Wow, LOWORBIT, you are good. I love the sites, thanks, it will help. To answer your comment, i am not knew to openGL, OR 3D. If i was, i wouldn''t have decided to create this object. It seems damn near impossible to me now. But i will still go on, if i figure it out then i will tell you all. Again thanks for all of your info!

I don''t have much experience on OpenGL or on PCs period with this sort of thing, but I did get a rotating 4-d cube working on my TI-83. It might take a little work, but here''s what I did: I found all of the vertices, then figured that I should draw a line from one vertex to another if and only if there was only one coordinate different. Going by that, I got a list of all of the lines to draw to make a hypercube. ''Course, that''s just good for a wireframe model, but maybe you can work with it from there and make it more interesting.

CrystalFire

Oluseyi:
Not sure what exactly you mean by unfolded.

Anyhow, a hypercube assumes four spatial coordinates. This is perfectly valid, and can even be useful. For something like a hypercube rotating, you could try to figure out what it would look like in 3D and emulate it, or you can set up a 4D model using 4D vectors, rotate them around some plane with a simple 4D rotation matrix, and then project into 3-space. Once you''ve projected into 3-space, OpenGL will handle the rest. Maybe some pseudo-code will help?

v1:=[1,1,1,1];
rot:=
[[cos(t), -sin(t), 0,0],
[sin(t), cos(t), 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1]];

To perform the rotation, just multiply the vector by the matrix (which in this case is a rotation matrix around the z-w plane):

v2:=v1*rot;

Now, we want to project this onto a three-space, just like opengl projects our 3D objects onto a two-space. I haven''t done this much, but it looks like openGL uses a projection matrix from 3 space to 2 space using a 4x4 matrix, so we probably want a 5x5 matrix. This means that we need to put a new weighting variable
into the v2, making it a 5-vector:

v2:=[v2[1], v2[2], v2[3], v2[4], 1];

Now, we can set up a 5x5 matrix to do the projection. I''m pretty sure that it goes like this:

proj:=
[[1, 0, 0, 0, 0],
[0, 1, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 1, 0],
[0, 0, 0, 1/d, 0]];

When we multiply the projection by the v2, we will get something that doesn''t have 1 as it''s last component, so we have to normalize it with respect to the weight:

v2:=v2*proj;
v2:=[v2[1]/v2[5], v2[2]/v2[5], v2[3]/v2[5], v2[4]/v2[5], 1];

By the properties of the projection matrix, the w term (second from last) is d, which is the solid that the hypercube is being projected to. So, we can just make a new vector, this one it 3-space, that only uses the first three components of the 5D vector. This works because every vector going through the matrix will have the same w value, so it can essentially be dropped. Thus:

v3:=[v2[1], v2[2], v2[3]];

and we can now do the normal openGL thing:

glVertex3fv(v3);

Do this for all your verts, and you''re set!

well, I guess I sucked the fun right out of that one...

quote:Original post by tsuraan
Oluseyi:
Not sure what exactly you mean by unfolded.

We live in a 3D world, so we can''t actually fathom what 4 dimensions would look like. We therefore take a page from the translation of a cube to 2D space: if we unfold the sides of a cube, we obtain 6 squares (2d figures). By analogy, if we unfold a tesseract/hypercube, we obtain 8 cubes. We then try to fold them back into place, and the result is cubes that are at once inside and outside each other (hences the habitual representation of continuous "inter-rotation".)

Your other math and logic is accurate (it did take the fun out, though...)

WOW, i never excpected this much response to the question. I love the idea tsuraan, i dont think i ever would have thought of it. A few things tho...
CrystalFire im not sure if you will see this, but could i have that source for your ti 83, i have one too, and it would really help. Second, what do i say?!?!

glLoadIdentity();
glTranslatef(1.5f,0.0f,-7.0f); // Move Right And Into The Screen

glRotatef(rquad,1.0f,1.0f,1.0f); // Rotate The Cube On X, Y & Z

glBegin(GL_QUADS); // Start Drawing The Cube

what do i do with that, i mean, use your matrix v3 or v2. Or the prj, i just dont konw, maybe i am just alittle to inexpericed for this now.