From dd5a7115cf7cf5fb46efb1dbec45772f814bbcda Mon Sep 17 00:00:00 2001
From: Alessio Quaglino <quaglino@google.com>
Date: Wed, 20 Sep 2023 08:59:26 -0700
Subject: [PATCH] Add shell plugin.

- Add bending passive force
- Add two examples (plate and poncho)
- Add stretching constraints for particles using tendons on mesh edges

PiperOrigin-RevId: 566980584
Change-Id: Id0cd8e1084c05560f1008518a8afbd5311d563e2
---
 doc/XMLreference.rst                      |    2 +-
 doc/changelog.rst                         |   57 +-
 model/plugin/elasticity/mannequin.xml     |  171 +++
 model/plugin/elasticity/plate.xml         |   54 +
 model/plugin/elasticity/poncho.xml        | 1417 +++++++++++++++++++++
 plugin/elasticity/CMakeLists.txt          |    2 +
 plugin/elasticity/register.cc             |    2 +
 plugin/elasticity/shell.cc                |  305 +++++
 plugin/elasticity/shell.h                 |   79 ++
 src/user/user_composite.cc                |   48 +-
 test/engine/engine_plugin_test.cc         |    2 +-
 test/plugin/elasticity/elasticity_test.cc |   64 +-
 12 files changed, 2171 insertions(+), 32 deletions(-)
 create mode 100644 model/plugin/elasticity/mannequin.xml
 create mode 100644 model/plugin/elasticity/plate.xml
 create mode 100644 model/plugin/elasticity/poncho.xml
 create mode 100644 plugin/elasticity/shell.cc
 create mode 100644 plugin/elasticity/shell.h

diff --git a/doc/XMLreference.rst b/doc/XMLreference.rst
index b605c1dc..b8e1b949 100644
--- a/doc/XMLreference.rst
+++ b/doc/XMLreference.rst
@@ -3346,7 +3346,7 @@ coordinates results in compiler error. See :ref:`CComposite` in the modeling gui
 .. _body-composite-vertex:
 
 :at:`vertex`: :at-val:`real(3*nvert), optional`
-   Vertex 3D positions in global coordinates (cable only).
+   Vertex 3D positions in global coordinates (cable and shell).
 
 .. _body-composite-face:
 
diff --git a/doc/changelog.rst b/doc/changelog.rst
index 20e8110c..988c1ef5 100644
--- a/doc/changelog.rst
+++ b/doc/changelog.rst
@@ -31,27 +31,38 @@ New features
 3. Added :ref:`mjThreadPool` and :ref:`mjTask` which allow for multi-threaded operations within the MuJoCo engine
    pipeline.
 
+.. youtube:: ra2bTiZHGlw
+   :align: right
+   :width: 240px
+
+4. Added capability to initialize :ref:`composite<body-composite>` particles with arbitrary positions.
+
+5. Added `shell <https://github.com/deepmind/mujoco/blob/main/plugin/elasticity/shell.cc>`_ passive force plugin:
+
+   - Collisions use spheres located at mesh vertices.
+   - Stretching as tendon constraints and bending using a constant precomputed Hessian (cotangent operator).
+
 General
 ^^^^^^^
 
 .. admonition:: Breaking API changes
    :class: attention
 
-   4. Removed the macros ``mjMARKSTACK`` and ``mjFREESTACK``.
+   6. Removed the macros ``mjMARKSTACK`` and ``mjFREESTACK``.
 
       **Migration:** These macros have been replaced by new functions :ref:`mj_markStack` and
       :ref:`mj_freeStack`. These functions manage the :ref:`mjData stack<siStack>` in a fully encapsulated way (i.e.,
       without introducing a local variable at the call site).
 
-   5. Renamed ``mj_stackAlloc`` to :ref:`mj_stackAllocNum`. The new function :ref:`mj_stackAllocByte` allocates an
+   7. Renamed ``mj_stackAlloc`` to :ref:`mj_stackAllocNum`. The new function :ref:`mj_stackAllocByte` allocates an
       arbitrary number of bytes and has an additional argument for specifying the alignment of the returned pointer.
 
       **Migration:** The functionality for allocating ``mjtNum`` arrays is now available via :ref:`mj_stackAllocNum`.
 
-   6. Renamed the ``nstack`` field in :ref:`mjModel` and :ref:`mjData` to ``narena``. Changed ``narena``, ``pstack``,
+   8. Renamed the ``nstack`` field in :ref:`mjModel` and :ref:`mjData` to ``narena``. Changed ``narena``, ``pstack``,
       and ``maxuse_stack`` to count number of bytes rather than number of :ref:`mjtNum` |-| s.
 
-   7. Changed :ref:`mjData.solver<mjData>`, the array used to collect solver diagnostic information.
+   9. Changed :ref:`mjData.solver<mjData>`, the array used to collect solver diagnostic information.
       This array of :ref:`mjSolverStat` structs is now of length ``mjNISLAND * mjNSOLVER``, interpreted as as a matrix.
       Each row of length ``mjNSOLVER`` contains separate solver statistics for each constraint island.
       If the solver does not use islands, only row 0 is filled.
@@ -62,46 +73,46 @@ General
       - Renamed ``mjData.solver_iter`` to ``solver_niter``. Both this member and ``mjData.solver_nnz`` are now integer
         vectors of length ``mjNISLAND``.
 
-   8. Removed ``mjOption.collision`` and the associated ``option/collision`` attribute.
+   10. Removed ``mjOption.collision`` and the associated ``option/collision`` attribute.
 
-      **Migration:**
+       **Migration:**
 
-      - For models which have ``<option collision="all"/>``, delete the attribute.
-      - For models which have ``<option collision="dynamic"/>``, delete all :ref:`pair<contact-pair>` elements.
-      - For models which have ``<option collision="pair"/>``, disable all dynamic collisions (determined
-        via contype/conaffinity) by first deleting all :ref:`contype<body-geom-contype>` and
-        :ref:`conaffinity<body-geom-conaffinity>` attributes in the model and then setting them globally to ``0`` using
-        |br| ``<default> <geom contype="0" conaffinity="0"/> </default>``.
+       - For models which have ``<option collision="all"/>``, delete the attribute.
+       - For models which have ``<option collision="dynamic"/>``, delete all :ref:`pair<contact-pair>` elements.
+       - For models which have ``<option collision="pair"/>``, disable all dynamic collisions (determined
+         via contype/conaffinity) by first deleting all :ref:`contype<body-geom-contype>` and
+         :ref:`conaffinity<body-geom-conaffinity>` attributes in the model and then setting them globally to ``0`` using
+         |br| ``<default> <geom contype="0" conaffinity="0"/> </default>``.
 
-9. Added a new :ref:`dyntype<actuator-general-dyntype>`, ``filterexact``, which updates first-order filter states with
-   the exact formula rather than with Euler integration.
-10. Added an actuator attribute, :ref:`actearly<actuator-general-actearly>`, which uses semi-implicit integration for
+11. Added a new :ref:`dyntype<actuator-general-dyntype>`, ``filterexact``, which updates first-order filter states with
+    the exact formula rather than with Euler integration.
+12. Added an actuator attribute, :ref:`actearly<actuator-general-actearly>`, which uses semi-implicit integration for
     actuator forces: using the next step's actuator state to compute the current actuator forces at the current timestep.
-11. Renamed ``actuatorforcerange`` and ``actuatorforcelimited``, introduced in the previous version to
+13. Renamed ``actuatorforcerange`` and ``actuatorforcelimited``, introduced in the previous version to
     :ref:`actuatorfrcrange<body-joint-actuatorfrcrange>` and
     :ref:`actuatorfrclimited<body-joint-actuatorfrclimited>`, respectively.
-12. Added the flag :ref:`eulerdamp<option-flag-eulerdamp>`, which disables implicit integration of joint damping in the
+14. Added the flag :ref:`eulerdamp<option-flag-eulerdamp>`, which disables implicit integration of joint damping in the
     Euler integrator. See the :ref:`Numerical Integration<geIntegration>` section for more details.
-13. Added the flag :ref:`invdiscrete<option-flag-invdiscrete>`, which enables discrete-time inverse dynamics for all
+15. Added the flag :ref:`invdiscrete<option-flag-invdiscrete>`, which enables discrete-time inverse dynamics for all
     :ref:`integrators<option-integrator>` other than ``RK4``. See the flag documentation for more details.
-14. Added :ref:`ls_iterations<option-ls_iterations>` and :ref:`ls_tolerance<option-ls_tolerance>` options for adjusting
+16. Added :ref:`ls_iterations<option-ls_iterations>` and :ref:`ls_tolerance<option-ls_tolerance>` options for adjusting
     linesearch stopping criteria in CG and Newton solvers. These can be useful for performance tuning.
-15. Added ``mesh_pos`` and ``mesh_quat`` fields to :ref:`mjModel` to store the normalizing transformation applied to
+17. Added ``mesh_pos`` and ``mesh_quat`` fields to :ref:`mjModel` to store the normalizing transformation applied to
     mesh assets. Fixes `#409 <https://github.com/google-deepmind/mujoco/issues/409>`__ .
-16. Added camera :ref:`resolution<body-camera-resolution>` attribute and :ref:`camprojection<sensor-camprojection>`
+18. Added camera :ref:`resolution<body-camera-resolution>` attribute and :ref:`camprojection<sensor-camprojection>`
     sensor. If camera resolution is set to positive values, the camera projection sensor will report the location of a
     target site, projected onto the camera image, in pixel coordinates.
 
