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/Plank/frames/frame-1.svg

@@ -1,6 +1,6 @@
 <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 180" fill="none">
   <title>Plank</title>
-  <rect x="16" y="150.8" width="288" height="10.4" rx="3" fill="none" stroke="#b9bec9" stroke-width="3"/>
+  <path d="M 42.3 160.6 L 270.6 160.6 L 270.6 150.2 L 42.3 150.2 Z" fill="none" stroke="#b9bec9" stroke-width="3" stroke-linejoin="round"/>
   <path id="arm_r" d="M 93.2 121.4 L 93.2 150.9 L 63.2 150.9" stroke="#a9afba" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="leg_r" d="M 177.9 114.8 L 204.3 151.9 L 244.3 151.9 L 244.3 162.7" stroke="#a9afba" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="girdle" d="M 87.3 123.2 L 87.3 121.3 L 93.2 121.4" stroke="#0d9488" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>

Exercise Library/Plank/frames/frame-2.svg

@@ -1,6 +1,6 @@
 <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 180" fill="none">
   <title>Plank</title>
-  <rect x="16" y="150.8" width="288" height="10.4" rx="3" fill="none" stroke="#b9bec9" stroke-width="3"/>
+  <path d="M 42.3 160.9 L 270.6 160.9 L 270.6 150.5 L 42.3 150.5 Z" fill="none" stroke="#b9bec9" stroke-width="3" stroke-linejoin="round"/>
   <path id="arm_r" d="M 90.2 122.5 L 90.2 152.1 L 60.2 152.1" stroke="#a9afba" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="leg_r" d="M 173.9 137.8 L 219.2 145.6 L 258.6 152.5 L 256.7 163.1" stroke="#a9afba" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="girdle" d="M 84.3 124.4 L 84.3 122.5 L 90.2 122.5" stroke="#0d9488" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>