Warp & Blend of multiple displays with standard BlendOrder

I have a problem with the blending of multiple displays in standard BlendOrder (WarpAfterBlend). I am using Linux but I guess the problem exists on Windows too. On Linux the screen is the area where you can place windows and move them around and the display is “frame” through which you look on the screen. Usually the screen has the same size as the display and the origin of the display is at the origin of the screen. But especially if you have multiple displays the screen can be larger than one display e.g. two 1920x1080 displays and a 3840x1080 screen. Warp & Blend is done per display and changes way the content on the screen is shown on the display. Warping changes the geometric placement and blending the color of each pixel in the coordinate system of the display. A warping mesh consists of pairs of coordinates (normalized to the display space, 0,0 in the upper left corner) that specify where a pixel in the unwarped display should be displayed on the warped display e.g. 0.0,0.0 → 0.1,0.1 means that the pixel in the upper left corner is warped 10% to the right and 10% down. The warp matrix needs to have at least 4 points (e.g. the corners) passed to the GPU as triangles or triangle strip. But warping coordinates can also lie outside of the display (i.e. <0.0 or >1.0) meaning that pixels on the screen are warped outside the display or pixels from outside the display are warped into it. If the screen is only as large as the display this can result in black areas on the warped display, as there are no pixel around the screen, but in the case of a larger screen with multiple displays pixel from a neighboring display can be warped into the display.
And here is my problem: the standard BlendOrder is WarpAfterBlend meaning that the pixel in display space are first blended with
Output = Input * blendTexture ...
and then warped. However regardless of the size or aspect ratio of the blendTexture it is always scaled to fill the display completely but everything outside the display on the screen is black. So even if there are pixels on the screen from outside the display warped into it they are not visible, regardless of the blendTexture itself. These pixels are visible when only warping is applied, but as soon as any blendTexture is loaded these pixel are black. In a setup with only one display this is no problem, but for a multi-display setup this is a problem.
Is there a way to solve this problem by e.g. saying “just display everything from outside the display” or apply the blendTexture to the entire screen?


PS: Sorry for this lengthy post, but it took me a while to understand the problem and I use the post also for my own documentation;-)