 Python bindings
 ^^^^^^^^^^^^^^^
 
-17. Fixed `#870 <https://github.com/google-deepmind/mujoco/issues/870>`__ where calling ``update_scene`` with an invalid
+19. Fixed `#870 <https://github.com/google-deepmind/mujoco/issues/870>`__ where calling ``update_scene`` with an invalid
     camera name used the default camera.
 
 Bug fixes
 ^^^^^^^^^
 
-18. Fixed a bug that was causing :ref:`geom margin<body-geom-margin>` to be ignored during the construction of
+20. Fixed a bug that was causing :ref:`geom margin<body-geom-margin>` to be ignored during the construction of
     midphase collision trees.
 
 
diff --git a/model/plugin/elasticity/mannequin.xml b/model/plugin/elasticity/mannequin.xml
new file mode 100644
index 00000000..ad036287
--- /dev/null
+++ b/model/plugin/elasticity/mannequin.xml
@@ -0,0 +1,171 @@
+<!-- Copyright 2021 DeepMind Technologies Limited
+
+     Licensed under the Apache License, Version 2.0 (the "License");
+     you may not use this file except in compliance with the License.
+     You may obtain a copy of the License at
+
+         http://www.apache.org/licenses/LICENSE-2.0
+
+     Unless required by applicable law or agreed to in writing, software
+     distributed under the License is distributed on an "AS IS" BASIS,
+     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+     See the License for the specific language governing permissions and
+     limitations under the License.
+-->
+
+<mujoco model="Mannequin">
+  <!-- Static humanoid model with all joints removed -->
+  <option timestep="0.005"/>
+
+  <visual>
+    <map force="0.1" zfar="30"/>
+    <rgba haze="0.15 0.25 0.35 1"/>
+    <global offwidth="2560" offheight="1440" elevation="-20" azimuth="120"/>
+  </visual>
+
+  <statistic center="0 0 0.7"/>
+
+  <asset>
+    <texture type="skybox" builtin="gradient" rgb1=".3 .5 .7" rgb2="0 0 0" width="32" height="512"/>
+    <texture name="body" type="cube" builtin="flat" mark="cross" width="128" height="128" rgb1="0.8 0.6 0.4" rgb2="0.8 0.6 0.4" markrgb="1 1 1" random="0.01"/>
+    <material name="body" texture="body" texuniform="true" rgba="0.8 0.6 .4 1"/>
+    <texture name="grid" type="2d" builtin="checker" width="512" height="512" rgb1=".1 .2 .3" rgb2=".2 .3 .4"/>
+    <material name="grid" texture="grid" texrepeat="1 1" texuniform="true" reflectance=".2"/>
+  </asset>
+
+  <default>
+    <motor ctrlrange="-1 1" ctrllimited="true"/>
+    <default class="body">
+
+      <!-- geoms -->
+      <geom type="capsule" condim="1" friction=".7" solimp=".9 .99 .003" solref=".015 1" material="body"/>
+      <default class="thigh">
+        <geom size=".06"/>
+      </default>
+      <default class="shin">
+        <geom fromto="0 0 0 0 0 -.3"  size=".049"/>
+      </default>
+      <default class="foot">
+        <geom size=".027"/>
+        <default class="foot1">
+          <geom fromto="-.07 -.01 0 .14 -.03 0"/>
+        </default>
+        <default class="foot2">
+          <geom fromto="-.07 .01 0 .14  .03 0"/>
+        </default>
+      </default>
+      <default class="arm_upper">
+        <geom size=".04"/>
+      </default>
+      <default class="arm_lower">
+        <geom size=".031"/>
+      </default>
+      <default class="hand">
+        <geom type="sphere" size=".04"/>
+      </default>
+
+      <!-- joints -->
+      <joint type="hinge" damping=".2" stiffness="1" armature=".01" limited="true" solimplimit="0 .99 .01"/>
+      <default class="joint_big">
+        <joint damping="5" stiffness="10"/>
+        <default class="hip_x">
+          <joint range="-30 10"/>
+        </default>
+        <default class="hip_z">
+          <joint range="-60 35"/>
+        </default>
+        <default class="hip_y">
+          <joint axis="0 1 0" range="-150 20"/>
+        </default>
+        <default class="joint_big_stiff">
+          <joint stiffness="20"/>
+        </default>
+      </default>
+      <default class="knee">
+        <joint pos="0 0 .02" axis="0 -1 0" range="-160 2"/>
+      </default>
+      <default class="ankle">
+        <joint range="-50 50"/>
+        <default class="ankle_y">
+          <joint pos="0 0 .08" axis="0 1 0" stiffness="6"/>
+        </default>
+        <default class="ankle_x">
+          <joint pos="0 0 .04" stiffness="3"/>
+        </default>
+      </default>
+      <default class="shoulder">
+        <joint range="-85 60"/>
+      </default>
+      <default class="elbow">
+        <joint range="-100 50" stiffness="0"/>
+      </default>
+    </default>
+  </default>
+
+  <worldbody>
+    <geom name="floor" size="0 0 .05" type="plane" material="grid" condim="3"/>
+    <light name="spotlight" mode="targetbodycom" target="torso" diffuse=".8 .8 .8" specular="0.3 0.3 0.3" pos="0 -6 4" cutoff="30"/>
+    <body name="torso" pos="0 0 1.282" childclass="body">
+      <light name="top" pos="0 0 2" mode="trackcom"/>
+      <camera name="back" pos="-3 0 1" xyaxes="0 -1 0 1 0 2" mode="trackcom"/>
+      <camera name="side" pos="0 -3 1" xyaxes="1 0 0 0 1 2" mode="trackcom"/>
+      <freejoint name="root"/>
+      <geom name="torso" fromto="0 -.07 0 0 .07 0" size=".07"/>
+      <geom name="waist_upper" fromto="-.01 -.06 -.12 -.01 .06 -.12" size=".06"/>
+      <body name="head" pos="0 0 .19">
+        <geom name="head" type="sphere" size=".09"/>
+        <camera name="egocentric" pos=".09 0 0" xyaxes="0 -1 0 .1 0 1" fovy="80"/>
+      </body>
+      <body name="waist_lower" pos="-.01 0 -.26">
+        <geom name="waist_lower" fromto="0 -.06 0 0 .06 0" size=".06"/>
+        <body name="pelvis" pos="0 0 -.165">
+          <geom name="butt" fromto="-.02 -.07 0 -.02 .07 0" size=".09"/>
+          <body name="thigh_right" pos="0 -.1 -.04">
+            <geom name="thigh_right" fromto="0 0 0 0 .01 -.34" class="thigh"/>
+            <body name="shin_right" pos="0 .01 -.4">
+              <geom name="shin_right" class="shin"/>
+              <body name="foot_right" pos="0 0 -.39">
+                <geom name="foot1_right" class="foot1"/>
+                <geom name="foot2_right" class="foot2"/>
+              </body>
+            </body>
+          </body>
+          <body name="thigh_left" pos="0 .1 -.04">
+            <geom name="thigh_left" fromto="0 0 0 0 -.01 -.34" class="thigh"/>
+            <body name="shin_left" pos="0 -.01 -.4">
+              <geom name="shin_left" fromto="0 0 0 0 0 -.3" class="shin"/>
+              <body name="foot_left" pos="0 0 -.39">
+                <geom name="foot1_left" class="foot1"/>
+                <geom name="foot2_left" class="foot2"/>
+              </body>
+            </body>
+          </body>
+        </body>
+      </body>
+      <body name="upper_arm_right" pos="0 -.17 .06">
+        <geom name="upper_arm_right" fromto="0 0 0 0 -.22 0" class="arm_upper"/>
+        <body name="lower_arm_right" pos="0 -.22 0">
+          <geom name="lower_arm_right" fromto=".01 .01 .01 0 -.21 -.05" class="arm_lower"/>
+          <body name="hand_right" pos="0 -.22 -.05">
+            <geom name="hand_right" zaxis="1 1 1" class="hand"/>
+          </body>
+        </body>
+      </body>
+      <body name="upper_arm_left" pos="0 .17 .06">
+        <geom name="upper_arm_left" fromto="0 0 0 0 .22 0" class="arm_upper"/>
+        <body name="lower_arm_left" pos="0 .22 0">
+          <geom name="lower_arm_left" fromto=".01 -.01 .01 0 .21 -.05" class="arm_lower"/>
+          <body name="hand_left" pos="0 .22 -.05">
+            <geom name="hand_left" zaxis="1 -1 1" class="hand"/>
+          </body>
+        </body>
+      </body>
+    </body>
+  </worldbody>
+
+  <contact>
+    <exclude body1="waist_lower" body2="thigh_right"/>
+    <exclude body1="waist_lower" body2="thigh_left"/>
