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_____ _ _ _ _ |___ / __| |_ _(_)___(_) ___ _ __ __| | ___ ___ |_ \ / _` \ \ / / / __| |/ _ \| '_ \ / _` |/ _ \ / __| ___) | (_| |\ V /| \__ \ | (_) | | | || (_| | (_) | (__ |____/ \__,_| \_/ |_|___/_|\___/|_| |_(_)__,_|\___/ \___| ------------ INTRODUCTION ------------ 3DVISION is a set of programs that display 3-dimensional objects and allow you to make real-time rotations with them. It works on IBM AT compatibles, with EGA or VGA videos. 3DVISION was inspired on the 3DV.EXE program, written by Oscar García from New Zealand. 3DVISION has some capabilities that 3DV doesn't have, as the ramdom displaying of objects on screen, and the changing of colors. However, the original 3DV.EXE runs at a faster rate and has a better user interface. The 3DVISION and 3DV data files are 100% compatible. You can get the 3DV program at the SimTel's msdos/graphics subdirectory or from many others sites with names that look like 3DV25.ZIP or 3DKIT1.ZIP. The package 3DVISION contains the executables 3DVISION.EXE, 3DVRAND.EXE, 3DVSURF.EXE, 3DVCOLOR.COM, RNDCOLOR.COM and about 40 data files containing 3D objects, all of them constructed on mathematical parametric curves and surfaces equations. See the end of each *.3DV data file to get the equations used (this can be made writting C:\> COMMENT file_name[.3dv]). All the programs were written and compiled with the old Turbo C 2.0. I did purchased the Borland C++ 4.0 license on december/1994, but I am still without courage to learn how it works. Press the ESC key to quit any of the programs. When the mouse is enabled, press any buttom to quit. All of the programs will use the extension .3DV as default, that is, you don't need to append it. ------------ 3DVISION.EXE ------------ The main program is 3DVISION.EXE. It displays the objects saved in *.3DV files. It can works with the keyboard or with the mouse. You can alternate the usage between keyboard/mouse only using the configuration files (see the item CONFIGURATION below). Data files are given as parameters at the DOS command line: C:\> 3DVISION Data_File [Config_File] where Data_file is a text file with the scene description in 3DV format and Config_File is an optional parameter with the configuration file name After the displaying, press one of the following keys: Right, left arrows: Rotate around the z axis Up, down arrows: Rotate around the y axis Ctrl-up, Ctrl-down arrows: Rotate around the x axis PgDn, PgUp: Zoom in/out F1: Change ramdomly the colors F2: Save the new colors (on files whose extensions are .1, .2, .3, ...) ESC: Quit Type 3DVISION ?, 3DVISION /? or 3DVISION /h at the DOS prompt to get a brief help screen. Example: To display a file named CURVE1.3DV using the default configuration or the standard configuration file 3DVISION.CFG, just type C:\> 3DVISION curve1 To display the same file using the configuration file CONFIG.CFG, type C:\> 3DVISION curve1 config ----------- 3DVRAND.EXE ----------- 3DVRAND displays a selected object on screen rotating it randomly. During the execution, press any key to freeze the image. Then, press another key to continue the ramdom rotations. The usage is the same as 3DVISION.EXE: C:\> 3DVRAND Data_File [Config_File] To get a help screen, type 3DVRAND ? or 3DVRAND /h at the DOS prompt. ----------- 3DVSURF.EXE ----------- 3DVSURF creates a 3DV file with points of a given surface in parametric form F(x, y) = (f1(x, y), f2(x, y), f3(x, y)). You can give the optional names of the variables as parameters (default = "x" and "y"). Hidden curves are displayed. The usage is: 3DVSURF file_name[.3DV] [variable_1] [variable_2] Using this parametric form, functions z = G(x, y) can be given as f1(x, y) = x f2(x, y) = y f3(x, y) = G(x, y) The valid operations are + (addition), - (subtraction), * (multiplica- tion), / (division) and ^ (power). The valid functions are the trigonometric SIN, COS, TG; the inverse trigonometric ARCSIN, ARCCOS, ARCTG; the natural logarithm LN; the exponential EXP; the hyperbolic SINH, COSH, TGH; the approximations to integers INT, ROUND; the square root SQRT; the square SQR; the absolute value ABS and the SIGN function. Examples of valid expressions are: 3*sin(x)*cos(y), (1 + (1 - x^2)/5)^2, (1 - u*cos(u))*sin(2*v)/3 and sqrt(abs(0.5 + round(u + v))). You have to give the [minimum, maximum] values of the variables and the number of subdivisions of these intervals. Example: Write at the DOS prompt C:\> 3DVSURF graph u v to create a file named GRAPH.3DV with the points of the graphics of the surface F(u, v) = (f1(u, v), f2(u, v), f3(u, v)), where f1, f2, f3 will be asked later. ------------ 3DVCOLOR.COM ------------ 3DVCOLOR is a simple utility to change the colors of 3DV files. The file names must be given as two parameters. The