Enter when you are not at the end of a function will either accept the function, or position the cursor on the first illegal character. If the function contains more open parenthesis than close parenthesis, then the necessary number of close parenthesis will be added to the right of the cursor, with the first one on the cursor. The computer will issue a high pitched beep (different from the error beep) to inform you that parentheses were added. You may accept the parentheses by pressing enter again, or you may delete them by pressing Ctrl-End. If you wish to edit functions which are on the screen, press PgUp to move up one function and PgDn to move down one function. If the current function is not legal, both of these will place the cursor on the first illegal character rather than changing functions. Pressing PgUp when on the top function will place you on the bottom function, and pressing PgDn when on the last function will move you to the first. PLOTTER keeps a list of the previous eight functions you have entered. You may scroll through these functions by using the up and down arrows. (CED users will find this arrangement familiar.) You enter the variables by pressing O, R, X, or Y. PLOTTER determines what kind of function is being entered by looking at the first two characters. If the function starts with an O that is not followed by a =, then O will be the only legal character, and the function will be r=f(Theta). If you start with O=, then r will be the only legal entry, and the function will be interpreted as Theta=f(r). If you do not start with a variable, then X will be the only legal variable, and the function will be y=f(x). If you enter an illegal variable, it will be changed into the legal one. The following are allowed in functions: Addition: This is denoted by a plus sign [+] between the quantities to be added. Subtraction: This is denoted by a minus sign [-] between the two involved quantities Multiplication: This is denoted by an astrisk [*] between the two values to be multiplied. This asterisk may be omitted unless two numbers are being multiplied. Division: Denoted by a slash [/] between the involved numbers. Exponentiation (Y to the X): This is denoted by the caret symbol [^] between the involved numbers Roots: This is denoted by a backslash [displayed as a root symbol] between the involved numbers. [3\x is the cube root of x] The Sine function: This is denoted by an S in front of the quanitity to be sined. The Cosine function: This is denoted by a C The Tangent function: This is denoted by a T Hyperbolic functions are entered by hitting H after S, C, or T. Arc functions: The Arcsine, Arccosine, arctangent, Arc hyperbolic sine, arc hyperbolic cosine, and arc hyperbolic tangent functions can be obtained by pressing A before an S, C, or T. The Log [base 10] function: This is denoted by an L The Natural log function: This is denoted by an N The absolute Value function is denoted by the letter V (think Value) The greatest Integer function by the letter I (only permitted in Cartesian and polar functions) User defined function: This function is entered by hitting F, and can be set to any combination of the above (sorry, no recursive functions are allowed), and referred to whenever a function is requested. Press Ctrl-F to change the user function. It defaults to f(x)=x. Gamma function: Press G to get this function. The gamma function is the factorial function for real numbers. If x is a non-negative integer, gamma(x+1)=x! Bessel functions: The bessel functions of the first and second kinds with positive integer orders from 0-49 are supported. Press B, followed by J for the first kind, or Y for the second kind. Then type the order. Follow the order with the argument in parenthesis. Derivative: The derivative operator. Press D, and follow it with a function in parenthesis. Underflow error precludes nesting derivatives more than three times. The following constants are currently supported: Pi-This is denoted by the letter P. e -This is denoted by the letter E. The following are provided to facilitate function entry: F2 = ^2 Alt/Ctrl/Shift F2 = 2√ [ = ( F3 = ^3 Alt/Ctrl/Shift F3 = 3√ ] = ) F4 = ^4 Alt/Ctrl/Shift F4 = 4√ F1 = ^ These operations are given the following precedence: F,G,Bessel : Evaluated 1st, right to left ^, implicit * not before SCTLNIV : Evaluated 2nd, right to left S,C,T,L,N,I,V : Evaluated 4rd, right to left imlicit * before SCTLNIV : Evaluated 4th, left to right \ : Evaluated 5th, right to left explicit *,/ : Evaluated 5th, left to right + - : Evaluated last, left to right The \ function is evaluated with different precedence levels on each side to obtain