+  </contact>
+
+</mujoco>
diff --git a/model/plugin/elasticity/plate.xml b/model/plugin/elasticity/plate.xml
new file mode 100644
index 00000000..6b742c31
--- /dev/null
+++ b/model/plugin/elasticity/plate.xml
@@ -0,0 +1,54 @@
+<!-- Copyright 2021 DeepMind Technologies Limited
+
+     Licensed under the Apache License, Version 2.0 (the "License");
+     you may not use this file except in compliance with the License.
+     You may obtain a copy of the License at
+
+         http://www.apache.org/licenses/LICENSE-2.0
+
+     Unless required by applicable law or agreed to in writing, software
+     distributed under the License is distributed on an "AS IS" BASIS,
+     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+     See the License for the specific language governing permissions and
+     limitations under the License.
+-->
+
+<mujoco model="Plate">
+  <include file="scene.xml"/>
+
+  <extension>
+    <plugin plugin="mujoco.elasticity.shell"/>
+  </extension>
+
+  <option solver="CG" tolerance="1e-6"/>
+
+  <size memory="10M"/>
+
+  <visual>
+    <map stiffness="100"/>
+  </visual>
+
+  <default>
+    <default class="wall">
+      <geom type="plane" size=".5 .5 .05"/>
+    </default>
+  </default>
+
+  <worldbody>
+    <body mocap="true" pos="-.1 .05 0" zaxis=".5 0 1">
+      <geom type="capsule" size=".1 .1" group="1"/>
+    </body>
+    <composite type="particle" count="16 16 1" spacing="0.05" offset="0 0 1">
+      <geom size=".02" rgba=".8 .2 .1 1" group="4" density="1000"
+            condim="3" solref="0.01 1" solimp=".95 .99 .0001"/>
+      <skin inflate="0.01" rgba=".4 0 .3 1" subgrid="4"/>
+      <plugin plugin="mujoco.elasticity.shell">
+        <config key="poisson" value="0"/>
+        <config key="damping" value="0.001"/>
+        <config key="thickness" value="1e-2"/>
+        <!--Units are in Pa (SI)-->
+        <config key="young" value="3e7"/>
+      </plugin>
+    </composite>
+  </worldbody>
+</mujoco>
diff --git a/model/plugin/elasticity/poncho.xml b/model/plugin/elasticity/poncho.xml
new file mode 100644
index 00000000..859bf95d
--- /dev/null
+++ b/model/plugin/elasticity/poncho.xml
@@ -0,0 +1,1417 @@
+<!-- Copyright 2023 DeepMind Technologies Limited
+
+     Licensed under the Apache License, Version 2.0 (the "License");
+     you may not use this file except in compliance with the License.
+     You may obtain a copy of the License at
+
+         http://www.apache.org/licenses/LICENSE-2.0
+
+     Unless required by applicable law or agreed to in writing, software
+     distributed under the License is distributed on an "AS IS" BASIS,
+     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+     See the License for the specific language governing permissions and
+     limitations under the License.
+-->
+
+<mujoco model="Poncho">
+  <include file="mannequin.xml"/>
+
+  <option solver="CG" tolerance="1e-6" timestep="0.004"/>
+
+  <size memory="50M"/>
+
+  <extension>
+    <plugin plugin="mujoco.elasticity.shell"/>
+  </extension>
+
+  <worldbody>
+    <composite type="particle" offset="0 0 2" vertex="
+      -1 1 0
+      -0.875 1 0
+      -0.833333333333 0.91666666513 0
+      -1 0.875 0
+      -0.916666667179 0.833333331284 0
+      -0.812500001409 0.81249999936 0
+      -0.750000001537 0.749999999488 0
+      -0.75 1 0
+      -0.718750000576 0.906249998143 0
+      -1 0.75 0
+      -0.906250000192 0.718749998527 0
+      -0.833333333333 0.666666665642 0
+      -0.734187703053 0.642350849083 0
+      -0.666666667691 0.833333331284 0
+      -0.612946163782 0.7237083968 0
+      -0.625 1 0
+      -0.583333333846 0.91666666513 0
+      -0.616996739355 0.622692032086 0
+      -0.719104332867 0.539663811624 0
+      -1 0.625 0
+      -0.916666667179 0.583333331797 0
+      -0.80969723436 0.526920937586 0
+      -0.532291254804 0.804324341663 0
+      -0.506101050606 0.604081197552 0
+      -0.484329717592 0.699035373329 0
+      -0.5 1 0
+      -0.446144899117 0.890322007975 0
+      -0.620892626346 0.525533370884 0
+      -0.704717288729 0.441717328263 0
+      -0.527201429221 0.512053329881 0
+      -0.442916397325 0.477752897868 0
+      -1 0.5 0
+      -0.890323749548 0.446145751463 0
+      -0.787495191849 0.395653921455 0
+      -0.406068846868 0.777075424862 0
+      -0.423568119224 0.58129737124 0
+      -0.363412129379 0.675839255169 0
+      -0.375 1 0
+      -0.336444644664 0.890322007975 0
+      -0.35276170024 0.535166987623 0
+      -0.690990727014 0.348267404594 0
+      -0.609096078117 0.430160367238 0
+      -0.5236950543 0.43016304926 0
+      -0.440517550279 0.399063026439 0
+      -0.374727431754 0.371856753595 0
+      -0.363128922938 0.445282783495 0
+      -1 0.375 0
+      -0.890323749548 0.33644525319 0
+      -0.787495191849 0.300297692232 0
+      -0.690990727014 0.266373255631 0
+      -0.300296553038 0.787491944327 0
+      -0.303687113341 0.600201238785 0
+      -0.266371665677 0.690986198924 0
+      -0.25 1 0
+      -0.224516377155 0.879814277198 0
+      -0.285740295598 0.4915025426 0
+      -0.600206817966 0.303689848635 0
+      -0.600206817966 0.234459778792 0
+      -0.520322583821 0.351400089126 0
+      -0.425534543884 0.311282357957 0
+      -0.31197059286 0.345904837591 0
+      -0.250355013041 0.407523490775 0
+      -1 0.25 0
+      -0.879814279247 0.224516375106 0
+      -0.767648116935 0.200733182859 0
+      -0.66294014972 0.178531392364 0
+      -0.200733184908 0.767648114886 0
+      -0.234457820034 0.600201238785 0
+      -0.178531394413 0.662940147671 0
+      -0.125 1 0
+      -0.108234201193 0.881968771277 0
+      -0.204599258215 0.515262924335 0
+      -0.176457340528 0.43520793201 0
+      -0.565601594248 0.15789217619 0
+      -0.515269609927 0.261983194167 0
+      -0.324206662946 0.258601640871 0
+      -0.435201750449 0.222667533273 0
+      -0.247102940592 0.299133860319 0
+      -0.271861512188 0.221080658884 0
+      -0.185877358435 0.360277137775 0
+      -1 0.125 0
+      -0.88197058866 0.108234457307 0
+      -0.771816855177 0.0925876205718 0
+      -0.662935359369 0.100549863838 0
+      -0.108145563312 0.767648114886 0
+      -0.157892178239 0.5656015922 0
+      -0.100550214202 0.662940147671 0
+      0 1 0
+      -1.02445474326e-09 0.771816853128 0
+      -1.02445474326e-09 0.881970586611 0
+      -0.1205911549 0.389682708205 0
+      -0.0868810916197 0.474500354169 0
+      -0.523096782922 0.0704802950569 0
+      -0.474500356218 0.138575492276 0
+      -0.360272421185 0.185875041118 0
+      -0.290000784015 0.151369611594 0
+      -0.186173128789 0.255202155519 0
+      -0.222463263127 0.16894673637 0
+      -0.125413489179 0.290004062271 0
+      -1 0 0
+      -0.88197058866 -1.02445474326e-09 0
+      -0.771816855177 -1.02445474326e-09 0
+      -0.668987502501 -1.02445474326e-09 0
+      -0.573395345428 -1.02445474326e-09 0
+      -1.02445474326e-09 0.668987500452 0
+      -0.0644018930983 0.573389319585 0
+      0.125 1 0
+      0.108234199144 0.881968771277 0
+      0.092587139078 0.771813468329 0
+      0.25 1 0
+      -0.0749939754372 0.310626958879 0
+      -0.0398633436671 0.400637927 0
+      -1.02445474326e-09 0.483928598449 0
+      -0.389688025126 0.0807289371087 0
+      -0.483928600497 -1.02445474326e-09 0
+      -0.45466396227 0.0757373956737 0
+      -0.310630663308 0.0749942417955 0
+      -0.236872738727 0.0881900334621 0
+      -0.118970424327 0.224018586356 0
+      -0.129616886777 0.120978572984 0
+      -0.157006743976 0.185982266707 0
+      -0.0696439608649 0.236872736678 0
+      -1 -0.125 0
+      -0.881968773326 -0.108234201193 0
+      -0.771813470378 -0.0925871411269 0
