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P10 `4 q8 q:8 q^8 8P+)P ]*P0+P@R-PP?/P`3Pp6Pq!7P$\<2<M==Q=Z=! >PY>U>8 :< :/ ;<'pKP'KPt'pLP~' LP' MP' NP' OP' ~PP'bQP'FRP'*SP'TPt'TPt'TPt'jUPt'UPt'RVPt'VPt':WPt)n#;*#t-130-1.11.1-13020.210.111011212MathGraph v2.2/U.A.R.K.1/MathPicts1a*sin(x)*exp(-abs(x/b)); place your comments heretsin(t) sin(x)*cos(y)0.21.51.52525  MathGraphics'(c) 1993 Utility Apfel Research KitchenMathGraphics v2.2 - by Dirk Frhling (c) 1993 Utility Apfel Research Kitchen Function Graphs: f(x); x(t), y(t)   ", ,,-  X-@-NnOoWw@SsDdQqZz@XxCcVv@112233@4455@@X@X@ File  Edit Graphics Color Plotter Windows About MathGraphics...NewOpen...Close Close AllQuickDraw PictureBitmapSave Save as... Page Setup...Print...QuitUndoCutCopyPasteClearPreferences...Choose Font...Draw...Function Value... Paired ValuesEnter Function(s)...Drawing Area...Axes & Grid... 320 x 100 640 x 200 640 x 400f(x) x(t), y(t)f(x,y) Activate... Deactivate Commands...Clean UpNo Open WindowP 2H8  IV0 OK I Vt0Cancel Function f(x):CtkP 8         /<;0 Zz Draw Value  >K;0  +;0 Compute   Function Value !7 x = $28 f(x) = * 0 0P 80 0001 0>K;00 Activate 0-:;00 ,0Activate HP-GL Plotter 1 111111 Connection 1 1Slot 11 1Slot 2P 8@ @@@@B B( @BBBBBBBBBBPen B BNo. 1B BNo. 2B BNo. 3B BNo. 4B BNo. 5B BNo. 6 @>K;0@ Send Text @-:;0@ ,@Send Plotter Commands@ <0@LBHello world!P 4JP PPPPPPP P P P P Per0 Pe=r0P PDraw Paired ValuesP !P P$;PQ P2~PQ P@~P Q PN PQ P$ / P P2 = P P@ K P Data File... x-Component 12345678910 y-Component  Radius  Angle Number Of Components Precision Polar Coordinates Transformation InterpolationMarksPPQQQ QPP Q Q Q QPPQQQ P PQQQQQQQQQQQ QQ QQ Q Q Q Q Q Q Q Q Q Q QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QP 8` ````ab `>K;0` OK `> Kn0`SsSave `>}K0` ,`Preferences a aa b# bbaaaabbbbbbbbStyle Digits a a Float Decimala a Fixed Decimalb b1b b2b b3b b4b b5b b6pppp p>K0pdD p>K0prR pQ^0peE pQ^0p Drawing Area Function RootExtremeCancelP 8xp P /H8q qqqqqqq qLY0 qL Yt0q qEnter Parameter Functionsq :qx(t) =q/ ::qy(t) =q<)tkq-<DtkP 8     2 @ !  ! " # $ Text ! ! Text Field" " f(x)# # x(t)$ $ y(t)% % f(x,y)  -:;0 OK  >K;0  , Draw Text  <0 MathGraphics23/Connection can't be established with LaserWriter/^Cancel23/Read-write Error on the LaserWriter/^Cancel23/Connection can't be established with ImageWriter/^CancelOKCancelYesNo+There are too many pictures in this window!Printer Error No. Scale drawing area?Loading PICT File...Loading Bitmap...Load which picture...Save picture as: Untitled.No Open Window This file type is not supported.Sorry, can't open more windows. ($15 fee)Saving the clipboard...Selected area:Text file with paired values:@:MathGr.prefs40/Save '*0' before closing?/Discard/Cancel/^Save42/The x values have to be monotone increasing due to interpolation./^Cancel42/The choosen x or y component is bigger than the number of components./^Cancel42/The choosen radius or angle component is bigger than the number of components./^Cancel22/Unknown error (*0)./^Continue42/Function values can only be computed for functions of the type f(x)./^Cancel43/The settings of the frontmost window have been saved as standard preferences./^OK42/The standard preferences could not be saved./^Cancel OKCancelAxesFrameCoordinate SystemCoordinate GridLabelsx-Axis:y-Axis:Grid Distance:x Marker Distance: Arrowheadsy Marker Distance: OK MathGraphics v2.2 - Operators: Functions: Constants: , Germany-Written using ORCA/Pascal, ORCA/C and ORCA/M, (c) 1984-93 The Byte Works, Inc.OKCancel Drawing Area Interval: Wrong entry.7The drawing interval has to be inside the drawing area.9Minimum must be >= 1 when drawing in a logarithmic scale.OKCancel Draw Function Constant A: Constant B: Constant C: Constant D:Precision (1..10):No function root found.Cannot reach accuracy.Function root at x = 'No extreme found - too many iterations. Maximum f( Minimum f( Draw ValueH#0__}_]uW__]}}]u}]}U}]}}U]}}u]}}_]uU__]}UU__U]]]____]}]_]_____]U_]__U_U_]U_]____U_]u]]__]}_]}uU__]}_}___ }__𰃃 }__𰃃 U]W U]W __U ;__U_ ;]u}__U_]uu_U}WW_}U}WUW_U_}u_UW__]u_]u__]}_]}_U_ ___ ???_???P??___Z   0<?????<< ???? ?????? ?ZUUU|UZUU|UU|ZU??? ?UUjUZU|UZUU|ZUU|U?_?? V?UVUVUVꪪꪩUU|UU?U_W?? U[?UUjUUVꪪꪩUUU?U_UW?? UU?UUUZꪥꪪꪥUZ?UUUU?? UW?U_UUꪩUꪪVUU?UUjU[?? S?U_UUꪩUU|ꪪUVUV?UVV?? ?_UZUU|UZUU|UZU|Uj=V?? ???? ????? ???? ???? ???? ???? ???? ??<???$D7 MathGraphics Version 2.2 Utility Apfel Research Kitchen Copyright (c) 1993 Dirk Froehling Oerlinghauser Weg 8 D-44149 Dortmund Germany Internet: dirk@gaga.maschinenbau.uni-dortmund.de -------------------------------------------------------------------- This program contains material from the ORCA/Pascal and ORCA/C Run-Time Libraries, copyright 1984-1993 by the Byte Works, Inc. Used with permission. -------------------------------------------------------------------- Introduction >>t  cp D#SW@T !"#$%&'()*+,-./0123456 MathGraphics does not run without System Software 6.0 or higher! And it must be copied by a program that supports extended files, e.g. the Finder. This program can be used to draw graphs of functions of the type f(x) or x(t)/y(t) and to draw paired values from text files. MathGraphics uses the standard IIGS graphical interface. The computed graphs are QuickDraw pictures which can be imported into DTP programs like AppleWorks GS, manipulated and printed at any resolution. MathGraphics saves the function, the drawing area etc. as a resource together with the drawing. You can also use a HP-GL compatible plotter to display the function. This program is SHAREWARE, so everyone can copy and try it. If you like it and want to use it after a two weeks trial period, send $15 (or a roughly corresponding amount in your country's currency) to