A question on the transformation pipeline in OpenGL superbible 5th

The author used the following data structure for the convenience of representing a frame of reference (on Page 168 of the book)

class GLFrame{
         float vLocation[3];
         float vUp[3];
         float vForward[3];


Then he provided a function that calculates a matrix which is unclear to me (on Page 168 of the book):

void GetMatrix(M3DMatrix44f matrix, bool bRotationOnly = false)
   // Calculate the right side (x) vector, drop it right into the matrix
   M3DVector3f vXAxis;
   m3dCrossProduct3(vXAxis, vUp, vForward);

   // Set matrix column does not fill in the fourth value...
   m3dSetMatrixColumn44(matrix, vXAxis, 0);
   matrix[3] = 0.0f;
   // Y Column
   m3dSetMatrixColumn44(matrix, vUp, 1);
   matrix[7] = 0.0f;       
   // Z Column
   m3dSetMatrixColumn44(matrix, vForward, 2);
   matrix[11] = 0.0f;

   // Translation (already done)
   if(bRotationOnly == true) 
      matrix[12] = 0.0f;
      matrix[13] = 0.0f;
      matrix[14] = 0.0f;
      m3dSetMatrixColumn44(matrix, vOrigin, 3);

    matrix[15] = 1.0f;

He used the matrix on Page 174 through

modelViewMatrix.MultMatrix(spheres[i]); //it equals to multiply the matrix got from spheres[i].GetMatrix()

Here, spheres[i] is an object of the GLFrame class.
I think the author actually wanted to multiply the object’s model transform matrix, but he misused the GetMatrix() function.
Could anyone help me verify my assumption?

Sorry for my rough description.

I assume modelViewMatrix is of type M3DMatrix44f? My guess is there is an overload of MultMatrix that takes a GLFrame, like so:

void M3DMatrix44f::MultMatrix(const GLFrame& frame)
    M3DMatrix44f frameMatrix;


This assumes that the signature of GetMatrix is actually:

void GLFrame::GetMatrix(M3DMatrix44f& matrix, bool bRotationOnly = false) const

Note the “&” to allow modifying the argument.

But the call of [LEFT]GLFrame::GetMatrix() does not return an identity matrix by default. In fact, it is

{-1, 0, 0, 0,
   0, 1, 0, 0,
   0, 0,-1, 0,
   0, 0, 0, 1
}//in column major

I expect it to be an identity matrix.

Because when GLFrame was first initialized,
vUp is {0, 1, 0},
vForward is {0, 0, -1},
vLocation is {0, 0, 0}
In the function GetMatrix(), the author first computed vRight which is the cross product of vUp and vForward, and then drop the three vectors into the resulting matrix:

{vRight_x, vRight_y, vRight_z, 0
vUp_x, vUp_y, vUp_z, 0
vForward_x, vForward_y, vForward_z, 0
vLocation_x, vLocation_y, vLocation_z,  1
}//in column major

but it should return an identity matrix.[/LEFT]