+      -0.662935359369 -0.100549865887 0
+      -0.565595459813 -0.0934889851077 0
+      -0.474739199667 -0.086898415151 0
+      -1 -0.25 0
+      0.100550212153 0.662940147671 0
+      0.0644018910494 0.573389319585 0
+      0.375 1 0
+      0.5 1 0
+      0.224516375106 0.879814277198 0
+      0.200733182859 0.767648114886 0
+      0.178531392364 0.662940147671 0
+      0.336444642615 0.890322007975 0
+      0.0398633416182 0.400637927 0
+      -0.0185463953005 0.250566612138 0
+      -1.02445474326e-09 0.322995335258 0
+      0.0868810895708 0.474500354169 0
+      0.11924415661 0.416042609248 0
+      -0.322995337307 -1.02445474326e-09 0
+      -0.400637929049 -0.0398633436671 0
+      -0.243719676457 0.0348218190808 0
+      -0.250566614187 -0.0185463953005 0
+      -0.168124336813 0.0646570581614 0
+      -0.103923048454 0.06 0
+      -0.06 0.103923048454 0
+      -0.0646569823517 0.168123257037 0
+      0.00895588352248 0.183049418482 0
+      -0.87981243113 -0.224515985813 0
+      -0.767644670669 -0.200732455496 0
+      -0.662935359369 -0.178530378154 0
+      -0.389688025126 -0.1205922818 0
+      -0.540429204368 -0.177734444363 0
+      -0.454973566863 -0.154784494503 0
+      -1 -0.375 0
+      -0.890323749548 -0.336445255239 0
+      0.15789217619 0.5656015922 0
+      0.451521756455 0.884947740459 0
+      0.75 1 0
+      0.625 1 0
+      0.583333331797 0.91666666513 0
+      0.300296550989 0.787491944327 0
+      0.234457817985 0.600201238785 0
+      0.266371663628 0.690986198924 0
+      0.395653921455 0.7874951898 0
+      0.0749939733883 0.310626958879 0
+      0.069643958816 0.236872736678 0
+      0.176457338479 0.43520793201 0
+      0.150116744312 0.360277137775 0
+      -0.310630663308 -0.0749942438444 0
+      -0.183049420531 -0.00895588557139 0
+      -0.236875017115 -0.0696441268266 0
+      -0.12 6.79864667718e-17 0
+      7.34788079488e-18 0.12 0
+      0.0804343079966 0.162052298768 0
+      -0.787495191849 -0.300297694281 0
+      -0.690990727014 -0.26637325768 0
+      -0.600206817966 -0.234459780841 0
+      -0.515262926384 -0.261979915911 0
+      -0.360277139824 -0.185877358435 0
+      -0.29000406432 -0.151371224086 0
+      -0.435207934058 -0.222670571807 0
+      -1 -0.5 0
+      -0.787491946376 -0.395652327403 0
+      -0.890322010024 -0.446144899117 0
+      1 1 0
+      0.261983194167 0.515269607879 0
+      0.875 1 0
+      0.833333331284 0.91666666513 0
+      0.594506861916 0.828334436313 0
+      0.509090102472 0.775491920929 0
+      0.699999997951 0.849999998463 0
+      0.363414127066 0.675844002493 0
+      0.323286530397 0.580610132106 0
+      0.484338339404 0.699040026403 0
+      0.157005826064 0.185980094863 0
+      0.118969406019 0.224016514909 0
+      0.12541348713 0.290004062271 0
+      0.250352277747 0.407517003927 0
+      0.217232599591 0.328914860663 0
+      -0.224018588405 -0.118970424327 0
+      -0.168124336813 -0.0736129447572 0
+      -0.103923048454 -0.06 0
+      0.06 0.103923048454 0
+      0.121243302358 0.125297729881 0
+      -0.690986200972 -0.348265183576 0
+      -0.600201240834 -0.303687113341 0
+      -0.520318504442 -0.351398001287 0
+      -0.457882268688 -0.319360573608 0
+      -0.238088598603 -0.203286691851 0
+      -0.372952791185 -0.247076480973 0
+      -0.312596323725 -0.233558176582 0
+      -0.386166943131 -0.310875530551 0
+      -0.704714623098 -0.441720926149 0
+      -1 -0.625 0
+      -0.916666667179 -0.583333333846 0
+      -0.782873769554 -0.553798958709 0
+      1 0.875 0
+      0.319207167643 0.457821483685 0
+      0.91666666513 0.833333333333 0
+      0.81249999936 0.81249999936 0
+      0.612962307141 0.723713039629 0
+      0.749999999488 0.749999999488 0
+      0.445307145031 0.593949296227 0
+      0.392515206982 0.511379375878 0
+      0.574917894299 0.633609854182 0
+      0.538696836902 0.547825044997 0
+      0.190512205186 0.144098776993 0
+      0.230228993418 0.181682351121 0
+      0.186171678161 0.255198715399 0
+      0.337270521221 0.359765701238 0
+      0.264914112319 0.281235691888 0
+      -0.157006743976 -0.185982268756 0
+      -0.129616886777 -0.120978575033 0
+      -0.06 -0.103923048454 0
+      0.162052298768 0.0885431609941 0
+      0.103923048454 0.06 0
+      -0.466027375093 -0.405631082976 0
+      -0.609092697417 -0.430158695327 0
+      -0.400501610991 -0.376741231304 0
+      -0.186173128789 -0.255202157567 0
+      -0.288755464916 -0.294057606714 0
+      -0.315226920895 -0.362257222517 0
+      -0.669443067321 -0.532534986951 0
+      -1 -0.75 0
+      -0.906250000192 -0.718750000576 0
+      -0.833333333333 -0.666666667691 0
+      -0.574182186159 -0.509108755746 0
+      -0.734189159827 -0.642368031239 0
+      1 0.75 0
+      0.420774076433 0.418806494138 0
+      0.906249998143 0.718749998527 0
+      0.833333331284 0.666666665642 0
+      0.734186510587 0.642350113524 0
+      0.694812709833 0.538652902133 0
+      0.50425642338 0.466257455355 0
+      0.610331785782 0.524133750446 0
+      0.46801849936 0.340393202976 0
+      0.224018586356 0.102217461171 0
+      0.393952133967 0.298267837426 0
+      0.290004062271 0.151371222037 0
+      0.271862942327 0.221080111825 0
+      0.324208851181 0.258601233138 0
+      0.451292518295 0.256822931168 0
+      -0.118969408068 -0.224016516957 0
+      -0.0736127152793 -0.168123259086 0
+      -2.20436423847e-17 -0.12 0
+      0.12 0 0
+      0.172550330006 0.039793713521 0
+      0.103923048454 -0.06 0
+      -0.411736243695 -0.459864162616 0
+      -0.483661408335 -0.486848192277 0
+      -0.343120953295 -0.434121889001 0
+      -0.125412337692 -0.290000784015 0
+      -0.21723468743 -0.328919810829 0
+      -0.222667535322 -0.435201750449 0
+      -0.611610553331 -0.621956989841 0
+      -0.906250000192 -0.812500001409 0
+      -1 -0.875 0
+      -0.812500001409 -0.812500001409 0
+      -0.750000001537 -0.750000001537 0
+      -0.52673094629 -0.607660454239 0
+      -0.612946294912 -0.723708409093 0
+      1 0.625 0
+      0.530972560151 0.372917865471 0
+      0.91666666513 0.583333331797 0
+      0.782868163737 0.5537863866 0
+      0.704713807632 0.441715504734 0
+      0.609093180959 0.430159885744 0
+      0.515262924335 0.261979913862 0
+      0.237291480542 0.0418356917257 0
+      0.310630661259 0.0749942417955 0
+      0.360277137775 0.185877356386 0
+      0.43520793201 0.176457338479 0
+      -0.0696441268266 -0.236875017115 0
+      -0.0749942438444 -0.310630663308 0
+      0.06 -0.103923048454 0
+      0.125297729881 -0.12529773193 0
+      0.00895573190316 -0.183048365342 0
+      0.162052298768 -0.088543163043 0
+      0.183048363294 -0.00895573395207 0
+      0.250564374729 -0.0185460777195 0
+      -0.363025688625 -0.541120848657 0
+      -0.445305653424 -0.593945737271 0
+      -0.285740295598 -0.491502544648 0
+      -0.1205911549 -0.389682710254 0
+      -0.204601606265 -0.515269609927 0
+      -0.154782976261 -0.454970475058 0
+      -1 -1 0
+      -0.833333333333 -0.916666667179 0
+      -0.875 -1 0
+      -0.7 -0.9 0
+      -0.598371156769 -0.818680168613 0
+      -0.516170900703 -0.768407834199 0
+      -0.479811625909 -0.678895474392 0
+      1 0.5 0
+      0.600201238785 0.303687111292 0
+      0.890322007975 0.446144897068 0
+      0.787491944327 0.395652325354 0
+      0.690986198924 0.348265181527 0
+      0.600201238785 0.234457817985 0
+      0.5656015922 0.15789217619 0
+      0.474739197618 0.086898413102 0
+      0.322998970023 -1.02445474326e-09 0
+      0.389688023077 0.0807289371087 0
+      -1.02445474326e-09 -0.250564376778 0
+      -0.0398633436671 -0.400637929049 0