the address above. You will get the newest version of MathGraphics and you will be able to get updates at a small charge. I also welcome your comments! Let me know if you have a FPE or NumberCruncher coprocessor card, so I can send you a version of MathGraphics which uses these cards directly and operates much faster. Updates since version 1.8: 2.0 - parameter functions (x(t), y(t)) - logarithmic drawing area - finding roots and extremes of functions - drawing function strings - dottet lines for grid and function values - animated cursor (courtesy of Wilfried - Hi, Wilfried!) - a few of minor changes 2.1 - removed bug concerning e^x - textcursor 2.2 - every window has its own settings, functions, etc. - choosable font - GS/OSclass 1 calls - requires System 6.0 or higher - rearranged menus - input file for the drawing of paired values has to be a formatted text file - MathGraphics uses a new, more complete format for storing settings in the picture files Manual Mouse Handling Inside the content area of an active window the cursor becomes a cross. If you click on a point inside the active window, an alarm box will be displayed, showing you the function value and the derivatives at this point. If you hold the mouse button and drag the mouse, a rectangle will be drawn that lets you define an area which will be displayed in a dialog box when you release the mouse button. This dialog gives you the choice to use this area as the drawing area by pressing 'Drawing Area', or to find the function root or an extreme by pressing 'Function Root' or 'Extreme', respectivly. To find a root, the function graph must cut the x-axis inside the area. In order to find an extreme, this must also lay inside the selected area. The program is able to distinguish between a minimum and a maximum. The extreme can then be drawn if you like. The two buttons 'Function Root' and 'Extreme' are disabled when you use the parameter option (described below). If you click on a point inside the window while holding down the option key, a dialog appears, which lets you choose between drawing one of the function strings or any text you like at this point. Apple Menu About MathGraphics... This command displays a dialog box with information about MathGraphics (version number, build-in functions etc.). (Desk Accessories) Desk Accessories are supported by MathGraphics. File Menu New Open... Close Close All The 'New' command creates a new, empty window. There can be up to four windows open at once. With 'Open' you can load a document of type $C1 (a QuickDraw picture or an unpacked bitmap) created by MathGraphics or another program. It will be displayed in a new window. A QuickDraw picture is a recording of QuickDraw drawing commands that will be played back when you want to see or print it. It can be resized and uses the maximum resolution of the device it is displayed on. So you get a better looking result when you print it as if it was a bitmap. Files created by MathGraphics contain information about the function, drawing area and more in the resource fork. If no such information is found, the standard preferences will be used. The 'Close' command closes the active window, 'Close All' closes all windows (you guessed it!). If you have made any changes to the document you're closeing, you get the chance to change your mind and leave it open, save it or discard the changes. QuickDraw Picture Bitmap You can change the kind of graphic that will be saved with this command. The active option has a check mark in front of its name. 'QuickDraw Picture'should be preferred, but the 'Bitmap'option is useful for importing MathGraphics drawings into GraphicWriter III v1.0, for example. Save Save As... The 'Save' command puts a copy of the active document on disk. If it hasn't been named already, you have to name it in the Standard File dialog. 'Save As' lets you change the name and path of the document. The active preferences will be saved in the resource fork. The file is still compatible with all graphic or DTP programs that can load $C1 files, but you will loose this information if you load a file into such a program and save it again under the same name. Page Setup... This command displays the page setup dialog of the currently active printer. To alter the active printer you have to use the control panel. Print... The 'Print' command prints a copy of the current document according to your specifications. Since QuickDraw pictures are used, MathGraphics can print the graphic at any resolution. Quit Quit lets you exit MathGraphics and return to the launching program, e.g. the Finder. The current content of the clipboard will be saved on disk. Edit Menu Undo Cut Copy Paste Clear If the active window is a MathGraphics window, the commands do the following: 'Undo' reverses the last drawing activity. You can undo all the drawings you made (e.g. overlaying function graphs) until the window is empty. 