Yes Charles,
Of course you can.
glGet() gives you access to the matrix currently selected with
glMatrixMode() - either a projection, or modelview, or texture matrix. Conversely, you can always prepare your own matrix and upload it using
glLoadMatrix(). The on-screen objects will all be transformed accordingly in the next frame rendered. Naturally this will only be seen if the respective matrix is not cleared to identity at the beginning of the frame.
In fact, immediate-mode OpenGL uses
glTranslate() and/or
glRotate() calls to operate on the modelview matrix' members atomically. But there's nothing prevents you from uploading a precomputed matrix in one go with
glLoadMatrix() in each frame too.
The current modelview matrix that you copy in your own array with a
glGetFloatv(GL_MODELVIEW_MATRIX, mtxArray) call can also be used to calculate the current vertex coordinates for all the polygons in a given 3D model (a.k.a. mesh, a.k.a. object) associated with that matrix. That is a simple task for a static object; you just multiply each one of the model's vertices by the matrix.
Compound dynamically moving models are constructed as a hierarchy of objects and are more difficult to calculate. To simplify the calc, modern 3D models are usually split into several dozens of polygon groups (meshes) each of which is spatially bound to one or more parental "bones". The bones are interconnected into a tree-like "skeleton" pretty much like the bones in the skeleton of a living creature. Matrix (or better, quaternion) transforms are applied not to each vertex of the model but rather to the "joints" between the bones in the skeleton, so that each joint drags the associated bone which in its turn drags the associated mesh of polygons in the model. Please run the attached exe for a movie capture of a 3D model and its skeleton as it walks on my desktop in my 3D model viewer.
That's why the dynamic actors of a scene such as e.g. players or monsters are conventionally stored in a standard basic state called "T-pose" looking straight ahead, mouth closed, arms spread wide apart at the shoulder level, palms down, legs straight, feet parallel (see the snapshot attached below).
Matrix calc based on OpenGL's current modelview matrix is however computationally intensive so simpler tasks like determining the object under the cursor are usually fulfilled using simpler tweaks that can be performed almost entirely on the GPU.
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