meaningful interaction with the SCTLNIV functions. Example: Sin 2 \ Sin 3. This is evaluated as sin (2 \ sin 3). This complicated precedence system is designed to mimic standard algebraic notation as closely as possible. When in doubt, use parenthesis. If no parenthesis are used, the functions such as Sin and Cos extend until a *, /, + ,-, or another similar function. A root \ extends to the right until a *, /, +, or -. A ^ extends to the right until a Sin or Cos, unless that function is the first symbol after the ^. Division continues to the right until a *, +, -, or another /. Examples: Sin 2x = Sin (2x) Sin x^2 = Sin (x^2) 2x^2x^2x = 2*(x^(2*(x^(2x)))) Fx^2 = (F(x))^2 Sin 2x+3 = Sin(2*x) + 3 Sin 2x*x = Sin(2*x) * x Sin x Cos x = Sin(x)*Cos(x) Sin 2\Sin x Cos x = Sin(2\(sin(x)*cos(x))) 2\3\4 = 2\(3\4) 2^2Sin x = (2^2)*sin(x) 9/16x^2 = 9/(16*(x^2)) The plus or minus operator is also supported. Press Alt -, or Alt = to get a + or - symbol. You may include as many as you like in your functions, but it is not permitted in parametrics. There are four function entry modes: Cartesian/Polar mode, Parametric mode, Lame (with an accent on the e) mode, and Quad mode. Cartesian/Polar mode is the default. If you wish to switch to a mode, you must press the appropriate key. Cartesian : Alt-C Parametric: Alt-P Lame' : Alt-L Quad : Alt-Q If you wish to enter a Cartesian or polar equation, you just type it in. Cartesian inequalities are supported. Enter y>f(x), y<f(x), x>f(y) or x<f(y) to plot inequalities. If you wish to enter a curve defined parametrically, enter Parametric mode by pressing Alt-P. You must now enter the X function. All of the variable keys will produce a t. Once the X function is complete, press enter and key in the Y function. If you wish to plot a Lame' function, press Alt-L. Now you must enter the appropriate constants (a,n,b, and m in that order) to fit the following: n m | x | + | y | |---| - |---| =1 | a | | b | Once you have entered a and n, the cursor will be placed on a plus sign. Press enter to accept the plus sign, or press a minus sign to change it. To back up you may hit left when the cursor is already on the left of the field. You may press return to keep defaults. Quad mode is used to plot equations which fits the pattern: 4 4 3 4 2 4 4 4 4 3 3 3 2 3 3 3 4 2 3 2 ax y + bx y + cx y + dxy + ey + fx y + gx y + hx y + ixy + jy + kx y + lx y + 2 2 2 2 4 3 2 4 3 2 mx y + nxy + oy + px y + qx y + rx y + sxy + ty + ux + vx + wx + zx + C = 0 where the letters a-w, z, and C are constant coefficients. These equations are entered by pressing Alt-Q. The cursor, normally a solid block, will now have a Q in is. (Note that the cursor will always be a solid block unless it is at the end of the function) You may enter any legal quad. Do not enter the "=0" at the end. You must use F2-F4 to enter the superscripts. The standard ^ character is illegal after variables when in Quad mode. If you wish, you may 2 enter expressions such as (e^2Tan 17/2pi)x y, and these will be treated properly. However, the variables MUST be at the end. Note: It is possible to enter functions such as Theta=Tan r, and the result is QUITE fascinating. However, this results in a total loss of significance. It is not possible for an ANGLE to be infinite, so unless one is merely searching for pretty graphs, functions that limit to infinity on the plot interval should not be entered. If you use the up and down arrows to scroll through functions of different types than the current mode, the mode will be changed to match the new function except in the case of parametrics. If you are in parametric mode, you will stay in parametric mode even if you scroll to a function of a different type. These other functions will be adjusted to fit parametric mode. If you are not in parametric mode and scroll to a function which is, you will be placed in cartesian mode. Note that if you are in parametric mode and attempt to scroll to a Lame', you will stay in parametric mode, and a null function will be provided instead of the Lame', and that any occurences of the Gint function in the new expression will be deleted (since the Gint function is not permited in parametrics). Differential equations. To specify a differential equation of the form y'=f(x,y), start by typing y' and then continue the function. The boundary conditions are displayed in the form (x,y) and default to (0,0). To change them, press Tab. To specify a differential equation of the form y"=f(x,y,y') start by typing y" and then continue the function. The initial conditions are displayed in the form (x,y,y') and default to (0,0,0). Again, change them by pressing Tab. If you wish