Object orientation within an opengl scene - opengl

Question

I'm having difficulty getting the right orientation from my objects within a scene. The objects are defined in standard Cartesian coordinates in the same units as I define the scene.
I then define my scenes matrix with the following code:
void SVIS_SetLookAt (double eyePos[3], double center[3], double up[3])
{
// Determine the new n
double vN[3] = {eyePos[0] - center[0], eyePos[1] - center[1], eyePos[2] - center[2]};
// Don't I need to normalize the above?
// Determine the new up by crossing witht he Up Vector.
double vU[3];
MATH_crossproduct(up, vN, vU);
MATH_NormalizeVector(vN);
MATH_NormalizeVector(vU);
// Determine V by crossing n and u...
double vV[3];
MATH_crossproduct(vN, vU, vV);
MATH_NormalizeVector(vV);
// Create the model view matrix.
double modelView[16] = {
vU[0], vV[0], vN[0], 0,
vU[1], vV[1], vN[1], 0,
vU[2], vV[2], vN[2], 0,
// -MATH_Dotd(eyePos, vU), -MATH_Dotd(eyePos, vV), -MATH_Dotd(eyePos, vN), 1
0, 0, 0, 1
};
// Load the modelview matrix. The model view matrix shoudl already be active.
glLoadMatrixd(modelView);
}
I am attempting to display n-1 objects such that each object is facing the object in front of it, excluding the first object which is not displayed. So for each object, I define the up, right, and forward vectors as such:
lal_to_ecef(curcen, pHits->u); // up vector is our position normalized
MATH_subtractVec3D((SVN_VEC3D*) prevcenter, (SVN_VEC3D*) curcen, (SVN_VEC3D*) pHits->f);
MATH_NormalizeVector(pHits->u);
MATH_NormalizeVector(pHits->f);
MATH_crossproduct(pHits->u, pHits->f, pHits->r);
MATH_NormalizeVector(pHits->r);
MATH_crossproduct(pHits->f, pHits->r, pHits->u);
MATH_NormalizeVector(pHits->u);
I then go on to display each object with the following code:
double p[3] = {pHits->cen[0] - position[0],
pHits->cen[1] - position[1],
pHits->cen[2] - position[2]};
glPushMatrix();
SVIS_LookAt(pHits->u, pHits->f, pHits->r, p);
glCallList(G_svisHitsListId);
glPopMatrix();
void SVIS_LookAt (double u[3], double f[3], double l[3], double pos[3])
{
double model[16] = {
l[0], u[0], f[0], 0,
l[1], u[1], f[1], 0,
l[2], u[2], f[2], 0,
pos[0], pos[1], pos[2], 1
};
glMultMatrixd(model);
}
I would expect this to work for any object such that the output would be whatever was defined in the Cartesian coordinate system would be present at the given point oriented such that it was pointed at the proceeding object with 0,1,0 and 0,-1,0 from the defined object would be aligned vertically on the screen. What I am seeing instead (by using simple rectangle as the object to be displayed) is that the objects are consistently rotated about the forward axis.
Can anyone point out what I am doing wrong here?
[Edit]
I've displayed an axis grid without translating by taking the three vectors multiplying a scalar and adding/subtracting it to the centre point. Doing this, the axis align up as I would expect. Overlaying the object described above shows the object to not be aligned the same way. Is there a relationship between the object space forward, right, and up vectors and the desired world-space vectors that I am missing? Am I simply completely off the mark with regards to my rotation translation matrix?

Answer 1

You are conflicted here; part of that matrix is transposed and part of
it is correct... you have the 4th column correct but your top-left 3x3
matrix is transposed. Each column of the 3x3 matrix (row in that array
of 16 double) is supposed to be one of your axes. It should be:
l[0],l[1],l[2],0, u[0],u[1],u[2],0, f[0],f[1],f[2],0,
pos[0],pos[1],pos[2],1. – Andon M. Coleman
This was dead on. Thanks Andon.

Answer 2

Building an entirely new modelview matrix from scratch using a 'lookat' implementation for each object is, frankly, crazy (or will at least drive you crazy). What you're doing is tantamount to trying to build a scene by having set of objects which are always in a fixed location, and constantly repositioning a camera to catch them from different angles.
A lookat style function should be called once to set up the camera (the view portion of the modelview matrix) position, and subsequently you should be using the matrix stack to position objects within the scene (the model portion of the modelview matrix). That's why it's called the modelview matrix, and not just the view matrix.
In code terms, it would look something like this
// Set up camera position
SVIS_LookAt(....);
for (int i = 0; i < n; ++i) {
glPushMatrix();
// move the object to it's location relative to the world coordinate system
glTranslate(...);
// rotate the object to have the correct orientation
glRotate(...);
// render the geometry
glCallList(...);
glPopMatrix();
}
Of course this assumes that everything has it's position defined in world coordinates. If you have a hierarchy of objects, then you would need to descend into an objects children between the glCallList and glPopMatrix in order to have their locations applied relative to their parent object.