[protoman3000]

A related question, how do GUIs actually resolve quickly on which element under the cursor a click lands?

How is the click propagated recursively through every component and is the position compared repeatedly at every step?

[badsectoracula]

They just enumerate all child windows, these events are not frequent enough for this to be a performance bottleneck. The check is something along the lines of

    Win* GetChildAt(Win* w, int x, int y)
    {
        size_t i;
        if (x >= w->ScreenX1 && y >= w->ScreenY1 &&
            x <= w->ScreenX2 && y <= w->ScreenY2) {
            for (i=0; i < w->ChildCount; i++) {
                Win* child = GetChildAt(w->Child[i], x, y);
                if (child) return child;
            }
            return w;
        }
        return NULL;
    }

Call this on the root window and you have the deepest child at the given coordinates.

(though there is usually a bit extra logic for handling, e.g., invisible and disabled windows)

[pixel_tracing]

I believe this can be resolved using a quad tree to resolve point locations and map them to a view in a view hierarchy