+      -1.02445474326e-09 -0.322995337307 0
+      0.0885431609941 -0.162052300816 0
+      0.185980094863 -0.157005828113 0
+      0.0881900334621 -0.236872738727 0
+      0.224018586356 -0.10221746322 0
+      0.310630661259 -0.0749942438444 0
+      0.527892038811 0.00535506411023 0
+      -0.303689850684 -0.600206817966 0
+      -0.363412129379 -0.675839257218 0
+      -0.234459780841 -0.600206817966 0
+      -0.086898415151 -0.474739199667 0
+      -0.157892178239 -0.565601594248 0
+      -0.75 -1 0
+      -0.625 -1 0
+      -0.583333333846 -0.916666667179 0
+      -0.446145753512 -0.890323749548 0
+      -0.406068846868 -0.777075426911 0
+      1 0.375 0
+      0.690986198924 0.266371663628 0
+      0.890322007975 0.336444642615 0
+      0.787491944327 0.300296550989 0
+      0.662940147671 0.178531392364 0
+      0.573395343379 0.0644027474936 0
+      0.66293535732 0.100549863838 0
+      0.400637927 -1.02445474326e-09 0
+      0.483928598449 -0.05169440373 0
+      -0.0176020077594 -0.479333900082 0
+      0.0749942417955 -0.310630663308 0
+      0.0398625999129 -0.400632708427 0
+      0.168946447474 -0.222464330608 0
+      0.236393732332 -0.188236710698 0
+      0.151371222037 -0.29000406432 0
+      0.290004062271 -0.151371224086 0
+      0.389682708205 -0.1205911549 0
+      0.289517657263 -0.221146592797 0
+      0.573395343379 -0.0644027495425 0
+      -0.26637325768 -0.690990727014 0
+      -0.300297694281 -0.787495191849 0
+      -0.178531394413 -0.66294014972 0
+      -0.0789460906563 -0.569498470863 0
+      -0.100549865887 -0.662935359369 0
+      -1.02445474326e-09 -0.573395345428 0
+      -0.5 -1 0
+      -0.375 -1 0
+      -0.336445255239 -0.890323749548 0
+      1 0.25 0
+      0.767648114886 0.200733182859 0
+      0.879814277198 0.224516375106 0
+      0.771816853128 0.0925876205718 0
+      0.668982798205 -1.02445474326e-09 0
+      0.66293535732 -0.100549865887 0
+      0.459568265229 -0.114075872129 0
+      0.0516944016811 -0.483928600497 0
+      0.0789460865585 -0.569498470863 0
+      0.120591152851 -0.389682710254 0
+      0.185877356386 -0.360277139824 0
+      0.219917513356 -0.255837969068 0
+      0.43520793201 -0.176457340528 0
+      0.360277137775 -0.185877358435 0
+      0.323722542472 -0.277689176777 0
+      0.5656015922 -0.157892178239 0
+      -0.200733184908 -0.767648116935 0
+      -0.224516377155 -0.879814279247 0
+      -0.108145313345 -0.767644670669 0
+      -1.02445474326e-09 -0.668987502501 0
+      0.0779811791871 -0.668987502501 0
+      -0.25 -1 0
+      1 0.125 0
+      0.881970586611 0.108234457307 0
+      0.881968771277 -1.02445474326e-09 0
+      0.771813468329 -1.02445474326e-09 0
+      0.76764466862 -0.108145313345 0
+      0.662940147671 -0.178531394413 0
+      0.515262924335 -0.204599258215 0
+      0.138575492276 -0.474500356218 0
+      0.15789217619 -0.565601594248 0
+      0.222670569758 -0.435207934058 0
+      0.258601233138 -0.324208855279 0
+      0.407517003927 -0.250352279796 0
+      0.359765701238 -0.337270525319 0
+      0.600201238785 -0.234457820034 0
+      -0.125 -1 0
+      -0.108234201193 -0.881968773326 0
+      -1.02445474326e-09 -0.771816855177 0
+      -1.02445474326e-09 -0.88197058866 0
+      0.108145311296 -0.767644670669 0
+      0.178531392364 -0.66294014972 0
+      1 0 0
+      0.881970586611 -0.108234459356 0
+      0.767648114886 -0.200733184908 0
+      0.690986198924 -0.266371665677 0
+      0.234457817985 -0.600201240834 0
+      0.491509553968 -0.285743250126 0
+      0.261979913862 -0.515262926384 0
+      0.311277989681 -0.425529200328 0
+      0.445287291096 -0.36312995354 0
+      0.376744732891 -0.400503088255 0
+      0.580610132106 -0.323286532446 0
+      0 -1 0
+      0.108234457307 -0.88197058866 0
+      0.200733182859 -0.767648116935 0
+      0.266371663628 -0.690986200972 0
+      1 -0.125 0
+      0.879814277198 -0.224516377155 0
+      0.787491944327 -0.300296553038 0
+      0.675844002493 -0.363414129115 0
+      0.303687111292 -0.600201240834 0
+      0.511379375878 -0.39251521108 0
+      0.372917865471 -0.530972564249 0
+      0.44214861965 -0.461743887665 0
+      0.593949294178 -0.445307153226 0
+      0.125 -1 0
+      0.224516375106 -0.879814279247 0
+      0.300296550989 -0.787491946376 0
+      0.348265181527 -0.690986200972 0
+      1 -0.25 0
+      0.890322007975 -0.336444644664 0
+      0.787491944327 -0.395652327403 0
+      0.699040026403 -0.48433834555 0
+      0.430159877548 -0.60909319735 0
+      0.512054585863 -0.527200175288 0
+      0.591967652265 -0.550704387995 0
+      0.67558199612 -0.575297225337 0
+      0.25 -1 0
+      0.441715482196 -0.704713787143 0
+      0.336444642615 -0.890322010024 0
+      0.395652325354 -0.787491946376 0
+      1 -0.375 0
+      0.884947740459 -0.451521758504 0
+      0.777506214266 -0.559169134553 0
+      0.567517669003 -0.640802301598 0
+      0.702340676451 -0.661082350054 0
+      0.375 -1 0
+      0.509088950985 -0.775489730644 0
+      0.446144897068 -0.890322010024 0
+      1 -0.5 0
+      0.833333331284 -0.666666667691 0
+      0.91666666513 -0.583333333846 0
+      0.627175140686 -0.762995565555 0
+      0.749999999488 -0.750000001537 0
+      0.5 -1 0
+      0.583333331797 -0.916666667179 0
+      1 -0.625 0
+      0.81249999936 -0.812500001409 0
+      0.906249998143 -0.718750000576 0
+      0.699999997951 -0.850000000512 0
+      0.625 -1 0
+      1 -0.75 0
+      0.81249999936 -0.906250000192 0
+      0.91666666513 -0.833333333333 0
+      0.75 -1 0
+      1 -0.875 0
+      0.875 -1 0
+      1 -1 0" face="
+      301 273 300
+      333 301 332
+      303 273 301
+      299 329 298
+      299 331 329
+      309 299 277
+      330 331 299
+      358 362 334
+      359 358 331
+      359 385 358
+      295 328 296
+      294 305 327
+      272 294 262
+      272 304 294
+      327 328 295
+      303 335 304
+      364 382 355
+      203 202 172
+      235 203 233
+      265 235 233
+      199 232 233
+      264 296 265
+      288 293 320
+      234 263 254
+      234 266 263
+      171 190 160
+      235 234 203
+      261 263 267
+      326 297 328
+      355 326 328
+      353 325 326
+      222 228 197
+      202 222 190
+      202 234 222
+      324 320 293
+      325 324 293
+      326 325 297
+      353 354 325
+      352 349 324
+      225 226 195
+      194 198 225
+      161 194 193
+      161 168 194
+      260 292 291
+      258 260 291
+      290 258 291
+      290 257 258
+      229 227 230
+      254 259 228
+      222 234 254
+      263 266 296
+      267 263 296
+      293 267 297
+      293 261 267
+      261 254 263
+      291 322 290
+      349 323 320
+      377 349 352
+      354 379 352
+      350 376 348
+      399 378 377
+      399 398 378
+      350 378 376
+      321 350 348
+      351 323 349
+      321 322 350
+      290 289 256
+      161 164 133
+      198 227 229
+      193 194 225
+      196 197 227
+      165 196 168
+      197 228 227
+      224 192 195
+      304 273 303
+      351 322 323
+      378 351 377
+      350 322 351
+      289 321 319
+      305 304 335
+      363 336 335
+      327 295 294
+      239 272 262
+      271 273 304
+      351 349 377
+      226 224 195
+      256 289 255
+      257 290 256
+      225 257 226
+      225 229 257
+      290 321 289
+      351 378 350
+      348 319 321
+      287 253 255
+      189 191 221
+      192 162 195
+      223 192 224
+      191 162 192
+      223 191 192
+      162 163 195
+      223 255 253
+      191 223 221
+      224 255 223
+      164 161 193
+      198 194 168
+      163 164 195
+      163 133 164
+      133 132 161
+      223 253 221
+      226 256 224