'Clear' does that all at once. With 'Cut', 'Copy' and 'Paste' you can move the whole graphic into the clipboard and back. The clipboard will be saved if you exit MathGraphics, so you can use its contents in another program. If the active window belongs to a NDA, the meanings of the Edit menu commands depend on this NDA. Preferences... With this dialog you can control the appearance of numbers in dialogs and as labels of the coordinate system. You can choose between float and fixed format (e.g. 1.234e+5 or 25.00) and enter the number of decimal places you like. Pressing 'Save'lets you replace the standard preferences of MathGraphics by the settings of the frontmost window. They are saved at '@:MathGr.prefs', where '@' is the prefix of the folder containing MathGraphics, or if you started it from a server, of the user folder. Choose Font... You can change the font of the active window with the standard Choose Font dialog here. Graphics Menu Enter Function(s)... You can enter function strings with a lenght up to 255 characters. Upper or lower case makes no difference, spaces are allowed. The string can be edited like normal text, and you can cut, copy and paste it with control-x, -c, -v. The function will be evaluated useing the common mathematical rules (braces first, then * /, then + - etc.). The available functions are listed in the 'About' dialog: abs(x) - positive value int(x) - round to nearest integer frac(x) - remainder of truncate to integer sqr(x) - square sqrt(x) - square root sin(x) - sine cos(x) - cosine tan(x) - tangent arctan(x)- arctangent exp(x) - base-e or natural exponential ln(x) - base-e or natural logarithm sinh(x) - sine hyperbolicus cosh(x) - cosine hyperbolicus tanh(x) - tangent hyperbolicus The arguments for the trigonometric functions and the result of arctan are expressed in radians. You can use four definable (a, b, c, d) and two predefined constants (pi = 3.14159..., e = 2.71828...). If the program finds an error in the string, it beeps. The appropriate dialog is choosen automatically, depending on whether f(x) or x(t), y(t) is used. If the 'Paired Values'option is active, this command is not available. Draw... 'Draw...' displays a dialog that depends on the type of function choosen (f(x), x(t)/y(t) or Paired Values). Drawing of a function: You can enter the values of the constants you can use in the function string. This is useful if you want to display the influence of a constant in the function by drawing it several times with a different value. Three radio buttons are provided to choose from displaying the function(s), its (their) first (slope) or second derivative(s). If you draw x(t) and y(t), both functions will be derivated if you choose f'(x) or f''(x). The 'polar' option lets you draw the function as r(phi), that means x corresponds to the angle and f(x) to the radius. It is deactivated when you use logarithmic scaling or parameter functions. Choosing a low accuracy gives a quick overview of the function graph, a higher is recommended for best printing results. If you select OK, the graph will be drawn. You can stop it at any time by pressing Open-Apple-period. Displaying a Data File: Although MathGraphics is able to draw a lot of trigonometric functions that can be combined to long and complex function terms, you may want to display a graph of a function that is not analytically describable (e.g. solutions of differential equations solved numerically) or other data. You can solve problems with your own programs and let MathGraphics draw it. MathGraphics suspects a text file with data set of two or more components. You can choose which component of the set contains the x or the y values. Maybe you have a solution of a movement equation. You save the time, place, velocity and accelleration of a state in a set with four elements. Then you you can take the time for for the x value and display the other elements against it, display accelleration against velocity or whatever you like. If the values are radius and angle, select Polar Coordinates Transformation in this dialog. MathGraphics has to know about the number of components. Otherwise it cannot use the correct step lenght and will draw funny looking pictures. To select the data file, press the corresponding button and use the Standard File dialog. MathGraphics scans the file for extrem values and suggests a drawing area. This is useful for the first graph you draw. But if you want to compare functions, you should leave the area as it is after the first graph. A data file has to have the following form:First the number of data sets, then the components of the sets, seperated by spaces, colons, tabs or returns. Everything after a '/' in a line will be ignored. MathGraphics uses the 'Number Of Components' setting in the dialog to assign each number to the correct set and component. Here is an example for such a file: / Data for MathGraphics / 3 / number of data sets / 0, 100, 20 / time, place, velocity 0.2, 110, 23 0.4, 90, 25 / / End Pascal example (just the important code snippets) for producing a data file: const n=100; var i: integer; a: array[1..n, 1..2] of extended; Textf: text; rewrite(Textf, 'Werte.txt'); writeln(Textf, n); for i := 1 to n do writeln(Textf, a[i,1], a[i,2]); close(Textf); C example: #define N 100; typedef double array[N][2]; int i; array a; FILE *Textf; Textf = fopen("Values.txt","w"); fprintf(Textf,"%d\n", N); for(i=0;i>t  G@@=@AB######################### ####### ################################################################################################################################################################# ####### #########################################################################  dd#"ez @@#">"d@"d  (b2.000"d)k4.000"d(b-2.000"dk(bl-4.000"d(b-6.000"d@"K@(KE1.000"2@(2E2.000"@(E3.000"}@*d-1.000"@*-2.000"@*-3.000"@*-4.000>DEF@??@??@?? "2*(sin(x)-sin(2*x)/2+sin(3*x)/3-sin(4*x)/4+sin(5*x)/5-sin(6*x)/6+sin(7*x)/7-sin(8*x)/8+sin(9*x)/9-sin(10*x)/10+sin(11*x)/11-sin(12*x)/12+sin(13*x)/13-sin(14*x)/14+sin(15*x)/15-sin(16*x)/16); Fourier f(x) = xCeNUedx$F X@X! <Z Z Z apaabbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnooooppooppppjjkkllmmnnooppaabbccddeeffgghhii?i~?j?k sin(x)*cos(y)?m?n?o?p??j3?X3?`F3?;3?&3?3?appiapR=~>K>q>CD\DDDDPQQSlQQQQQRQR_RRlptw  ;Tmv b nTQ.DAT JN  3333 @@ uu    KK    kk 55 dd SS CC 22 !!   