Position, Look At, Roll

The six parameters for the X, Y, Z Position from the camera and its "Look At" target plus the roll parameter define where the camera is positioned, where it is looking and how it is orientated.

As said in the introductory chapter where 3D Warping is compared with 2D Warping, you need to adjust the camera's and the object's position and orientation as well as the lens setting. Regarding the position and orientation, there are two possible ways to do so: manual measurement or marker-based calibration.
To measure distances and sizes manually, you should first define where the zero point of the coordinate system is; to simplify the process you can define that it lies on a certain corner of the object or projector. Based on that zero point, you need the relative X,Y and Z distances to the screen (exactly where the object's pivot point lies) and projector lens (center of the lens). Then you need the size of the real object to convert the measured "number" into the unit that has been used for the size of the virtual object. If the virtual size is 2 GU, and the real size is 200cm, the conversion factor is 1 GU / 100 cm. Thus, you know, that a distance of 150cm is 1.5 GU (distance * conversion factor).
Now you can calculate the XYZ position of the camera and the object (corresponding with the Look At Target) as well as their orientation. The orientation from the object results from its XYZ angle. The orientation of the camera is the result of the difference between the position and the Look At target plus the Roll parameter

FOV, Lens

The parameters FOV and Lens express the same setting: the opening angle. When you enter the FOV, the Lens parameter is automatically calculated and vice versa.

There are two ways to find out the opening angle: manual measurement or iteration.
For manual measurement you need the width of the projected image plus the distance between the center points of the lens and the image (at the depth where the width was measured). These two numbers can be entered in the FOV calculator available with the Calc button. The measuring unit does not matter as long as it applies to both values. Click "Apply" to transfer the calculated value to the main tab.

Alternatively you can simply try out and approximate what the lens factor is. If you have a lens with a fixed zoom, use this lens factor and try out whether a slightly higher or lower number gives better results. (Even fixed zoom lenses, can slightly change due to mechanical vibrations.) If the lens has a variable zoom, start with the smallest lens factor and increase it slowly. It is clearly visible in the projected image whether you are approaching the correct factor or not.

Aspect

The Aspect parameter expresses whether the cameras aspect mode is the same one as the output's aspect mode.

Near Plane, Far Plane

Near and Far plane define what part of the cameras cone is rendered. If an object lies outside of the range, it is not seen and rendered by the camera. In 99.9% of all cases the default values give good results and should be not be changed.

Lens Shift

The Lens Shift parameters define how much a projector is lens shifted. For 3D Warping (either measuring or marker-based) it is strongly recommended to reset the projector(s) lens shift to 0,0. However, some projectors have a build in lens shift that cannot be adjusted. You can see that easily by looking onto the lens if the projected image is in the center of the lens. If it is outside of the center, there is an active lens shift. Or, you can see it from the side: check whether the lens' center matches the center of the projected image. In the left image, one can clearly see that the projected blue outlines image is above the projector itself. If the projector had no lens shift applied, the image would look like the one with the orange outline.

In the case that the lens shift cannot be adjusted in the projector, use the lens shift parameters in the Warper. In practice you can measure the lens' center to the floor and mark it on your screen depending on the projectors angle, or you can use a laser. At the end you should be able to know where the unshifted image center should be.

Then adjust the lens shift so that the center of a default mesh is at the same height and width as the marked lens center. That could mean of course that parts of the mesh are outside of the projected image. This will be corrected after adjusting the position and orientation of the camera.