TOC
INDEX

Hints For Using 3D-Filmstrip

• About This Object... (ATO) You should get into the habit of checking the About This Object... item of the Documentation menu the first time you select a new object. In many cases this will contain a lot of interesting information about the object, and may suggest one or more interesting morphs. Objects with an extensive ATO are marked by a blue diamond in the Main menu.
  
  
• Color Settings Your monitor should normally be set to Thousands of Colors, either using the Monitors control panel before launching, or the Set Monitor submenu of the programs Settings menu at any time while the program is running. The program will also work reasonably well at 256 colors. and there are some objects that look even better in Millions of Colors.
  
  
• Pausing Holding down the SpaceBar is a signal to 3D-Filmstrip to pause any drawing or animation activity. The program will continue from where it left off when the SpaceBar is released.
  
  
• Aborting There are two ways to abort lengthy drawing operations if you become impatient. Typing Escape or Command period (i.e., holding down the key marked with a cloverleaf while you type a period (".") will abort the creation of an object almost instantaneously (leaving it partially drawn). For most purposes, pressing the mouse button will act just like Escape or Command period, but in other cases it is a slower and more careful abort signal. For example, if a filmstrip is being created, then typing Command period will abort the creation (and initiate playback) immediately, while holding down the mouse button will abort the creation and initiate playback when the next frame is finished. Similarly, if a filmstrip is being played back, holding down the mouse button will stop the playback the next time the filmstrip reaches its end. In both cases you must continue to hold down the mouse button until the process aborts. When a filmstrip is stopped in this way, typing Command P will restart if from the beginning.
  
  
• Manipulating 3D Objects After creating a 3D object, the cursor changes to a semi-circular double-ended arrow. This is a signal that you have entered "Virtual-Sphere Mode". In this mode, as soon as you depress the mouse button, the 3D object will become temporarily embedded in a virtual transparent hard plastic sphere (called the virtual sphere) that is centered at the screen center. The equator obtained by intersecting the screen and the virtual sphere will be visible. Place the cursor anywhere on the top surface of the virtual sphere and drag the sphere to rotate it, carrying the embedded object along. (For speed, a surface will be shown in wire-frame style as you drag it, unless you depress the Caps-lock key.) If, while you are rotating, you hold down the Control key, the cursor changes to four arrows and you can now translate the object in a plane parallel to the screen. If instead you hold down Shift, then the cursor changes to an up-down arrow and you can "zoom" the object toward or away from you. In essence, you can move along an arbitrary path in the Euclidean group, and have the object "follow along".
  
  There is a second way to use the Virtual Sphere. If you select Spin from the Animate menu, then a three-dimensional object will start spinning around a default axis (which is visible). When you rotate the virtual sphere with the mouse, the 3D object will stay fixed, but the rotation axis will rotate with the sphere. If you release the mouse button, the object will start rotating about the new axis, and continues rotating until you again depress the mouse button and start rotating the axis. You can keep alternating these two phases as long as you like. To leave Spin mode, either press the Escape key, type Command-Period or Command Click, or simply click in the menubar. Needless to say, while Spin mode does not require being in stereo mode, it isn't too useful without it.
  
  Finally, do not forget that when working with three dimensional objects it is ususally a good idea to try switching to stereo viewing by selecting Stereo Vision from the View menu.
  
  
• User Defined Objects For all categories except the Polyhedra category, the Main menu contains one or more User Defined... items. When one of these is selected, it brings up a dialog permiting the user to enter formulas describing some object of the category. These formulas can contain the nine global parameters, aa, bb, ...,ii as well as appropriate variables (that depend on the current category). Clicking the Create of the dialog will give a default view of the object described by the formulas, or a user can instead click OK and go on to set various parameters and viewing options as usual before selecting Create from the Action menu to see the current object redrawn with the current choices of parameters and options.
  
  This ability of 3D-Filmstrip to work with User Defined... objects is based on a set of excellent expression parsing and evaluation routines written by David Eck. Expressions can include the operators: +, -, *, /, and ^ . The available built-in functions are: sin, cos, tan, cot, csc, sec, sinh, cosh, tanh, coth, arcsin, arccos, arctan, arccot, exp, ln, sqrt, cubert, abs, round, trunc, sign (or signum or sgn) and the three basic Jacobi elliptic functions, sn, cn, dn.. (Note that: "sqrt" denotes the sqare root and cubert the cube root. Also, "abs" returns the absolute value, "round" the nearest integer, while trunc throws away the fractional part.
  
  
• Window Size. When 3D-Filmstrip starts up it checks the size of the main monitor and the amount of memory available to it and creates the Graphics Window with an aspect ratio of approximately a golden rectangle in landscape mode and as large as memory allows up to a certain maximum. The user may then reshape the window to any size that will fit on the monitor as available memory allows. When you change the window size, any object that has been drawn will be redrawn with an appropriate change of scale. If you try to select a window size beyond what memory allows, the window will snap back to the biggest size possible with the same aspect ratio as the one you chose. (Well, almost. For technical reasons, the window width is rounded down to a multiple of sixteen pixels.)

