TOC
INDEX

Hints For Using 3D-XplorMath

• 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.
  
  
• Pausing Holding down the SpaceBar is a signal to 3D-XplorMath 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.) When you stop dragging an object to rotate it by releasing the mouse button, it will continue to rotate until you click the mouse again. 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 This kind of zooming merely changes the magnification of the object. If you are in stereo mode and want to make the object really zoom towards or away from you, hold down the Option key as well as the SHIFT key (and be prepared to duck)..
  
  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-XplorMath 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), min, max, 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-XplorMath 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.)

  
  

• Mouse and Keyboard Controls For easy reference, we collect here various ways of controlling 3D-XplorMath 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 holding down TAB will switch to patch mode (but will be SLOW), and engaging Caps-Lock will rotate a surface in a faster "rough" 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 (change the magnification of ) a 3D object 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.).Holding down both Shift and Option and dragging while in stereo mode will make the object move closer to or further from the Viewpoint.