uu      " ## ######## ################# #####>>t  G@?HKLM### ################# ######## ################# ######## ################# ######## ################# ######## ################# # ####### # ################# ######## #############  dd @@"d@"du  (bw10.00"d)520.00"d)630.00"d)540.00"dK)550.00"d (b -10.00"d(b-20.00"d(b-30.00"dk(bl-40.00"d5(b7-50.00"d(b-60.00"d@":@(:E0.50"@(E1.00"@*}-0.50"@*)-1.00IOPQ@@????@?? -a*sin(x)*exp(-abs(x/b)); gedmpfte Schwingungtsin(t) Lissajou.txt U [  wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww3333  QQ         44 FF VV ee ss   vv __ NN AA 66 -- %%          "  (4.00")8.00")L12.00" >>t  G?@?@SVWXYZ)616.00"4))20.00"V)#24.00"s)28.00"v(v4.00"N(N8.00"6(612.00"%(%16.00"(20.00" ( 24.00"(28.00 "###############################################################################################################################( f(x) = x^0.5 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU"###############################################################################################################################(o=f(x) = x DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"###############################################################################################################################(X f(x) = x^2 "###############################################################################################################################(4 f(x) = x^3T\]^?@@@@@?@?? !x^3.5(x)*exp(-abs(x/b)); gedmpfte Schwingungtsin(t) b g  3333  >> gg   66 __     -- WW  dd RR @@ --   vv      dd#"et #""d"d|  +b}5.00"d)h10.00"dJ)g15.00"d>>t  GD@̌̌?`cdef)g20.00"d)g25.00"d"R(R0.20"@(@0.40"-(-0.60"(0.80" ( 1.00"v*m-0.20"*-0.40"*-0.60"*-0.80"*-1.00 "############ # ###### # ##################### # ##################################################################################### UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU">##### ######## #################### # # # # ########################################################################################## DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"# ##!#*## # ################## # # # # # # ################################################################################################(C> gg   66 __     -- WW  dd RR @@ --   vv     "############################>>t  Gp@̌̌?lopqrst#################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################### dd "d"d|  +b}5.00"d)h10.00"dJ)g15.00"d)g20.00"d)g25.00"d"R(R0.20"@(@0.40"-(-0.60"(0.80" ( 1.00"v*m-0.20"*-0.40"*-0.60"*-0.80"*-1.00(!)f(x) = a*sin(x)*exp(-abs(x/b))+c*cos(d*x)mvwx@@?@??@?@  !"a*sin(x)*exp(-abs(x/b))+c*cos(d*x)biFiYfq+ >fd< b4hubu${--Tk^@qf@Af@ UaUCe-t   Vt  Xv@ 0,@ .H$y@  .H0^F.H@  HAGf sin(x)*cos(y)(T /(T "&n  ,1-:Sofa1:Pascal:FktGraphik:FktKram:Schwingungen Schwingungen k  BS%_kB qx Rw=,{@h@@V@TQ.DAT |n   3333 @@  @@    @@  dd SS CC 22 !!   uu       dd "d"d@  +bB0.50"d)@1.00"d)@1.50"d)@2.00"d@)@2.50"d)@3.00"d)@3>>t  Gt@@z}~.50"d)@4.00"d@)@4.50"d"S(S0.50"C(C1.00"2(21.50"!(!2.00"(2.50"u*d-0.50"*-1.00"*-1.50"*-2.00"*-2.50"*-3.00"d######### ############ # ########## #### ####### ## # ################### ##### ####################### ##################### ######## #### ################### ######################## ### ######## # # ########### # # ####### ### #################### #### ####################### ############################# #### # ####################### ##################### # ####### # # # #################### # ## # #################### # ## # #################### # # ############################## #### ################### # ## # # ############################ # # # # ################### # ### ###################### # # ############################# # # ###################### # # # # #################### # # # ###########( 'sf(x) = exp(-0.25*x) * (0.006*cos(70.71*x) - 0.739*sin(70.71*x)) + 1.047 * sin(15*x-0.002) + 1.219 * sin(30*x-0.004){@?????@??  !exp(-0.25*x) * (0.006*cos(70.71*x) - 0.739*sin(70.71*x)) + 1.047 * sin(15*x-0.002) + 1.219 * sin(30*x-0.004); forced oscillation of an one mass oscillator (amplitude over time)5ua@CHsin(t)   V,ucos(t)  Xv 0,_0v .HoDv  .H_0^F.Hv  HA|, ?  3333 @@ ``        @@ ``     `` @@ dd ZZ PP FF << 22 ((     nn xx         DDDDDDDDDDDDDDDD>>t  G$@@DDDDDDDDDDDDDDDD"bC####### ## 6#A# ####D#j#,#####'?!#^#!0#%#5!!^!}#!"=!@#B!#!#3!!(#I!!!bZ!!!X#Ve!!~u  dd @@"d@"d  (b20.00"d@)40.00"d(b-20.00"d@(bB-40.00"d@"<@(<E20.00"@(E40.00"@*x-20.00"@*(-40.00 "`A"dA"^9"b9"a+"e+"h-"l-"lG"pG"ec"ic"Y`"]`"R7"V7"[ "_ "m"q"x>"|>"o"s"W"["FJ"JJ"N"R"k"o" " "}""\"`"=r"Ar"?"C"b"f"""""i"m":">". "2 "S"W"""\"\"{""?"C" ;"$;">"B"t"t"!"!"""K&"O&"""&"*"o;"s;"""""`X"dX"""""V"Z"y"y"""|s"s@@????@?? !a*sin(x)*exp(-abs(x/b));g|f"NUNU6==<<Z46=@zHTf|f =6|f brmu5ua@CzHtsin(t) Spirale.txt   3333 @@ kk     @@ kk  kk @@   xx ]] CC ((    #"z @@#">"@"u  (w5.00")510.00")615.00")520.00"K)525.00" ( -5.00"(-10.00"(-15.00"k(l-20.00"5>>t  G@̌?(7-25.00"(-30.00"@"x@(xE0.20"]@(]E0.40"C@(CE0.60"(@((E0.80" @( E1.00"@*-0.20"@*-0.40 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU" @##############################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################################@@?@??@??  !-a*sin(x)*exp(-abs(x/b)); gedmpfte Schwingung a*t*cos(t)"g|f"NUNU6==?46=<H46=@zHTf|f |f brmu5ua@1@CH 1/t*sin(t)NUNNUNU""""""""""""`d(NUzNUz ?$$bH AA~A<p    333333333333333333333333333333333333 @@    @@   @@    xx nn dd ZZ PP FF << 22 ((            @@"@"  (2.00")@>~>t  G4@@4.00")@6.00"@)@8.00"(-2.00"(-4.00"(-6.00"@(B-8.00"(-10.00"@"@(E4.00"n@(nE8.00"Z@(ZE12.00"F@(FE16.00"2@(2E20.00"@(E24.00" @( E28.00"@*-4.00"@*-8.00"############################################################################################################################### "######### # # # # # # # # # # # # # # # # # # ## ##################################################################################################(C = 1(sC = 2 DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD 7!X !!!!!b#! (! -!Q 2! 