3D-XplorMath has a large number of "parameters" and environmental variables whose values collectively determine how an object selected from the Main menu will be displayed. At the moment an object is selected, all the relevant variables are given carefully chosen default values that determine the default view of the object. A user never has to worry about choosing different values for these variables if he or she is content with this default view. However, for the more adventurous users, there is a simple and fairly uniform way of giving them new values. Namely, the various items of the Settings menu bring up different dialog boxes in which the user can type in new values to replace the current values. (Several other variables that act as switches are instead set using the View menu.) Below we give brief descriptions of some of the more important variables that are accessed from the Settings menu.
The integer "Scale" is just the number of screen pixels per unit of length. Suppose your screen resolution is 95 dots per inch and you set Scale to 95, If you are in the Plane Curve Category and select Circle from the menu, then the radius of the circle is the Parameter aa whose default value is 1, so the circle will have a radius of 1 inch. If you increase Scale to 190, the circle will be redrawn with a radius of two inches. (Similarly, if you leave Scale at 95, but set aa to 2 in the Set Parameters dialog, you will again get a circle of radius 2 inches.) The larger you set Scale, the larger details will look on the screen. However this will not show any extra detail unless you also increase the resolution parameters at the same time.
The Set Parameters dialog allows a user to set the values of nine parameters called aa,b,cc,...,ii. Most objects in the 3D-XplorMath galleries live in families that are described by one or more of these parameters. For example, as mentioned above, a circle has a radius which is given by aa, while an ellipse has two semi axis lengths, given by aa and bb.
[Note: The boxes in the Set Parameters dialog accept algebraic expressions, so you can enter 2 * pi instead of 6.283..., or sqrt(2) for 1.414..., or e for 2.71828.... Moreover, these expressions are evaluated in alphabetic order, so if you put 2*pi in the aa box and sqrt(aa) in the bb box, and e * bb in the cc box, then the parameter cc will get the value (2.71828...) * sqrt(6.283...). The expression evaluator understands all the standard functions such as exp, sin, abs, round, etc.]
The Set Morphing... dialog allows you to set the initial and final values of the nine parameters, aa, bb, ..., ii, used during a morph (and, for the surface category, the initial and final values of umin, umax, vmin, vmax). That is, during a morphing animation the initial and final frames are drawn using these initial and final values, and the values for the intermediate frames are determined by linear interpolation. Often it is convenient to set the initial and final values to the current values and then make a few modifications. To do this, click on the button "Init to Current Parameters".
The Number of Frames (N) in a filmstrip determines how an animation will play out, and can be chosen independently for the three types of filmstrips (morphing, oscillation, and rotation). For example, if you choose Rotate from the Animate Menu, the filmstrip created will consist of a full rotation of 360 degrees about the Rotation Axis, each frame being 360/N degrees rotated from the preceding. Making N large will give a smoother rotation that takes longer to play through the loop once. Choosing Oscillate from the Animate Menu will create a sequence of N frames, each rotated 5 degrees from the preceding one, and Playback will go through the loop and then back. This give a quick way of seeing a smooth rotation through a smaller range.
The Custom... item of the Set Light Sources submenu of the Settings menu brings up one of the more complex dialogs of the program. This lets the user set the color of the five light sources (Source0, Source1, Source2, Source3, and AmbientSource) and the direction of the light rays from Source1, Source2, Source3. The two parameters that determine the characteristics of specular reflection from a surface (Specular Exponent and Specular Ratio) are also set using this dialog. This dialog is used in combination with the Set Coloration submenu of the Surface menu to determine the color of a surface when the Color item of the View menu is chosen. See the section on color for more details.
Set Rotation Axis controls the axis about which an object rotates when one choses Rotate from the Animate menu.
Three dimensional objects in 3D-XplorMath are always centered at the origin, and they are "looked at" from a point in 3D space called Viewpoint. (The viewing camera actually looks at the origin.) Set Viewpoint allows you to set the value of Viewpoint manually, However it is usually easier to use the mouse to rotate the object into a good position. (This does not really rotate the object, but rather rotates Viewpoint in the opposite direction.)
Setting the Focal Length can be used to change the 3D-impression of objects viewed in perspective, Similarly, setting eye separation changes the amount of stereo separation when 3D objects are viwed in stereo mode.
There is an imaginary plane called the Clip Plane that is between the Viewpoint and the origin and perpendicular to the line joining them. Its distance from the Viewpoint is called the Clipping Distance and can be set using Set Clipping Distance. Any part of the object that is "behind" the Clip Plane (i.e., closer to Viewpoint) is invisible. This allows you to see inside a 3D object. To seehow this works, choose Pinkall's Flat Tori from the Surface menu, set Clipping Distance to 14, and use the mouse to start rotating the torus towards you, after putting CapsLock down.
Set Timings controls how fast the drawings are made and how fast animations proceed