+      289 287 255
+      136 109 130
+      193 195 164
+      196 198 168
+      225 195 193
+      257 256 226
+      229 260 258
+      257 229 258
+      288 292 259
+      288 320 292
+      323 322 291
+      322 321 290
+      256 255 224
+      161 132 137
+      289 319 287
+      166 190 197
+      167 165 135
+      166 167 136
+      196 165 167
+      160 130 131
+      484 482 483
+      480 483 482
+      478 480 482
+      475 467 474
+      478 475 480
+      478 473 475
+      479 474 476
+      483 479 481
+      483 480 479
+      479 480 474
+      466 459 468
+      476 477 481
+      459 466 458
+      272 240 271
+      264 265 232
+      208 207 240
+      231 208 239
+      178 207 208
+      139 151 170
+      170 151 178
+      199 200 178
+      201 169 170
+      111 139 140
+      122 151 139
+      150 177 151
+      208 240 239
+      137 132 110
+      107 108 134
+      168 161 137
+      107 134 110
+      136 135 109
+      167 166 197
+      89 85 105
+      108 90 109
+      71 85 89
+      70 71 88
+      70 54 55
+      178 151 177
+      296 328 297
+      231 239 262
+      264 232 262
+      199 208 231
+      201 200 233
+      178 208 199
+      272 271 304
+      305 294 304
+      239 240 272
+      108 107 88
+      90 108 88
+      71 90 88
+      71 89 90
+      109 135 108
+      105 109 89
+      160 190 166
+      169 172 142
+      139 170 140
+      233 203 201
+      296 264 295
+      261 288 254
+      325 293 297
+      222 197 190
+      288 259 254
+      293 288 261
+      320 323 292
+      292 323 291
+      264 262 295
+      266 265 296
+      232 199 231
+      262 232 231
+      265 233 232
+      165 168 137
+      134 165 137
+      135 136 167
+      113 92 112
+      131 113 141
+      160 131 141
+      171 160 141
+      166 136 160
+      130 105 131
+      106 92 113
+      227 228 259
+      230 227 259
+      260 230 259
+      260 229 230
+      292 260 259
+      225 198 229
+      198 196 227
+      196 167 197
+      234 202 203
+      266 234 235
+      265 266 235
+      296 297 267
+      254 228 222
+      142 138 169
+      171 142 172
+      141 138 142
+      136 130 160
+      131 105 106
+      172 201 203
+      200 199 233
+      170 200 201
+      170 178 200
+      320 324 349
+      134 137 110
+      135 134 108
+      135 165 134
+      67 55 51
+      54 39 55
+      38 39 54
+      177 150 149
+      177 207 178
+      68 69 53
+      56 68 52
+      86 69 68
+      92 86 72
+      106 87 86
+      138 141 113
+      87 69 86
+      105 87 106
+      105 85 87
+      109 105 130
+      85 69 87
+      109 90 89
+      119 99 97
+      150 119 121
+      122 99 119
+      91 80 99
+      111 91 99
+      122 111 99
+      140 112 111
+      92 72 73
+      112 92 91
+      111 112 91
+      138 113 112
+      169 138 140
+      170 169 140
+      201 172 169
+      171 202 190
+      142 171 141
+      172 202 171
+      72 56 62
+      106 86 92
+      86 68 72
+      140 138 112
+      55 39 51
+      71 55 67
+      71 70 55
+      23 35 27
+      30 31 36
+      52 68 53
+      72 68 56
+      13 15 7
+      12 13 7
+      19 28 18
+      29 19 22
+      29 42 28
+      53 51 37
+      52 53 37
+      69 67 53
+      17 26 16
+      39 27 35
+      39 38 27
+      26 27 38
+      23 27 17
+      14 23 17
+      25 36 37
+      15 25 23
+      24 30 36
+      15 18 25
+      18 13 19
+      24 18 28
+      15 13 18
+      103 83 102
+      93 74 84
+      115 93 104
+      94 74 93
+      66 50 65
+      74 66 84
+      58 75 57
+      104 93 84
+      94 77 75
+      52 37 36
+      9 16 8
+      12 22 13
+      17 16 9
+      15 23 14
+      27 26 17
+      21 32 33
+      22 21 33
+      60 59 75
+      7 6 12
+      11 20 21
+      33 32 47
+      48 33 47
+      63 48 47
+      64 49 48
+      22 12 21
+      34 22 33
+      34 41 29
+      19 13 22
+      12 11 21
+      49 50 41
+      33 48 34
+      64 82 65
+      84 66 83
+      74 94 75
+      116 94 93
+      144 173 143
+      144 155 173
+      114 144 143
+      115 127 128
+      128 157 155
+      278 279 309
+      244 278 277
+      268 244 277
+      213 204 184
+      241 243 212
+      246 216 243
+      244 245 278
+      215 183 214
+      213 215 245
+      213 184 215
+      185 182 212
+      156 127 154
+      182 156 181
+      157 128 156
+      144 128 155
+      144 115 128
+      212 211 241
+      185 212 216
+      182 211 212
+      174 176 147
+      175 174 146
+      205 176 174
+      62 78 80
+      56 46 62
+      95 96 79
+      94 95 77
+      96 98 79
+      114 117 95
+      117 118 96
+      98 118 120
+      97 98 121
+      96 118 98
+      143 117 114
+      116 144 114
+      173 146 143
+      143 145 117
+      147 120 118
+      119 150 122
+      79 98 97
+      78 79 97
+      80 78 97
+      61 76 78
+      76 95 79
+      147 148 120
+      121 120 150
+      1 4 2
+      5 10 11
+      5 3 4
+      10 5 4
+      11 12 6
+      6 9 3
+      11 10 20
+      48 49 34
+      6 5 11
+      14 6 7
+      3 5 6
+      8 3 9
+      2 4 3
+      32 21 20
+      9 14 17
+      2 3 8
+      6 14 9
+      63 64 48
+      64 63 81
+      65 49 64
+      66 65 83
+      50 49 65
+      49 41 34
+      117 96 95
+      113 131 106
+      78 62 61
+      82 81 100
+      83 82 101
+      64 81 82
+      147 176 148
+      120 121 98
+      149 120 148
+      149 150 120
+      124 100 123
+      67 69 85
+      71 67 85
+      51 53 67
+      35 51 39
+      35 37 51
+      40 46 56
+      52 40 56
+      36 31 40
+      35 25 37
+      57 42 41
+      25 24 36
+      35 23 25
+      14 7 15
+      59 42 57
+      24 25 18
+      22 34 29
+      73 80 91
+      78 76 79
+      46 61 62
+      46 44 45
+      77 95 76
+      73 62 80
+      92 73 91
+      72 62 73
+      61 60 76
+      60 75 77
+      76 60 77
+      28 30 24
+      29 28 19
+      42 30 28
+      41 42 29
+      43 30 42
+      59 43 42
+      59 44 43
+      75 59 57
+      44 31 43
+      45 44 60
+      61 45 60
+      61 46 45
+      31 30 43
+      46 31 44
+      46 40 31
+      52 36 40
+      44 59 60
+      50 57 41
+      50 66 58
+      58 66 74
+      75 58 74
+      57 50 58
+      94 114 95
+      97 99 80
+      82 100 101
+      129 152 123
+      82 83 65
+      124 101 100
+      103 126 104
+      83 103 84
+      125 126 103
+      124 125 101
+      179 159 187
+      153 179 180
+      154 153 180
+      125 124 153
+      152 159 179
+      153 152 179
+      124 123 152
+      158 159 129
+      249 283 250
+      145 147 118
+      298 329 302
+      269 298 302
+      206 237 238
+      268 298 269
+      184 155 183
+      175 173 204
+      146 145 143
+      277 298 268
+      236 244 268
+      311 310 342
+      309 311 341
+      279 310 311
+      277 299 298
+      159 152 129
+      186 188 158
+      180 209 210
+      125 153 154
+      179 187 209
+      246 278 245
+      152 153 124
+      127 104 126
+      182 185 156
+      115 104 127
+      104 84 103
+      154 127 126
+      116 114 94
+      115 116 93
+      115 144 116
+      284 283 315
+      220 219 250
+      252 220 250
+      159 188 187
+      186 219 188
+      186 218 219
+      218 248 249
+      312 314 282
+      313 282 314
+      313 343 315
+      281 313 283
+      314 343 313
+      315 344 345
+      281 248 282
+      313 281 282
+      373 346 345
+      252 284 286
+      249 248 281
+      283 249 281
+      250 219 249
+      157 156 185
+      183 157 185
+      128 127 156
+      154 181 156
+      125 154 126
+      180 179 209