7! <!x A! F!Z K!P!RU##############################################################################################!Y0!5!F:!?!D!~I!N!1S!X!]! b!Ig!~l!q!v!{!(6C = 3@@@@@?@@? x^c "(g|f"(5==:=_AH=ДHTf|f |f brm5a@C&xHtsin(t) Kan1 Oscillation.2%  dd @@"d@"dq  (bs0.20"d)10.40"d)10.60"d)20.80"d6)11.00"dg)11.20"d(b-0.20"d(b-0.40"d(b-0.60"d{(b}-0.80"dJ(bK-1.00"d(b-1.20"d@"U@(UE0.20"E@(EE0.40"6@(6E0.60"&@(&E0.80"@(E1.00"@(E1.20"s@*k-0.20"@*-0.40"@*-0.60"@*-0.80"@*-1.00"@*-1.20 DDDDD>>t  Gffffffffffffff?ffffffffffffff?DDDDDDDDDDDDDDDDDDDDDDDDDDD"@'#%#$#!##### ####################### #####!#$#%#'#&#&#$#!##### ####################### #####!#$#%#'#&#&#$#!##### ####################### #####!#$#%#'#&#&#$#!##### ####################### #####!#$#%#'#&#&#$#!##### ####################### #####!#$#%#'#&#&#$# ##### ####################### #####!#$#%#'#&#&#$# ##### ####################### #####!#$#%#'#&#&###!##### ####################### #####!#$#%#'QQ@@??????? ""-a*sin(x)*exp(-abs(x/b)); gedmpfte Schwingungsin(t*a)"g|f"NUNU6==;46=AH46=@zHTf|f |f $$ 6brmu5ua@-@CdHcos(t*b)NUNNUNU""""""""""""8}pNUzNUz<t̎tbABA~A<p 1(q$`*B MATHGRAPHICS MATHGRAPH.DOC5B MATHPICTS5SAMPLES5ICONSSAMPLESv*'  ',LISSAJOU.TXT}~6SQUARE.TXTtXSINE.TXT޸:$*SPIRAL.TXT}~7)GENDATA.P9?- @}$FINDER.DATA~7p 201 / number of paired values 4.20735492e+001 1.00000000e+000 4.27357095e+001 9.68912422e-001 4.33711613e+001 8.77582562e-001 4.39795075e+001 7.31688869e-001 4.45603680e+001 5.40302306e-001 4.51133797e+001 3.15322362e-001 4.56381970e+001 7.07372017e-002 4.61344919e+001 -1.78246056e-001 4.66019543e+001 -4.16146837e-001 4.70402920e+001 -6.28173623e-001 4.74492310e+001 -8.01143616e-001 4.78285158e+001 -9.24302379e-001 4.81779093e+001 -9.89992497e-001 4.84971932e+001 -9.94129676e-001 4.87861679e+001 -9.36456687e-001 4.90446529e+001 -8.20559357e-001 4.92724865e+001 -6.53643621e-001 4.94695264e+001 -4.46087490e-001 4.96356496e+001 -2.10795799e-001 4.97707520e+001 3.76021529e-002 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-1.51664971e+001 8.70054994e-001 -1.39707749e+001 9.64966028e-001 20 0 -2 1 -2 2 -2 2.9 -2 2.95 -2 3 -2 3.05 2 3.1 2 3.15 2 4 2 5 2 5.9 2 5.95 2 5.98 2 6 0 6.02 0 6.05 0 7 0 8 0 9 0  10 5.0e-1 4.8e-1 1.0e+0 8.4e-1 1.5e+0 1.0e+0 2.0e+0 9.1e-1 2.5e+0 6.0e-1 3.0e+0 1.4e-1 3.5e+0 -3.5e-1 4.0e+0 -7.6e-1 4.5e+0 -9.8e-1 5.0e+0 -9.6e-1 50 / number of paired values 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 { GenData sample program to illustrate the generation of paired values for MathGraphics } {$keep 'GenData'} program GenData; var f:text; i:integer; a: array[1..2] of double; begin rewrite(f,'Lissajou.txt'); writeln(f,'201 / number of paired values'); for i := 0 to 200 do begin a[1] := sin(i/40+1)*50; a[2] := cos(i/4); writeln(f,a[1],' ',a[2]); end; close(f); rewrite(f,'Spiral.txt'); writeln(f,'50 / number of paired values'); for i := 1 to 50 do begin writeln(f,i,' ',i); end; close(f); end. 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Music Composer version 1.0 Written by Clayburn W. Juniel, III Music Composer is a MIDI Synth sequence editor. With this program you can create a program from scratch. Load an existing sequence and edit that. You can add notes, delete notes, modify note volumes, and change the note channels. You can add notes via a MIDI keyboard or use the keyboard on the screen to add notes exactly where you want them. You can also add and modify all types of MIDI messages including system exclusive messages. MENU OPTIONS FILE MENU About Window gives name and version of program. Also author's name and copyright information. Show icons Shows and gives names for all of the icons used in the program. New Set to create a new sequence. Open Open a sequence file from disk. Including the instrument bank and wave. If you don't want to load the instrument bank and wave hold down the command key. Open Instrument Open a instrument bank and wave. If you don't want to load the wave file hold down the command key. Open wave Open a wave file. Import sequence A sequence file created with this program can have up to 64 blocks. Each block is like a separate sequence file without the header information. When you import a sequence file you create another block and add that file to blocks that already exist. Close Close a new desk accessory window. Save Save the sequence file currently in memory. Save as Save the sequence file currently in memory. Allowing you to rename it. Revert to saved Revert the sequence to the lasted saved sequence. Delete sequence Delete a sequence file that is not locked. Initialize disk This will initialize 5 1/4 and 3 1/2 inch disk only if you need them to save your work to. If the disk to be initialized was already initialized once it will just be erased. Page setup This function does not work in this version. Print This function does not work in this version. Quit Exit this program. EDIT MENU Undo Does nothing in this program Cut Copies the selected information to an internal clipboard only. It then deletes the selected information. You can cut tracks, measures, beats and single notes. See the section on COMPOSER SPREAD SHEET for more detailed information on this and the other edit functions. Copy Copies the selected information to an internal clipboard only. Without deleting it from the spread sheet cells. You can copy the same as in the cut above. Paste Paste the information from the internal clipboard to the spread sheet cells at the point of the selection. If more then one cell is selected then it is