Shared join module for transport pieces; belt drawing uses it (t67 phase 1)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/DESIGN.md

@@ -486,11 +486,16 @@ above, including:
   on warns first that the save will be marked, and the mark stays with the world; any future
   achievements won't unlock in a marked world. Besides money, items and upgrades it may have
   game speed and other things just for fun.
-- **Screw conveyors only join a diagonal on the same row (t62, 2026-10-27).** A straight screw
-  joins a diagonal when it sits right beside the diagonal's end block, and that join is drawn
-  as an elbow. When the diagonal instead starts one block lower or higher, so the two only touch
-  corner to corner, they stay two separate ends and nothing passes between them. The owner tried
-  a corner join and found it looked odd, and building it that way is unusual anyway.
+- **One join rule for every transport piece (2026-10-27, replaces the t62 same-row rule).** The
+  owner wants all pieces to place and join the same way, so players know what to expect when
+  building. At a diagonal piece's end, call E the block diagonally past its last block (the
+  block its end points into). Another diagonal of the same slope continues in E. A horizontal
+  piece (flat belt, flat filter, horizontal screw) joins on the same row at the high end, and
+  in E, one block lower, at the low end: the rule sloped belts already had. A vertical screw
+  joins in E at either end. Straight pieces join the next block along their axis. Any other
+  placement is two separate ends and nothing passes between them. The owner found the old
+  screw rule, which needed the horizontal placed over the diagonal's last block at the low
+  end, inconsistent with every other piece.
 
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