Draw the ground as an exercise mat that rotates with the figure

The floor rectangle was screen-locked, which broke the illusion the
moment the camera orbited. It is now a world-space quad on the ground
plane, sized to each motion's projected footprint across its key frames
and rotated through the same camera as the figure - a long rectangle in
profile, a parallelogram mid-orbit, end-on when face-on. Both renderers
in lockstep; fixtures unaffected (the mat is a pure addition).

Claude-Session: https://claude.ai/code/session_01LEoff8bXGBS83tK1c55Mf7

Exercise Library/SYSTEM.md

@@ -79,11 +79,14 @@ never touches a motion script** — proportions are the skeleton's problem.
   proportions. Face-on machines (abductor/adductor, rotary torso) author
   genuine abduction or spine rotation and let projection do the rest. The
   camera can also orbit while the motion loops (`--orbit`).
-- **Elevation** — the default viewpoint pitches down 10° (`CAMERA_PITCH`;
-  override per motion via `"camera": {"pitch": ...}`), so the floor reads as
-  a plane — drawn as a rectangle — and near/far contacts straddle it.
-  Elevation is pure presentation: pins solve in the flat authored view and
-  the *posed* body tilts, so authored canvas targets never go out of reach.
+- **Elevation & the mat** — the default viewpoint pitches down 10°
+  (`CAMERA_PITCH`; override per motion via `"camera": {"pitch": ...}`), and
+  the ground is drawn as an **exercise mat**: a world-space quad sized to the
+  motion's footprint (`mat_bounds`) that rotates with the camera about the
+  figure — a long rectangle in profile, a parallelogram mid-orbit, end-on
+  when face-on. Near/far contacts straddle it. Elevation is pure
+  presentation: pins solve in the flat authored view and the *posed* body
+  tilts, so authored canvas targets never go out of reach.
 - **Feet** — each leg ends in a foot bone off the ankle. Dorsiflexion 0 keeps
   the foot perpendicular to the shin (right for standing, seated machines,
   planks); kneeling poses trail it back (−55), raises point it.