pasted starting at the upper left cell of the selection. If tracks are pasted then the tracks pasted to are erased then the items are pasted to the tracks. If rows are pasted then the rows beneath that are moved down (or MIDI notes and messages are moved up in clock ticks). Clear Clears the selected information from the spread sheet cells Change instrument Changes the instruments (channels) in the selected area. Move Instrument Move instrument only works when an entire single track is selected. See the section on COMPOSER SPREAD SHEET for more details on selecting an entire cell. You can move all the instruments of a certain number to any of the 8 tracks. Block This controls the creation, deletion and editing of the sequence blocks. A dialog window is created with several options. Delete block deletes the block number chosen with the scroll bar beneath it. Edit block sets the spread sheet cells to edit the block number beneath it. When this button is chosen the dialog window is removed and you are ready to edit that block. Block count tells you how many blocks there presently are. New block creates a new sequence block. When this button is chose the dialog window is removed and you are ready to edit that block. Continue removes the dialog window without changing which block you were editing. Key equivalents: Delete block -- DELETE KEY Edit block -- E KEY New Block -- N KEY Goto stop This will take you to the place in the spread sheet where the music stop playing. Or if the music is still playing to where it played the last note. Fade in The volume of notes and volume control will "fade in" in the selected area. Fade out The volume of notes and volume control will "fade out" in the selected area. Play zone The notes in the selected area will be played. Find system exclusive This will bring the spread sheet to the next MIDI system exclusive message. SETUP MIDI This control MIDI input and output. A dialog window is created with several options. Choose one of the Omni, Poly, and Multi radio buttons for the mode. Omni means all MIDI message channels (instruments) are accepted through MIDI and forced to one channel (the basic channel). Poly means only those MIDI messages that match the basic channel are accepted. Multi means all MIDI message channels are accepted without being changed. Choose a basic channel with the scroll bar. With SysEx in checked when a system exclusive message is received it will be recorded in the spread sheet cell. MIDI in and MIDI out control whether MIDI in or out is enabled. Vel Comp adds the value to the volume of the incoming MIDI note message. Keyboard equivalents: Omni -- O KEY Poly -- P KEY Multi -- M KEY SysEx in -- S KEY MIDI in -- I KEY MIDI out -- X KEY Sequencer This controls the sequencer functions. The clock can be set to internal or MIDI port. Count off beats lets that many beats "count off" after the play or record button is pressed before playing or recording starts. With metronome check a metronome plays to the beat. With Key start pressed playing or recording doesn't start until after a key up (note off) MIDI message is received. This program will recognized MIDI START, CONTINUE and STOP messages. What the MIDI record and MIDI play radio buttons do is decide whether these messages are for recording or playing. If you click on the radio button that is chosen then both will be not chosen. When a recording is made, it must be merged with the present sequence block. Also when a paste is down that must be merged with the present sequence block. If there is a MIDI system exclusive message in the sequence block then "Fast merge" must be UN-CHECKED or the merge will not go correctly. Beat to controls the timing of the beats. The beat time effects the metronome as well as how many notes appear in a beat in the spread sheet. See COMPOSER SPREAD SHEET for more information. Key equivalents: Internal -- I KEY MIDI port -- X KEY Metronome -- M KEY Key start -- K KEY MIDI Record -- R KEY MIDI Play -- P KEY Beat to -- 1 - 5 KEY Track out Track out controls where the output of the sequencer goes for each track. A dialog window is created allowing you to chose. Track to channel Track to channel will map each track of the sequencer to a certain instrument. A dialog window is created allowing you to set this. If that channel is set to 0 then it will play what the MIDI instrument says. Volumes Volumes brings up a dialog window that lets you chose the volume that each instrument is played at through the sequencer. It also lets you choose the system volume. MUSIC Player Player brings up a dialog window letting you choose which blocks to play when. You can choose the number of play positions up to 128. For each play position (up to the number of play positions) set a sequence block number. You can play the same block several times. With loop checked when the last play positioned is played it will "loop" to first and start again. Key equivalents: Loop -- L KEY Play block Play block plays the sequence block that you are editing Kill all notes Kill all notes will stop any hung notes from playing. INSTRUMENTS Choose an instrument for the basic channel Key equivalents: Instruments 1-10 -- OPTION KEY 1-0 Instruments 11-16 -- OPTION KEYPAD 1-6 KEYBOARD This is the keyboard on the screen. With it you can play and record notes from instruments. You can set the keyboard volume and whether the first key on the left is C1 or C2. In recording mode you can record a single note. The note recorded will be the last note played before you press Done. For every note recorded there is a MIDI note on and note off. The time till the note off is when you released the last key. To exit