to solve a second order equation for y' press Alt-1. A y' will appear below the function. If you wish to plot y", then press Alt-2. A y" will appear below the function. Press Alt-0 to return to the standard mode where y is solved for. Entering constants. Whenever you need to enter a constant, you may use all the operations allowed in function input. Variables are not allowed. It is necessary to enter constants when changing the window size, plot interval, stepsize, and in Lame' functions. When entering a Lame', window size, or plot interval, pressing left arrow when on the first character of the number will move you to the previous number. (So if you meant to enter -4 for the start of a plot interval but accidentally entered -5, you could press left arrow and fix it.) Pressing the space bar at any time invokes the pop up calculator. You may enter an expression and have it evaluated for you. (If you enter 1/0 or 10000^10000, you will be rewarded by "ERROR.") Press any key and enter another expression. Finally, press enter on a blank line, or ESC to exit. Displaying of numbers PLOTTER attempts to display numbers with a floating point, showing all digits. When this is not possible, PLOTTER reverts to scientific notation, separating the two parts of a number with a space. For example, "-4 22" means -4*10^22. When displaying the coordinates of the cross hairs, a number will sometimes wrap around from the first line to the second. Changing the plotting parameters Ctrl-R, at any time, resets all plotting parameters to the default. However, if you wish to change these parameters to values other than the default, the pop up options residing on the control keys must be used. To change the stepsize, press Ctrl-S and then enter the desired number of steps. If asymtotes were not plotted properly, or the greatest integer function was not properly dealt with, increasing the number of steps should solve the problem. If the status box is not visible when Ctrl-S is pressed, it will be displayed. To change the window, press Ctrl-W. You must now enter a new domain and range. You may use either the comma or the enter key to separate the numbers or you may press ESC to return to where you left off. If you wish to go backwards, press the left arrow, and you will be permitted to edit values you have already entered. Note that these changes will not take effect as soon as they are entered. If you change the window while plotting is already in progress, the changes will be reflected on the NEXT plot. If you change the stepsize, then the change will manifest on the next function plotted. Graphics If you wish to force CGA mode or VGA mode (overriding the autodetection), invoke plotter with the desired mode as a parameter. "PLOTTER cga" will run in CGA mode even if a VGA is detected. (This saves you 65k of RAM!). "PLOTTER vga" will run in VGA mode even though you don't seem to have a VGA. If the default colors prove unsatisfactory, press Ctrl-C to rotate through the 16 foreground colors. If you have an EGA, press Ctrl-B to rotate through the 16 background colors. Help Press Ctrl-H to display a short summary of commands. Press any of the keys listed to obtain further information. Press Ctrl-H again to see the original display, or press return to exit the help. Error! Errors are unfortunately, unavoidable. This program tries to minimize all errors, and use convenient error handling. However, the language I am using does not allow decent handling of mathematical overflows. Should an overflow occur, an error window will open at the lower left corner of the screen and an error message will be displayed. You may then press a key to return to the main screen. Should another critical error occur, the same error box will open and you may press a key to abort to DOS. When entering functions, error messages are displayed on the line where the function was. If, in Quad mode you enter a variable expression which is not allowed, you will get an Illegal Variables Error. If you enter an illegal coefficient as in (1/0)xy then you will get a Bad Coefficient Error. If an error occurs when you are entering a number, then the same error box will open, and complain about the problem. You will be asked to press a key, and then reenter the number. This error will occur when you enter something that is not a number, or when you enter an unacceptable number. The underflow error is yet another problem. Unfortunately, I have no way to detect underflow errors. They will be evident in obviously incorrect 2 2 graphs. One example is x y -y+1=0. Plot this on the normal interval and the lower section of the graph is smooth. Now zoom in. Somehow, (0,0) gets into the graph, even though it doesn't work in the equation [1=0?]