usage is: C:\> 3DVCOLOR Source_file[.3DV] Destination_file[.3DV] where Source_file is the file that originally contains the objects and Destination_file will be created by 3DVCOLOR and contains the same objects with new selected colors. The contents of the source_file remain unchanged. You can select the colors using the rigth and left arrows and pressing the ENTER key. Example: To create a file named FILE2.3DV with different colors from another file FILE1.3DV previously saved on disk, write C:\> 3DVCOLOR file1 file2 Then, you will be asked which colors you want to change. ------------ RNDCOLOR.COM ------------ RNDCOLOR changes ramdomly the colors on a .3DV file. Its usage is the same as 3DVCOLOR - just give the name of the files as parameters: C:\> RNDCOLOR original_3DV_file new_3DV_file Example: Using the file OLDLINES.3DV as source, RNDCOLOR creates a new file called NEWLINES.3DV with the same scene, but with randomly changed colors: C:\> RNDCOLOR OldLines.3dv NewLines.3dv ------------- CONFIGURATION ------------- You can define one or various configuration files to 3DVISION and 3DVRAND. The standard configuration file is 3DVISION.CFG. The default file extension is .CFG. When 3DVISION or 3DVRAND begin running, the first thing they do is to look for a file named 3DVISION.CFG. If they find this file, they interpret its lines one by one. Later, these programs verify whether there is a second configuration file name, given as a second parameter. If there is such second file, it will be opened and executed. For example, if you write at the DOS prompt C:\> 3DVISION house.3dv config2.cfg then, 3DVISION will display HOUSE.3DV using the configuration of the files 3DVISION.CFG (the standard) and CONFIG2.CFG. The commands in CONFIG2.CFG will overwrite those of 3DVISION.CFG. The configuration files don't need to have the same commands - they can compensate each other. To create a configuration file, use any text editor. Even the COPY command of DOS can be used (write COPY CON Config_File_Name and press F6 at the end). Beware of special characters that some text editors append to the files. Comments can be added, written after a semicolon. Some options of 3DVISION or 3DVRAND can be changed only using a configura- tion file. The mouse/keyboard usage and the method of projection are two examples of options that cannot be changed after the beginning of execution. The configuration file can have the following commands. N is a natural number. No matter if are used upper or lower case letters. Command What it does ---------------- ----------------------------------------------------------- mouse = 1 or 0 Enables (mouse = 1) or disables the mouse usage. The default is mouse = 0. size = N Size of the objects. If size <= 170, then the objects will not be clipped. The default is size = 170. method = 1 or 0 Defines the method of projection of the 3D objects. If method = 0 (default), parallel (orthogonal) projection will be used. If method = 1, a perspective projection will be used. file = File_Name File name in 3DV format to be displayed. bottom = 1 or 0 Displays or not a status line at the lower part of screen. The status line contains the file name being used and the variation of the rotation angles. The default is bottom =1. theta = N Rotation around the z axis increment (in degrees). The default is theta = 1°. phi = N Rotation around the y axis increment (in degrees). The default is phi = 1°. sigma = N Rotation around the x axis increment (in degrees). The default is sigma = 1°. delay = N Pause (in milliseconds) between two images. Used only by 3DVRAND. The default is delay = 50. sensibility = N Mouse sensibility. The default is sensibility = 50. proj = N The norm of orthogonal vectors that are the basis of the mouse movement plane. The default is proj = 1. lim1 = N Maximum random number of multiples of increments of theta. Used only by 3DVRAND. The default is lim1 = 10. lim2 = N Maximum random number of multiples of increments of phi. Used only by 3DVRAND. The default is lim2 = 10. lim3 = N Maximum random number of multiples of increments of sigma. Used only by 3DVRAND. The default is lim3 = 10. -------------- THE 3DV FORMAT -------------- A 3DV data file is a text (ASCII) file that contains a list of points, followed by a list of moving or drawing instructions. It has the following structure: N Total number of points to be drawn x1 y1 z1 1st. point x2 y2 z2 2nd. point ... ... xN yN zN The last point M Total number of movements or drawings p1 c1 1st. movement or drawing p2 c2 2nd. movement or drawing ... ... pM cM The last movement or drawing where ■ (xi, yi, zi) are the coordinates of the i-th point in 3D space ■ (p1, p2, ..., pM) is a sequence of integers greater than or equal to 1. It defines the order in which the points will be