recording mode without recording a note press the cancel button. To enter the recording mode you start at the spread sheet. While holding down the COMMAND KEY double click in an empty cell at the beat and track where you want the note to be. You will be taken to the keyboard in recording mode. When you press Done you will be take back to the spread sheet and the note will be in the spread sheet. Key equivalents: C1 -- 1 KEY C2 -- 2 KEY COMPOSER SPREAD SHEET The composer spread sheet is where you do your editing, recording, and playing of sequence files. At the top are several controls. Starting at the left are the play tracks. For each box that is checked that track will play. You can choose which tracks to play or not when recording and playing. Below that is the record track. You can choose only one of these to record your MIDI input to. If you select the track that is already chosen then it is not selected. You can set the play tempo with the tempo scroll bar. The Play button plays the sequence file according to the settings in the Player dialog window. The Record button starts recording MIDI input. It records into and plays the present sequence block set for editing. The track set for recording is erased then the recorded input is put in that track. The Stop button stops playing and recording. The Continue button continues playing from where you last stopped playing. If you hold down the OPTION KEY and choose the Continue button you will continue recording. This option doesn't erase the recorded track. It starts playing - recording at the beginning of the present sequence block set for editing. You can then start recording where you here you left off. While music is playing and/or recording most of the functions of the program are still available to use. I wouldn't recommend cutting, copying, pasting, or clearing anything at this time. The program could crash. Also if there is a MIDI system exclusive message some where in the sequence I be very careful doing anything with the program. If you are doing anything with the program when it gets to the MIDI system exclusive message the playing might hang. Key equivalents: Play tracks 1-8 -- 1-8 KEY Record tracks 1-8 -- 1-8 KEYPAD Play -- P KEY Record -- R KEY Continue playing -- C KEY Continue Recording -- OPTION-C KEY Stop -- S KEY Below The above controls are the 8 track names. Four tracks can be shown at once. To see other tracks use the scroll bar at the bottom. You can change the track names by clicking on the track name. This will bring up an edit window allowing you to change the name. SPREAD SHEET CELLS Below the track names are the spread sheet cells. This is where the MIDI notes and messages appear and are edited. Structure of the spread sheet cells There are 8 tracks. Four tracks can be seen at once. To see the other tracks use the scroll bar at the bottom of the window. Twelve cells at once can be seen for each track. To see other cells use the scroll bar at the right of the window. The 12 cells are divided into 2 beats or chords. There are 6 cells per beat. When MIDI notes or other messages appear in a beat they start at the top of the beat and go down. If there are more notes or messages then 6 per beat then the notes and messages pass 6 will not be seen. If that is the case here is what you can try to see more of the notes or messages. Many sequence files created have all the instruments (channels) in one track. You can use Move instrument to move some instruments to other tracks. You can go to the setup menu and choose Sequencer. Change the beat to to a faster beat. This will mean less notes or messages per beat. If you still think there are notes or messages that are not seen you can cut and paste notes to another track. See Editing cells below for more details on this. Selecting cell(s) There is a color bar just below the track names. If you click there and entire track will be selected. If you hold down the mouse and drag it you can select several tracks. If you move pass the right or left edge of the window the tracks will scroll. If you click on the color bar on the left all the tracks in that row will be selected. If you hold down the mouse and drag it you can select several rows. If you move pass the top or bottom of the spread sheet cells then the spread sheet will scroll. You can select an individual cell by clicking on that cell. If you hold down the mouse and drag it you can select several cells. If you move pass the boundaries of the cells the spread sheet will scroll. The edit menu commands Change instrument, Fade in, Fade out, and play zone work on entire beats. Therefore although only one MIDI note or message in a beat is selected, all the notes or messages in that beat will be effect by the action of the menu command. Editing cell(s) The Undo function in the edit menu does nothing to the spread sheet cells. To cut or copy select the area then choose the edit menu command. If you are cutting or copying more then one track (but not choosing the tracks by the color bar at the top of the spread sheet cells) All of the MIDI note or message items in the bottom selected beat area might not be cut or copied. You can possibly avoid this by dragging the mouse to select the next empty row below where you want to cut or copy. This paragraph describes why you might not copy what you selected. It gets a bit technical so you can skip it if you want. When MIDI notes and messages are created two things they are given is a track and a time stamp. The track is really a conceptual thing and has not much to do with how a note plays. But it does make editing sequences easier. The time stamp tells when to play the note or