  A strategy the program uses to create speedy animations is to keep all of the frames of a filmstrip in RAM. The program uses free memory to create frames for a blank filmstrip on an as needed basis---limited only by the available free memory. Since the amount of memory needed per frame depends on the size of the Graphics Window and the number of colors (or "pixel depth") of the monitor, if you have limited RAM and want a long filmstrip, you may need to reduce your window size. For example, a 400 by 600 pixel screen requires approximately 30 kilobytes of RAM per frame for black and white and 240 kilobytes of RAM per frame for 8-bit (i.e., 256) colors. For Oscillate and Morph, 12 frames are enough for good results, but for Rotate, 24 is close to the minimum required and 36 is really preferable. (To rotate an object with a filmstrip of length N, the program makes N frames, each showing an image of the object that has been rotated about the chosen axis of rotation by an increment of 360/N degrees from the previous frame, and a rotation increment of more than about 15 degrees looks too rough). So, for comfort, the program needs just for filmstrip memory about 24 X 30= 720 KBytes for black and white and 5.7 MBytes for 8-bit color. (It also needs another 2 MByte for its code, and its other data structures---windows, menus, etc.)

  So what do you do if you need more frames?

  First, quit all other applications that are running. This will make their memory available for extra frames. If you still need more frames, you can reduce the window size. If you change the size of the window from 400 by 600 pixels to 280 by 420 (still a pretty good size for most purposes) you will need only half as much memory per frame, so you can have twice as many frames. If that still isn't enough, go out and buy more memory. By the way, the program reports the maximum number of frames available for a filmstrip animation in the lower right corner of the graphics window. Each time you change the window size this number is readjusted, so you can easily adjust your window in stages until enough frames are available for your purposes.

  Of course, there is also the possibility of using real-time animation. This won't be quite as smooth, but for many purposes it is adequate. One rather special trick to make do with fewer frames in certain circumstances uses symmetry and was suggested by Hermann Karcher. It is implemented by setting a parameter called the Rotation Divisor in the dialog brought up by selecting the Set Number of Frames... item of the Settings menu. If a three-dimensional object happens to be invariant under a rotation of 360/n degrees about the rotation axis, then to create a rotation filmstrip with N frames it suffices to rotate the object only 360/(n N) degrees between frames, so a smooth rotation can be obtained with fewer frames. The integer n is the value that you should set as the Rotation Divisor. (One thing to be careful about: if you use this device with a surface that you have colored then you must make the surface coloration respect the symmetry.) To see this in action, select the Torus Knot from the Space Curves category. It is preserved by a 72 degree rotation about the z-axis. Try setting Rotation Divisor to 5 and rotating it.
  
  

• User Messages in the TitleBar 3D-Filmstrip occassionally communicates information to the user in a manner that is unusual for a Macintosh program, namely by putting messages in the title bar of the main (or "graphics") window. Customarily in Macintosh programs the title of a window is static. Frequently a window is associated with a file and its title is the name of the file. In 3D-Filmstrip the title is normally the name of an object that is being illustrated, but when the program needs to tell the user something it uses the title bar as a sort of billboard. For example, when a filmstrip is being created, the current frame and total number of frames are reported in the title.bar. (This is instead of a normal progress bar). And the first time after start-up that a filmstrip is played back, the user is told that to stop the animation he or she must type Command period or hold down the mouse button. In situations like the latter where the user might otherwise miss such advice or warning statements, the title bar is flashed a few times and a beep is sounded.
  
  
• Mouse and Keyboard Controls For easy reference, we collect here various ways of controlling 3D-Filmstrip using the mouse and/or special key combinations.

  ABORT Command period, Escape, or just holding down the mouse button will usually abort any ongoing operation. (The first two are equivalent and usually work instantly, while holding down the mouse will often permit some intermediate operation to complete before aborting.) Clicking the mouse is the correct way to stop the further evolution of an ODE or PDE initial value problem..
  
  CREATE Command K. After selecting an object, and changing various settings, press Command K to re-create the object wth the new settings. (This is equivalent to chooosing Create from the Action menu.)
  
  FAST MOTION To switch temporarily to drawing as fast as possible, hold down the DELETE key.
  
  PAUSE To temporarily pause the program, press the spacebar. The program continues where it left off when the spacebar is released. If you press the TAB key while the spacebar is down, and let the spacebar up while the TAB key is still down, you will be given the opportunity to take a picture of whatever was in the Graphics window when the spacebar was pressed and save it to disk.
  
  QUIT Command Q.
  
  ROTATE To Rotate a 3D object just drag it with the mouse. (A surface is usually rotated in wireframe, but engaging Caps-Lock will rotate a surface in patch mode.).
  
  SELECT In both the Plane Curve and Conformal Map categories, if the Command key is depressed, the cursor changes to a cross. You may then use the standard Macintosh technique to create a selection rectangle surrounding a part of the screen (click the mouse on the upper-left corner and drag to the lower-right corner). When the mouse is released (with the Control key still depressed) the contents of the rectangle will be zoomed to fill the whole window.
  
  SLOW MOTION To switch temporarily to Slow Motion Drawing, hold down the RETURN key.
  
  SWITCH In the Conformal Map category, to see the pre-image rather than the image, press Command and Option and hold down the mouse button.
  
  TRANSLATE To Translate a 3D object hold down the Control key while dragging it with the mouse. (A surface is usually translated in wireframe, but engaging Caps-Lock will translate a surface in patch mode.).
  
  ZOOM To zoom a 3D object in and out, hold down the SHIFT key while dragging the mouse vertically. (A surface is usually zoomed in wireframe, but engaging Caps-Lock will zoom a surface in patch mode.).