. One technique which can be effective in eliminating these errors is to increase or change the stepsize. Long and Tedious Version History 1.00 Original version 1.10 Error checking for numerical input added The bug with non-integer exponents was corrected The print screen to Okidata was added Functions can now be specified in terms of Y 1.40 The option to enter expressions for all numerical input was added The option to plot multiple functions The option to plot Lame' functions Critical error handling routines added The constants pi and e are suported The status window is now updated when the space bar is pressed only if scroll lock is in the right state The version number is now prominently displayed to avoid confusion 1.55 The status box now displays the correct value for the Y-Max The area for the status box is no longer erased after a function plot leaving the funny looking blank space The corners of the plot window are displayed at the edge of the window Functions involving e^x and a^-.5 and a^.5 will be plotted faster When you type S, C, O, N, A, or G the full name will be displayed Pressing the keypad keys while entering an expression no longer causes the expression to be replaced by a single letter If the plotting interval exceeds the windowsize, only the visible part will be plotted 2.00 Polar coordinates are now supported Parametric definition is now supported When entering expressions, illegal characters will have no effect Sinh and Cosh and Tan are now supported The program now will make a small beep when done plotting 2.10 The multiple function option works correctly now You can now enter polar coordinate functions in form r=f(Theta) ESC now exits function entering windows 3.00 Subtraction and unary negation now work properly The plotting routine was speeded up The 7 function buffer (obtained with the up arrow) was added The Cross hairs to locate specific points after a plot were added Cursor added on input Some cosmetic improvement was made in status box Input routines wouldn't accept some legal characters in previous versions The Okidata screen dump was greatly speeded up and improved 3.20 A bug in parametric plotting was removed The problem with the cross hairs was fixed The problem with the previous function buffer was removed. The entering of consecutive operations in functions was made illegal The handling of function errors was improved Error handling added for Lame' function 4.00 There is no constant plotting interval The plot one function selection was removed The interval may be explictly specified for each function Function keys 1 through 5 were defined The []'`O and R keys were defined to simplify function entry ESC no longer terminates. X does instead. Ctrl Home resets default window and stepsize values. The main menu and function plotting submenu were switched The Lame' function has been expanded The rescale option was added The status box now defaults to on 5.00 When )- occurs in expressions it is handled properly Up and down scaling added Full screen editing for functions Pop up calculator added Infinite intervals, and entering infinity Implied multiplication with parenthesis The bug which occured when the stepsize was set to a number of steps fixed Tanh function added All types of functions can be mixed The treatment of the crosshairs at the edge of the window was fixed A same size replot was added Implied multiplication added in front of unary functions The intervals for functions Theta=f(r) are now clipped Pop up stepsize adjustment Pop up window adjustment All menus removed Ctrl-X exits instead of X It is no longer possible to specify a specific stepsize Titles and numbers are printed with full sized lettering The quickline facility was added The status box was moved and is no longer optional Ctrl-R instead of Ctrl-Home resets window and stepsize values The extra "it" was removed from the error message The version number was changed to 5.00 Alt-X no longer enters a - Interval manipulation allowed for parametrics ESC was fixed to work properly Interval notation is used for inputing and displaying the window A dot is used for * It is no longer permitted to enter functions terminationg in an operation The unary + was added Quads were added Exponents are displayed properly Alt-C clears all functions 5.05 Arcsin, Arccos, and Arctan functions added Some bugs with roots display were fixed Alt-L no longer enters supercript 2 when in Lame' mode Popping calculator up during function entry no longer switches out of Quad and parametric modes Some bugs with interpreting Quad coefficients were removed