message. The spread sheet is separated into beats and tracks. Lets say a beat is 96 clock ticks long (This is set by the beat to in the setup menu sequencer window). Each beat would start at 0, 96, 192, 288 etc. The time stamps on the notes and messages could be anything (1, 103, 219, 307). The notes and messages within a beat fall within a 96 tick range. The notes and messages in the sequence are ordered by time stamp and not track. If you try and select say only two cells in a beat the program will count tell it reaches the third item in a beat range then it will cut or copy up to that. Track 1 might have time stamps of 0, 10, and 20. Track 2 has time stamps of 15, 30, 40 the program would stop when it found the third item in track 1 and would not find the second item in track 2. It has to stop here to keep the relative timing of the items the same. To edit an individual MIDI note or message double click on a single cell. To add a MIDI message double click on an empty cell. To add a MIDI note hold down the COMMAND KEY while double clicking on a empty cell. See KEYBOARD for further details of recording a single note. When you double click on a cell an edit MIDI item dialog window appears. In this dialog window there are 4 items that can be edited. The type (see list later). The channel (instrument). The Data1 and the Data2. An icon appears next to the type scroll arrow. And the name of the type appears next to the word type. Data1 may also have a an icon and it name is just below the type name. For some of the MIDI types certain things can not be edited. In most cases the scroll arrow next to that item is deactivated. If you double clicked on an existing MIDI item then the type scroll arrow is deactivated. Some MIDI items are not editable and will not bring up a dialog window when you click on them (see list below). When you click on an system exclusive item or choose the OK button when the data type - system exclusive - is showing then you get the MIDI system exclusive message editing dialog window. If this is a new MIDI system exclusive message then the byte # scroll arrow is deactivated. You choose each byte value (C - 127) then use the Add byte button to add the byte to the system exclusive message. You can then choose another byte value and repeat. The byte count shows how many bytes are in the message. You can have a total of 16,375 bytes in one message. If you double clicked on an existing MIDI system exclusive message then the Add byte and Cancel buttons are deactivated. You can't add any more bytes to the message but you can edit the bytes that are there. Just choose the byte # then edit that byte. Remember if you have a MIDI system exclusive message in a sequence block to not check Fast merge in the sequence controls window in the Setup menu. If you need to have a MIDI system exclusive message in a sequence block it is best if you put it in as the last thing. If it came with the sequence file or came in through the MIDI port you can always Cut it out and create a new sequence block and paste it there for safe keeping and then paste it back to were it was when you are through editing and testing the sequence. Key equivalents: Add byte -- A KEY List of MIDI messages and what in them can be edited. Type Editable Channel Data1 Data2 Marker x x x Set beat x x x Set tempo x x x Note off Note on x x Poly after touch x x x x Control x x x Program change x x x x Mono After touch x x x x Pitch bend x x x x System exclusive x x F1 Song position x x x Song select x x x F4 F5 Tune request End exclusive -- You should never see this icon MIDI clock F9 Start Continue stop FD Active sensing MUSICv*' ',DREAMLINE.SLN(8!)(RUSH.BNKd (8!))SYNTH.WAVp M!M !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcMSEQsynthLAB Rush.BNK.SLSL Dreamline by Rush  Conversion by Ian Schmidt of Two Meg using MIDIZap (tm) Two Meg '93!         '`6@8@;@<@?@B@ #'+/37; ?&C,G2K8O>SDWJ[P_Vc\gbkhonstwz{~9@3@G@} 9@ 3@ | G@{yL@9@x!9@$L@$w*u0t0Q@09@03@6s99@93@<Q@<qBpHoHL@H9@NmQ9@TL@TlZk`i`Q@`9@`3@fhi9@i3@lQ@lgrexdxS@x9@~c9@S@a`_Q@9@3@]9@3@Q@\[YL@9@X9@L@WUT9@3@G@S9@3@RG@POL@9@N9@L@LKJQ@9@3@H9@3@Q@GFDL@9@C9@L@B@ ? 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fM{ۄLD25ҕ_\̵jFHGfxIAǙ>j<:fXzsRqcvQ^{nNdYV_jhzoUzhvsrOaz_sqgpwvn]de|vrxuby}ynrt~ntpp~~s{tzsx}zzw|s}{wfustSF|]H oh6:&}UKbk@CjŸY-genȕEQA#xhN;Z8`OtGQzuH8={LU^}Z4nyzwlPYhqM^fygxUTSmzpuaXptqsrulxpmnw|qwk}suwxux|ks~YʶoMOLB;f5 1MJI5O;oTX^ʺ׭^G:vzhɿD-ƃS=t:T65aO==\ŭ7,\Ь4 bfm[SZ:.5dȾK'{ȹ:@XvPyY`ޔFY7:7|Uwv\!'s&?5ӦV^"ͦHIGOWsĀNKƼD=SNND.6rdxB6-ŴOg9y}3q2Qas`]x^Fh2YJ'KTI@;cD;5iƟd~~_j|Gm[k|a~A%T؟fiykgMEa7_tx>3ZskMrhk+Vk$z_xKClZ^Hgbh~j|}ntssc\k,CMusic.Comp ~ExpressLoad>(dd0B ,@Music.CompMusic.Comp( ,@Music.CompSEGJPTABLE&2X ,@Music.CompSplash hR[# ,@Music.CompStart d ,@Music.CompMusic.Compd"0K{" SK#"hv^6Splash Editor version 1.00 Written by Clayburn W. Juniel, III Copyright July 1992OoOKWwCloseSsDiskJjMidi...OKLlRevert to savedQqQuitFade in-_Fade outOK Edit Zz@UndoXxCutCcCopyVvPasteClearApplication Menu BarAbout GS Composer... New sequenceOpen sequence... Save sequenceS  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~xh t %H"h ֢#"#"HH"᭻H"᭹H""") 7dQd) _H,"`8 H)Z ~N 6O>//SoXzzzzzzzzzzzzzzzzzz[-0P1uaM6؎Iv"JcM`1"1"1"1"1" 1"(1"01"61"21"51"1"1")1" mj{?l{:  9~zz# - 0"ᥜ 00"`n{p{`0"0"0"0"0"` 0"60"20"50"`0"0"0"(0"60"20"50"0"0")0"`"h`ta"h S=HH"Hn"hH. "hHH "` #QJLRFCDDB Music Composer FCB version 1.03 Written by Clayburn W. Juniel, III copyright 1993 A MidiSynth sequence editor Clayburn W. Juniel, III 1928 E. Camelback Rd. Apt #623 Phoenix, Arizona 85016-4143 Phone: (602)274-6905 AOL: Clayburn Genie: C.JunielP a"h S`HH"Hn"hHH"
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