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/Bird Dog/visual.svg

@@ -1,6 +1,6 @@
 <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 180" fill="none">
   <title>Bird Dog</title>
-  <rect x="16" y="150.8" width="288" height="10.4" rx="3" fill="none" stroke="#b9bec9" stroke-width="3"/>
+  <path d="M 37.3 160.4 L 298.0 160.4 L 298.0 150.0 L 37.3 150.0 Z" fill="none" stroke="#b9bec9" stroke-width="3" stroke-linejoin="round"/>
   <path id="arm_r" d="M 112.0 93.0 L 115.9 122.2 L 111.0 151.4" stroke="#86cfc5" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="leg_r" d="M 195.9 106.8 L 240.3 95.0 L 279.0 84.8 L 286.0 93.1" stroke="#86cfc5" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="leg_l" d="M 190.0 107.2 L 195.6 152.2 L 235.6 152.2 L 244.6 158.4" stroke="#0d9488" stroke-width="6" stroke-linecap="round" stroke-linejoin="round"/>