Q:

WPF: Finding 3D-visuals that are partially inside a 2D rectangle

I am making a WPF program with the possibility to modify data graphically in 3D. In order to give the user the option to select multiple graphical objects at the same time, I want to implement a selection rectangle. (Just like the one in windows explorer.) A common functionality in programs like this one is to have 2 different functions for the selection rectangle, and that the user can somehow choose which of the methods should be used.

Any object that is partially or completely inside the rectangle is selected.
Only objects that are completely inside the rectangle are selected. 

The 2nd method is straight forward by using the bounding box of each object, and check if it is inside the rectangle. The 1st one on the other hand, seems to be quite some work. All my graphical objects are complicated 3D figures, and can be rotated by the user in any way. At the moment I am unable to find any other way than checking if any of the triangles in the mesh of any of the objects cross my 2D rectangle, and that can be quite time consuming.
I have little experience with WPF 3D, but I have done this before in OpenGL. Then I could tell OpenGL to draw a specific area of the screen, and the collect a list of objects that was visible in the specific area. All I needed to get the functionality I wanted was about 5 lines of code. 
I guess my question is this:

Is there a way to do this with WPF 3D, similar to the OpenGL approach?
If not, is there any other smart way to find all objects (Visual3D) in a viewport that is partially behind a 2D rectangle?

I refuse to believe I am the only one with this kind of problem, so I hope a clever mind can point me in the right direction.
Regards,
Sverre

Thank you for your answer!
The 2D-rectangle is just in front of the camera and extending infinitely forward. I want to get any object that is partially or completely inside that frustum.
The camera we are using is an orthographic or perspective projection camera (System.Windows.Media.Media3D.ProjectionCamera). The reason we are not using the matrix camera is that we are using a 3rd party tool that does not support the matrix camera. But I am sure there is a way to get the matrix from a projection camera as well, so that is hopefully not the problem.
In theory your solution sounds like just what we need, but I am not sure how to proceed. Do you have any links to sample-code, or can you give some more hints on how to actually implement this?
Btw: Since we are working with WPF, we do not have direct access to DirectX. At least that’s what we have concluded after some research. You mention use of the z-buffer, which we haven’t been able to access through WPF. If you know a way to access the z-buffer, it’s greatly appreciated! This is of-topic, but we have struggled to disable the z-buffer for some time, but have given up…
Best regards,
Sverre

A:

A 'smart' way would be to transform the rectangle into a box using the Camera's matrix
And then do a intersection of all the objects and the box. 

