Thanks a lot for the cogent example! I hadn't understood what a Picture Control really was, nor how the 2D drawing VI worked. I've now made a Picture Control that fills the entire screen, colored it black, and simply put all of my targets (so nicely specified, with circles characterized by their radius and center, no more upper, left, lower, right bounding box). Very quick, only a few messay Property Nodes. Now if I could only get rid of that 3-pixel-wide border around my picture ... [but I can probably live with that, too].
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