0) The idea of VR Mode (VR stands for Virtual Reality) is to provide a means
of moving around or even into 3D object to see it up close from interesting
and unusual perspectives.
1) To enter VR Mode, type Command V after selecting an object from the Surfaces
or Space Curves Categories. Exit VR Mode also by typing Command
V. (Typing Command period or Escape or clicking outside the 3D-XplorMath
window will also exit.
2) Expect an entirely different user interface while in VR mode. Menus do
not work and the keys and mouse behave differently. To get started you only
need the Wand S keys and the mouse, and they behave as follows:
a) The W key will move you towards the screen center (marked by a tiny red
cross) and the S key will move you away from it.
b) If the mouse button is depressed, then the screen center will move towards
the cursor (a cross in VR Mode). Note that this is the same behavior as in
a Quicktime VR Panorama.
c) So, to move towards a specific point P on an object, keep the cross cursor
on P and simultaneously hold down W.
d) For reasons of speed, objects are usually shown in lower resolution in
VR Mode, but holding down control for a few seconds will show a high resolution
image. (Pressing G for a moment will give a more long lasting resolution
increase.)
e) You can speed VR motion up by a factor of two to five by touching one
of the keys 2,3,4,5.
To get some practice with this, try flying through the hole of the torus.
The VR Mode in 3D-XplorMath gives the user a means for navigating in the vicinity
of a 3D object, to investigate it in ways that cannot be done otherwise. For
example, with it you can move through the handle of the Costa minimal surface,
looking around as you go or you can even fly into the interior of a surface
to study its anatomy. Consider what follows to be your basic training in using
VR mode.
I. VR Mode has a User Interface all of its Own !
The first thing to be aware of is that the entire user interface changes radically as soon as you enter VR mode. The menus become unavailable and the keyboard and mouse behave in ways completely different from how they behave outside of VR mode. This may seem disorienting at first, but you will quickly get used to it.
II. Entering and Leaving VR Mode.
To enter VR Mode, type Command V after selecting an exhibit from one of the 3D Category menus (Surfaces, Space Curves or Polyhedra). Similarly, to exit from VR Mode type Command V again. (You can also leave VR Mode, by typing Command Q or Command Period, or Escape, or you can click outside the 3D-XplorMath window with the mouse.)
III. Controlling VR Mode with Keys and the Mouse
After entering VR Mode you will notice a line of red text at the top left
of the main window advising you that you can leave VR Mode by typing Command
V, but otherwise nothing will change until you use one of the active controls
of VR Mode. These are:
A) The VR Mode Active Keys, namely:
1) W, A, S, D
2) The Arrow Keys
3) 1,2,3,4,5
4) R
5) F, C, G, and Shift
6) X and O
7) TAB, Control, Delete
B) The Mouse Button.
As soon as any one of these controls is used, you will see not just the selected
object, but rather a "scene" consisting ot the selected
object against a seascape backdrop. (This seascape is not there for aesthetics;
the extra scenery give visual clues concerning the way the viewpoint is moving
relatve to the object.) Notice that to speed up redrawing---so that moving
around is faster and smoother, the object may have a lower than normal resolution,
and so look less refined. However, if you hold down the Control key for a
few moments, the resolution will temporarily return to normal. Also, pressing
the G key will increase the resolution until VR
Mode is exited.
We now describe the effects of all the above controls.
III A 1) and 2)
Moving View Point using W, A, S, D, and the Arrow Keys
The game now is to move around in the scene. The most basic action is to
move the View Point toward or away from the screen center (i.e., in the View
Direction) and this is effectuated by pressing the W key or S key respectively.
Another basic action is shifting the View Point (i.e., the eye position)
either to the left (with the A key) or to the right (with the D key). Since
the View Direction always points at the screen center, of course the object
and the scene will seem to move in the
opposite direction, i.e., to the right or left. Since the screen center plays
such an important role, it is usually marked by a small red cross, to make
it easy to locate precisely. (However, if you do not like seeing the cross,
you can make it disappear by touching the X key. touching it again will bring
the red cross back.) Instead of using the A and D keys to move the View Point
left or right,you can also use the left and right arrow keys. You should
try to control motion as much as possible with the W key and the mouse, using
the other keys only when necessary.