+      180 210 181
+      154 180 181
+      252 250 284
+      251 242 247
+      220 188 219
+      251 285 275
+      242 251 275
+      247 280 251
+      252 280 247
+      286 317 318
+      187 188 220
+      158 188 159
+      316 284 315
+      318 285 286
+      347 318 317
+      285 280 286
+      307 285 318
+      307 275 285
+      306 308 276
+      339 306 307
+      338 308 306
+      242 209 217
+      217 187 220
+      375 346 374
+      242 210 209
+      274 306 276
+      243 274 276
+      275 306 274
+      246 279 278
+      345 344 373
+      316 315 345
+      346 316 345
+      286 284 316
+      280 285 251
+      339 307 318
+      339 338 306
+      250 283 284
+      315 343 344
+      346 317 316
+      283 313 315
+      218 249 219
+      204 213 236
+      173 184 204
+      213 244 236
+      183 215 184
+      215 214 245
+      176 205 206
+      245 244 213
+      269 236 268
+      183 155 157
+      214 183 185
+      216 214 185
+      216 245 214
+      184 173 155
+      237 204 236
+      175 146 173
+      205 175 204
+      205 174 175
+      122 139 111
+      97 121 119
+      150 151 122
+      102 101 125
+      103 102 125
+      83 101 102
+      393 397 412
+      346 375 347
+      317 346 347
+      339 318 347
+      286 316 317
+      373 374 346
+      374 397 375
+      145 146 174
+      147 145 174
+      118 117 145
+      413 394 392
+      413 393 412
+      430 429 442
+      396 395 414
+      413 429 415
+      237 206 205
+      430 443 431
+      429 430 415
+      442 443 430
+      443 442 454
+      456 443 454
+      431 416 430
+      408 387 386
+      332 360 333
+      334 362 360
+      302 329 334
+      300 302 332
+      270 238 269
+      309 279 311
+      330 309 341
+      357 330 341
+      359 331 330
+      277 278 309
+      210 211 182
+      181 210 182
+      247 220 252
+      247 217 220
+      286 280 252
+      242 217 247
+      241 242 275
+      211 210 242
+      209 187 217
+      368 392 367
+      375 368 347
+      375 393 368
+      276 308 279
+      246 276 279
+      216 246 245
+      243 276 246
+      212 243 216
+      241 275 274
+      243 241 274
+      211 242 241
+      275 307 306
+      367 338 339
+      340 308 338
+      367 340 338
+      369 342 340
+      394 395 371
+      472 471 477
+      444 456 457
+      445 444 457
+      455 450 445
+      464 455 457
+      464 469 461
+      437 422 432
+      431 443 444
+      463 471 465
+      371 342 369
+      357 383 359
+      370 357 341
+      372 383 357
+      384 405 383
+      417 406 396
+      422 424 406
+      417 422 406
+      416 417 396
+      432 444 445
+      437 424 422
+      385 359 383
+      407 385 405
+      386 362 385
+      309 330 299
+      383 405 385
+      330 357 359
+      384 396 406
+      405 384 406
+      372 396 384
+      370 371 395
+      357 370 372
+      342 371 370
+      311 342 341
+      310 340 342
+      372 384 383
+      385 362 358
+      279 308 310
+      340 310 308
+      339 368 367
+      396 414 416
+      392 394 369
+      367 392 369
+      340 367 369
+      339 347 368
+      393 413 392
+      368 393 392
+      375 397 393
+      413 415 414
+      429 413 412
+      395 396 372
+      370 395 372
+      341 342 370
+      369 394 371
+      414 415 430
+      394 414 395
+      394 413 414
+      302 270 269
+      237 269 238
+      204 237 205
+      236 269 237
+      456 463 465
+      469 476 470
+      467 460 462
+      464 465 472
+      461 455 464
+      462 461 469
+      451 450 461
+      457 465 464
+      447 459 458
+      446 447 458
+      435 448 447
+      434 435 447
+      381 403 402
+      421 436 435
+      402 403 420
+      428 436 421
+      448 459 447
+      436 448 435
+      436 449 448
+      420 421 435
+      450 439 437
+      457 455 445
+      453 462 460
+      441 452 449
+      461 462 453
+      424 407 405
+      427 426 410
+      408 425 410
+      440 451 438
+      439 440 427
+      439 451 440
+      407 386 385
+      425 407 424
+      439 425 424
+      427 410 425
+      425 408 407
+      365 390 389
+      437 439 424
+      426 409 410
+      411 423 428
+      404 409 423
+      361 363 335
+      390 365 387
+      410 390 408
+      410 409 390
+      389 363 365
+      388 389 409
+      391 382 404
+      364 389 388
+      333 303 301
+      336 327 305
+      364 336 363
+      364 355 336
+      335 336 305
+      438 428 423
+      440 438 426
+      441 449 436
+      451 441 438
+      452 461 453
+      449 452 453
+      451 461 452
+      455 461 450
+      441 436 428
+      472 476 469
+      471 472 465
+      477 476 472
+      460 467 468
+      459 460 468
+      462 469 470
+      449 453 460
+      452 441 451
+      428 438 441
+      462 470 467
+      474 470 476
+      481 479 476
+      480 475 474
+      449 460 448
+      474 467 470
+      475 473 468
+      416 431 417
+      302 300 270
+      450 451 439
+      456 444 443
+      463 456 454
+      417 432 422
+      465 457 456
+      464 472 469
+      439 427 425
+      445 450 437
+      426 423 409
+      440 426 427
+      438 423 426
+      424 405 406
+      416 414 430
+      325 354 352
+      355 356 337
+      327 355 328
+      327 336 355
+      411 391 404
+      421 411 428
+      403 381 391
+      421 403 411
+      421 420 403
+      401 380 402
+      411 404 423
+      366 391 381
+      366 356 382
+      337 356 366
+      326 337 353
+      326 355 337
+      364 388 382
+      434 447 446
+      300 332 301
+      468 473 466
+      448 460 459
+      467 475 468
+      434 446 433
+      420 434 419
+      420 435 434
+      411 403 391
+      418 400 419
+      380 379 354
+      262 294 295
+      387 360 362
+      390 387 408
+      361 333 360
+      365 361 387
+      365 363 361
+      364 363 389
+      335 333 361
+      366 381 380
+      337 366 353
+      382 388 404
+      366 382 391
+      356 355 382
+      432 445 437
+      431 432 417
+      431 444 432
+      404 388 409
+      358 329 331
+      358 334 329
+      386 387 362
+      407 408 386
+      390 409 389
+      360 332 334
+      387 361 360
+      335 303 333
+      332 302 334
+      419 434 433
+      400 418 399
+      379 401 400
+      377 379 399
+      377 352 379
+      419 433 418
+      401 419 400
+      402 420 419
+      325 352 324
+      366 380 353
+      379 400 399
+      380 401 379
+      353 380 354
+      381 402 380
+      402 419 401
+      398 399 418
+      398 376 378">
+      <geom size=".02" rgba=".8 .2 .1 1" group="4" density="1000"
+            condim="3" solref="0.01 1" solimp=".95 .99 .0001"/>
+      <skin inflate="0.001" rgba=".4 0 .3 1"/>
+      <plugin plugin="mujoco.elasticity.shell">
+        <config key="poisson" value="0"/>
+        <config key="damping" value="0.001"/>
+        <config key="thickness" value="8e-3"/>
+        <!--Units are in Pa (SI)-->
+        <config key="young" value="3e7"/>
+      </plugin>
+    </composite>
+  </worldbody>
+</mujoco>
diff --git a/plugin/elasticity/CMakeLists.txt b/plugin/elasticity/CMakeLists.txt
index 81946e9a..833e0c16 100644
--- a/plugin/elasticity/CMakeLists.txt
+++ b/plugin/elasticity/CMakeLists.txt
@@ -22,6 +22,8 @@ set(MUJOCO_ELASTICITY_SRCS
     elasticity.cc
     elasticity.h
     register.cc
+    shell.cc
+    shell.h
     solid.cc
     solid.h
 )
diff --git a/plugin/elasticity/register.cc b/plugin/elasticity/register.cc
index e349379f..c3747200 100644
--- a/plugin/elasticity/register.cc
+++ b/plugin/elasticity/register.cc
@@ -14,12 +14,14 @@
 