New error messages added for Quads Memory use adjusted so that COMMAND.COM is no longer reloaded Numbers are displayed differently The default window was changed Ctrl-R doesn't reset stepsize 5.10 Alt-O doesn't exit the program anymore Alt-E doesn't function as Ctrl-R Alt-I doesn't call up window alter Alt-R doesn't change step size F3 doesn't produce = anymore The Arc in Arc functions is entered first Problem with parametric toggling fixed Binary operations after ( are no longer permitted The display of powers was changed and is now more reliable The calculator catches errors An overflow error no longer results in an abort to DOS 5.20 Functions are plotted as much as 30% faster Help screen added The Grid and hatch marks added Return can now be used to replot a region being inclosed with insert Lines that contain illegal expressions are now plotted correctly ESC must now be used to exit the Parametric, Lame', and Quad modes You can no longer invoke Parametric mode when on the last line The bug with Lame' and the function stack has been fixed You can no longer get ambiguous parametric intervals The cross hairs work properly when the range and domain are less than one and (0,0) is not included When a function error occurs, the function is redisplayed so you may backspace instead of retyping the entire function Typing functions like X= is no longer permitted 5.30 Precedence of evaluation changed Roots are now entered in the standard order Gint can no longer be specified in Parametric or Polar graphs Some negative roots of negative numbers were improperly evaluated A - can now directly preceed a unary operator (-Sin X) Display of functions fixed The bug which caused undefined functions such as ln and log to produce an overflow error was corrected. Ins, End, Left and Right Arrow, Del, Home, End, and Ctrl-End support added. The bug which caused the help screen to be corrupted if it was invoked for the second time after an error was fixed. Several bugs with input routines fixed Improved checking for illegal characters in input Lame' functions are cropped to specified interval 5.40 Quad mode expanded to include cubes and fourth powers ArcSinh, ArcCosh, and ArcTanh functions added A bug used to let you get three cursors on the screen at once Bug occuring when combined length of functions exceeded 80 characters fixed Bug occuring when a Quad started with Y is fixed Expressions such as X^2X^3 are now plotted properly If you recall a Quad with up or down arrow while in Parametric mode, the superscripts will be converted to work properly in non-Quad modes. Gint can't be included in Parametrics by up or down arrow Arc functions were displayed with a space after the arc Bug occuring when a Quad was of certain lengths is fixed Decimal point before non-numerals made illegal Extra occurences " or " when blank functions are plotted is fixed The bug causing the last function to be placed on the stack twice if eight functions were entered was fixed The F2-F4 keys will produce superscripts after X and Y in Quad mode Ctrl-Left and Ctrl-Right changed to PgUp and PgDn respectively The downscale (Ctrl-PgDn) will now scale below the interval [-1,1] Enter will close any outstanding parentheses and beep rather than producing the "Function error" message If you attempt to terminate a function with an operator the computer will beep rather than producing the "Function error" message If you attempt to close more parenthesis than you have opened, the computer will beep ESC clears the current function when in cartesian mode Comma can be used to separate numbers when entering intervals The user defined function was added The Ctrl-K color toggle was added 6.00 Alt-N clears all functions Alt-C selects cartesian mode from any other mode Help extended ESC clears the current line PgUp and PgDn are cyclic F1 set to ^ Parametrics are surrounded by angle brackets on the display The grid is now xored onto the function and can be removed Added +/- operation Added +/- option in Lame' Changed Tab to Backtab Intervals can be change from from within Lame' Lame' now plots correct graph for n<0 and m<0 Differential equations of the form y'=f(x,y) can be solved Differential equations of the form y"=f(x,y,y') with initial conditions can be solved Derivative operator added Various I/O bugs fixed Precedences of operations changed Loosened restrictions on operations in functions. Added gamma function Added bessel functions of the first and second kinds Greatest integer added to polar graphs Added cartesian inequalities Ctrl-End to rescale around cross-hairs 6.10 Alt-B Backup command added Fixed bug with quads and 4th powers Added support for VGA