Remark. Note that we have explained how to move the View Point left and right and forward and back, but not how to move it up or down. In fact the recommended way to move the View Point up or down, is to use the mouse to point the View Direction up or down (see below) and then move the View Point forward with the W key. However, it is possible to move the View Point up and down by using the up arrow and down arrow keys.
III A 3)
Speedup with the Number Keys.
If moving View Point seems too slow, it can be speeded up using the number
keys 1,2,3,4,5. Touching 2 for example will make the motion go at twice the
standard speed, and similarly pressing 3 will make it three times as fast,
etc. (Of course there is a downside---you are not really speeding anything
up, but rather moving in larger jumps, so the motion will not be as smooth.)
You can return to standard speed at any time by pressing 1.
III A 4)
Reverse View Direction with R and Reflect View Point in Origin with Option
R.
If you move all the way through an object (using the W key) you may want to look
back at it by "turning your head 180 degrees", i.e., reversing
the ViewDirection. You can do this by pressing the R key for a moment. If you
also press Option then in addition the View Point (eye position) will be reflected
in the origin. Since most objects have their center of gravity near the origin,
this is a good quick way to "look at an object from the other side".
III A 5)
Change Focal Length, Clip Distance, Resolution, and Scale with F, C, G,
and Shift.
Holding down the F key will increase the Focal Length (i.e., the distance
from View Point to the Projection Plane) or decrease it if Option is also
pressed at the same time. Similarly, holding down C will increase the Clip
Distance, or decrease it if Option is pressed. (Clip Distance is the distance
from View Point to the Clip Plane, and parts of an object behind the Clip
Plane are not shown.) Pressing the G (for Grid) key will increase resolution,
or decrease it if Option is pressed. And finally, Shift and Option Shift
increase and decrease the Scale (i.e., pixels per unit length).
III A 6)
Hiding and Showing the Screen Center with X. Hiding and Showing Axes with
O
As already mentioned, there is normally a small red cross at the screen center,
marking where the View Direction meets the projection plane. This can be
quite helpful, particularly when rotating the View Direction by mouse (see
III B, below). However it can be hidden (and then shown again) by touching
the X key.
Similarly you can switch between showing and hiding the axes (hidden by default) using the O key.
III A 7)
Showing Viewing Parameters with TAB and using Control for Higher Resolution.
If the TAB key is depressed, various viewing parameters are displayed at
the top of the screen, namely: Focal Length, Clip Distance, Scale, View Direction
(latitude and longitude), View Point, and Image Plane Center. Recall also
that holding down Control will temporarily display a high resolution view
of the object. Sometimes you may get lost in VR Mode and be unable to find
the object. If you press the Delete key the View Parameters are reset to
their initial values.
III B. Moving the View Direction with the Mouse
The final basic action is rotating View Direction, and to do this you use the mouse. Namely, if the mouse button is depressed and the cursor is moved around on the main window, then View Direction (that is, the unit vector pointing from View Point towards the screen center) will be rotated in space, while the View Point itself remains fixed. (Think of it as rotating your head while keeping the position your head fixed.) This works in detail essentially the same as it does in a Quicktime VR panorama. If the cursor (a cross in VR Mode) is held right over the red cross marking the screen center, then View Direction does not rotate so the scene and the selected object remain stationary. However, if the cross cursor is moved off center (with the mouse button depressed) then the red cross at the screen center will chase the cursor at a speed proportional to the distance of the screen center from the cursor. Thus, suppose you want to manuever the View Point to a particular point P. The trick is to hold down W (to move View Point toward the red cross) while simultateously keeping the cross cursor on the point P, thus making the red cross approach the point P. See if you can use this technique first to maneuver the View Point through the whole in the torus or Klein Bottle, and then through the handle of the Costa minimal surface. It is easier than you might think, and "Practice Makes Perfect" !