How to position object using forward, top and center coordinates in opengl.

Question

Hello

I have a scene and an object placed in some coordinates. I can transform the object using glTranslate(center) and then glRotate...

But how do I rotate an object not using angles but rather directions top and forward?

Thanks

What I'm looking is translation between model coordinate system and global coordinate system.

Answer 1

Since OpenGL works just with matrices there is no concept of top, bottom and so on..

you'll have to find a corrispondence between the rotation you wanna give and the orientation needed. Since glRotates(angle,x,y,z,) wants an angle in degrees you can just use a bidimensional array and store all 16 possibilities (from one of top, bottom, left, right to one of the same.. otherwise you can just see how much 90° steps are needed from actual position to new one and multiply the value by 90..

eg:

from top to bottom = 2 steps = 180°

from right to top = 1 step backward = -90°

Answer 2

Say you know 3 axes for your object in object space. For simplicity we'll assume these are the cartesian axes (if it's not the case, the process described below can be applied twice to take care of that):

ox = (1, 0, 0)
oy = (0, 1, 0)
oz = (0, 0, 1)

And say you have 3 other orthogonal and normalized axes in world space, indicating the top, forward and side directions of your object [*]:

wx = (wx.x, wx.y, wx.z)
wy = (wy.x, wy.y, wy.z)
wz = (wz.x, wz.y, wz.z)

Then the following (assuming column vectors) is a rotation matrix taking you from object space to world space:

    [ wx.x  wx.y  wx.z ]
M = [ wy.x  wy.y  wy.z ]
    [ wz.x  wz.y  wz.z ]

It's a rotation matrix because the determinant is 1 (othogonal and normalized lines). To verify it goes from world space to object space, just note how M*wx = (1, 0, 0) etc.

Now you want the exact opposite: from object space to world space. Just invert the matrix. In that case, the inverse is the same as the transpose, so your final answer is:

objectToWorld = transpose(M)

Two things remain:

1) Loading this matrix in OpenGL. glMultMatrix will do this for you (be careful, glMultMatrix is column major and needs a 4x4 matrix):

double objectToWorld[] = [ wx.x, wy.x, wz.x, 0, 
                           wx.y, wy.y, wz.y, 0, 
                           wx.z, wy.z, wz.z, 0,
                              0,    0,    0, 1 ];
glMultMatrixd( objectToWorld ); 

2) Translating. This is done just by following this with a call to glTranslate.

[*] If you have only two of the three, say top and forward you can easily compute the side with a cross product. If they're not normalized, simply normalize them. If they're not orthogonal it all gets trickier.