drawn or the one which it will be moved to. The first point to be actually drawn or moved to is the p1-th point, the second is the p2-th point and so on. ■ (c1, c2, ..., cM) are their respective colors. They are integers from 0 to 15 (1 = blue, 2 = green, 3 = cyan, ..., 15 = white). ■ If ci = 0 then it means a movement to the pi-th point. If ci is not 0, it means a color number and that you have to draw a line from the current point to the pi-th point using the color ci. Example: A yellow (color = 14) cube with vertices (-1, -1, -1), (-1, 1, -1), (1, 1, -1), (1, -1, -1), (-1, -1, 1), (-1, 1, 1), (1, 1, 1), (1, -1, 1) can be described in 3DV format as 8 -1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 1 1 1 -1 1 16 1 0 2 14 3 14 4 14 1 14 5 14 6 14 7 14 8 14 5 14 2 0 6 14 3 0 7 14 4 0 8 14 -------------------------- PROJECTIVE TRANSFORMATIONS -------------------------- Projections of points in 3D space to a plane constitute a simple topic that some books and some persons use to complicate. The projections can be classified in parallel or in perspective. In a parallel projection, the objects are not deformed because the projection rays are parallel. In the perspective type, the projection rays are not parallel and you can see vanishing points. The simplest parallel projections are the 'orthographic' ones. They simply annul the information in one coordinate, e.g. as T(x, y, z) = (0, y, z). You can get good results with the 'axonometric' projections. They are rotations followed by an orthographic projection. An example of an axonometric projection (in matrix form) is: ┌ cos Θ sin Θ 0 ┐┌ cos φ 0 sin φ ┐┌ 0 0 0 ┐ T(x,y,z) = [ x y z ]│ -sin Θ cos Θ 0 ││ 0 1 0 ││ 0 1 0 │ └ 0 0 1 ┘└ -sin φ 0 cos φ ┘└ 0 0 1 ┘ that is, T(x, y, z) = (0, x sin Θ + y cos φ, x cos Θ sin φ - y sin Θ sin φ + z cos φ) Thus, if you want to plot the point (x, y, z) in 3D space, just plot the point ( x sin Θ + y cos φ, x cos Θ sin φ - y sin Θ sin φ + z cos φ) on the yOz plane. Here, Θ and φ are the rotation angles (in radians) about the z and y axis. If you want to rotate σ radians around the x axis too, just add the matrix ┌ 1 0 0 ┐ │ 0 cos σ sin σ │ └ 0 -sin σ cos σ ┘ as the fourth factor on the matrix product above. Thereby, you can use the following steps to plot a point (x, y, z): (1) Get the values of (x, y, z), reading them on the file. (2) Project (x, y, z) on a plane, using an axonometric (or a perspective) projection. This can be made by calling the function ProjectPoint(x, y, z, &X, &Y). The C source to ProjectPoint() can be: void ProjectPoint(float x, float y, float z, int *X_proj, int *Y_proj) { float Y, Z; Y = x*sin(theta) + y*cos(theta); Z = (x*cos(theta) - y*sin(theta))*sin(phi) + z*cos(phi); *X_proj = (int) (A + Size*Y); *Y_proj = (int) (B - Size*Z); } where ■ A, B, theta, phi and Size are global variables. ■ (A, B) are screen coordinates chosen as the origin of the cartesian system. ■ theta and phi are the rotation angles around the z and y axis. (3) Draw the (X, Y) point on screen: putpixel(X, Y, color). There are too many books about projections. I would like to refer only two, both from the McGraw-Hill catalogue: "Theory and problems of Computer Graphics" (Schaum's Outline Series) R. Plastock, G. Kalley and "Mathematical Elements for Computer Graphics" D. Rogers, J. Adams ----------- FINAL WORDS ----------- These programs may not be sold or included in another software. However, the complete 3DVIS10.ZIP file may be copied and widely distributed, keeping the original files and credits immutable. These programs were tested a large number of times and it is my hope that they will work properly. The author of these simple programs is not responsible for any damage supposedly caused for their misusage. Use them by your own risk. You wouldn't expect me to say something here different from this, would you? Comments and suggestions are welcome and will be appreciated. My eletronic mail is CCENDM03@TERRA.NPD.UFPB.BR or CCENDM03@BRUFPB.BITNET (note that the character 0 is zero). Like many things here in Brazil, it doesn't work as it should do. So, sometimes I don't receive messages sent to me. Under normal conditions, I always reply ALL the messages that reach me. My thanks to professor Antônio Sales da Silva who made precious hints and some corrections to the text in English. 3DVISION is freeware, completely free of charges. But, if you like it, I would be very pleased to receive a postcard from your city. ┌────────────────────────────────────────────────────────────────────────────┐ │ Lenimar Nunes de Andrade │ │ Rua Lindolfo Chaves, 381 │ │ 58051-200 Joao Pessoa, PB - BRAZIL │ │ │ │ *** At the most easterly place in our poor and beloved South America *** │ └────────────────────────────────────────────────────────────────────────────┘