## 3D visualization

Most mathematical software will allow you to create elegant graphs and objects in 3D; often you can then move your graph around with the mouse, finding the position at which it looks best. For complicated shapes like minimal surfaces, finding the parameters and position which produce the best view can be more time-consuming than creating the shape itself.

Of course, what you are seeing is a projection of a 3D scene onto the flat plane of your monitor, with all the lighting, shading, perspective and hidden line removal giving the strong impression of a 3D shape.

But how much more powerful the viewing experience would be if the software allowed some sort of stereo viewing! This wouldn’t be at all difficult; for stereo viewing all you need to do is to create two views of an object, from slightly different positions, and then display them simultaneously. And there are different ways of doing this:

1. “Free viewing”, which means placing the views side by side, for either cross-eyed viewing, or parallel viewing. For cross-eyed viewing, your right eye focuses on the left image, and your left eye on the right image. A 3D image will merge from the separate views. For parallel viewing, your right and left eyes focus on the right and left images – this can be done, with practise, by looking “through” the images – until the images again merge into a single 3D image. There’s a nice introduction at
http://www.angelfire.com/ca/erker/freeview.html
2. Create a red-cyan anaglyph image, in essence two views coloured differently and superimposed, so that when viewed with red-cyan glasses a 3D effect is observed. There are examples at the Wikipedia page
http://en.wikipedia.org/wiki/Anaglyph_image
3. Magic eye (autostereogram); otherwise known as a “Single Image Random Dot Stereogram” (SIRDS). Some people can’t see these at all; others have no difficulty. One problem with SIRDS images is that it is almost impossible to produce a coloured image.

Here are some websites of mathematical stereo interest:

1. Stereo 3D Graphics written with Maple:
http://www.math.tamu.edu/~yasskin/maplets/stereo/
Some very nice anaglyph stereo video images. Grab your anaglyph glasses and enjoy!
2. 3D-XplorMath-J:
http://3d-xplormath.org/j/index.html
This is a brilliant piece of software, which shows lots of different objects, in any 3D method of your choice. It is more of a mathematical museum, in that it is limited in its capacity to create totally new objects, but what it does do, it does superbly.

Just to whet your appetite, here is a cross-eyed image of a helix (click on the image to show it in full):

3. If you can see SIRDS images, this one is a beauty, an animation of two interlocked tori (again click on the image to show it in full):

## 3 thoughts on “3D visualization”

1. proportional says:

In the case of the helix, I think they must be fliped left->right. I get to join images but 3D result is very unpleasant. If you look at one of the helix endings you will realize.

2. Wow, I love these stereo images! And especially I want you to know that I CAN SEE THE SIRDS one. I’m very impressed with myself. Now I have to follow up your links to see what else is out there.