3D View Help

The Select 3D View menu allows you to select various methods of viewing the 3D plots created in CalcPlot3D.  Anaglyphs require 3D glasses, while Stereo Pair and Cross-eyed require some training of your eyes.  Using the 3D glasses tends to be less difficult (and generally should produce less eye strain), but try all the methods and decide which one(s) you prefer.

Standard Projection is the method used most of the time by most people.  It just creates a two dimensional projection of the three dimensional plot (in perspective or parallel views).  The other options all provide a more convincing 3D image than this method, although all require either 3D glasses or some concentration on the part of the viewer.

Most of the options are ANAGLYPHS.  This means that you will need to have 3D glasses of some sort to view the images in 3D.  I prefer to use the Red-Blue (Red-Cyan) 3D glasses.  Wear them with the red lens in front of your left eye and the blue lens in front of your right eye.  They actually work well for all but one of these options.  Amber-Blue 3D glasses were recently distributed for the Super bowl half-time show by many grocery and convenience stores.  They are sometimes called ColorCode 3D glasses because they are used for a proprietary Anaglyph method by this name.  These glasses give an almost full-color 3D image, but the images tend to be a little less sharp and a little on the dark side.  I have read that Red-Green 3D glasses are common in Europe.  They should work for the Red-Green Anaglyph.  You can obtain any of these types of 3D glasses cheaply either at a book store or online, or you can create your own 3D glasses using red and blue cellophane.  You can also find web sites that will send you free 3D glasses, for example Rainbow Symphony.

Colored Red-Cyan Anaglyph (on white) is my favorite.  It produces a sharp image with some nice (though limited) colors.  However, note that anything that would normally be red is black.  Wear the glasses so the red pane is in front of your left eye and the blue pane is in front of your right eye.

Amber-Blue (ColorCode) Anaglyph is also a very useful option, since it allows most colors, including red (but not much blue).  To use it you will need the special Amber-Blue 3D glasses mentioned above.  Note that this is the only option that works with this type of 3D glasses. Wear the glasses so the amber pane is in front of your left eye and the blue pane is in front of your right eye.   As mentioned above, the one draw-back of this type of Anaglyph is that the images tend to be a little less sharp than the other anaglyphs, and they tend to be a little on the dark side.

Grayscale Red-Cyan Anaglyph (on white) produces perhaps the sharpest 3D image, but it is drawn using black lines and grayscale surfaces on a white background.  You should have little trouble viewing the images as 3D.  Note the two options just above the 3D View Help.  These options allow you to adjust how close the plot appears to be.  Generally viewing anaglyph images is easiest on your eyes if you use the first option (projecting through the screen), but this type of anaglyph has the least amount of "ghosting" (shadows of the other eye's view) when you project the image in front of the screen, so I like to suggest trying it sometimes.

Red-Green Anaglyph (on black) adds some color to the view (mostly a yellow hue), but it is otherwise fairly similar to the previous Anaglyph style.  The image uses yellow lines (instead of black) on a black background, and the surface will use yellows of varying brightness.  This style of anaglyph produces more "ghosting" when you select the option to project in front of the screen though.

Red-Cyan Anaglyph (on black) a third option that produces white lines and grayscale surfaces on a black background.

 

The other two options do not require 3D glasses, but they do require some concentration and training.  They can also be a bit harder on the eyes than the Anaglyph options.

Stereo Pair presents two side-by-side images, the one on the left to be viewed by the left eye, the one on the right to be viewed by the right eye (sometimes called the parallel free-vision fusion [wall-eyed] technique).  This is one of the two full-color options to view the surface in more convincing 3D.  However, it does require some practice and concentration to use effectively.

    Recommended Technique:  One way to successfully train your eyes to view the 3D image using a stereo pair is to start by closing your right eye and view the pair with only your left eye. 

  1. Place your left index finger close to your face and position it between your eyes in such a way that it covers up the image on the right (or at least the left half of it).  Keep your left index finger in this position as you continue. 
  2. Now repeat this process with your right eye (closing your left eye) and using your right index finger to block the image on the left from reaching your right eye.
  3. Now open both eyes.  You should see two images.  Try to bring these images together to form a single image.
  4. Personally, I have to actually tilt my head slightly to the right to cause the images to align, but this will depend on your eyes.  It helps me to use the box around the 3D plot to bring the 3D image into focus.  It also may help to start rotating the image with the mouse.

After some practice, you should be able to bring the 3D image into focus at will without needing to use your index fingers in this way.  You should even be able to make adjustments and menu choices while keeping the 3D image in view (once you are comfortable with this method).

Cross-Eyed also presents two side-by-side images, but this time the one on the left is to be viewed by the right eye, and the one on the right to be viewed by the left eye (hence the cross-eyed name).  Some say this is easier for them than the Stereo Pair, but I do not agree.

Recommended Technique:  To be honest, I have had a lot of difficulty with this method.  But here is what I have read elsewhere to be an effective method to try:

  1. Place an index finger or a pencil between the images (I prefer to place it just below the images).
  2. Focus both eyes on your index finger (or the pencil).
  3. Slowly bring your finger (or pencil) towards your nose, staying focused on it, but paying attention to the background images in your peripheral vision. You will notice that instead of two images, you will see four images floating about.
  4. Continue bringing your finger (or pencil) closer to your nose, and hopefully you will see the two middle images merge into one.
  5. When this happens, stop moving your finger (or pencil). You should now see three images in the background. The middle one consists of the overlap of the two separate views.
  6. Slowly remove your finger (or pencil) from your field of vision, while keeping the middle images overlapped (as one image).
  7. Gradually force your focus out to the composite image in the middle.
  8. If you have problems keeping this middle image in focus, try leaving your finger (or pencil) just below the image for a while, while still focusing on the center image. Use your finger (or pencil) to refocus (compose) the middle image, as needed.
  9. If it does not seem to work at first, don't be too worried.  I still cannot get it to work well.  Rest your eyes for awhile and try again later.

 

This 3D help page was created by Paul Seeburger, Assistant Professor of Mathematics
at Monroe Community College in Rochester, NY, for CalcPlot3D, part of
a multivariable calculus visualization project funded in part by the NSF.

If you have comments or suggestions, please send me an email at:
pseeburger@monroecc.edu