 #include <mujoco/mjplugin.h>
 #include "cable.h"
+#include "shell.h"
 #include "solid.h"
 
 namespace mujoco::plugin::elasticity {
 
 mjPLUGIN_LIB_INIT {
   Cable::RegisterPlugin();
+  Shell::RegisterPlugin();
   Solid::RegisterPlugin();
 }
 
diff --git a/plugin/elasticity/shell.cc b/plugin/elasticity/shell.cc
new file mode 100644
index 00000000..8c671436
--- /dev/null
+++ b/plugin/elasticity/shell.cc
@@ -0,0 +1,305 @@
+// Copyright 2023 DeepMind Technologies Limited
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <algorithm>
+#include <cctype>
+#include <cmath>
+#include <cstddef>
+#include <cstdint>
+#include <cstdlib>
+#include <functional>
+#include <sstream>
+#include <optional>
+#include <string>
+#include <unordered_map>
+#include <utility>
+#include <vector>
+
+#include <mujoco/mjplugin.h>
+#include <mujoco/mjtnum.h>
+#include <mujoco/mujoco.h>
+#include "shell.h"
+
+
+namespace mujoco::plugin::elasticity {
+namespace {
+
+// local tetrahedron numbering
+constexpr int kNumEdges = Stencil2D::kNumEdges;
+constexpr int kNumVerts = Stencil2D::kNumVerts;
+constexpr int edge[kNumEdges][2] = {{1, 2}, {2, 0}, {0, 1}};
+
+// copied from void mjXUtil
+void String2Vector(const std::string& txt, std::vector<int>& vec) {
+  std::stringstream strm(txt);
+  vec.clear();
+
+  while (!strm.eof()) {
+    int num;
+    strm >> num;
+    if (strm.fail()) {
+      break;
+    } else {
+      vec.push_back(num);
+    }
+  }
+}
+
+// cotangent between two edges
+mjtNum cot(mjtNum* x, int v0, int v1, int v2) {
+  mjtNum normal[3];
+  mjtNum edge1[3];
+  mjtNum edge2[3];
+
+  mju_sub3(edge1, x+3*v1, x+3*v0);
+  mju_sub3(edge2, x+3*v2, x+3*v0);
+  mju_cross(normal, edge1, edge2);
+
+  return mju_dot3(edge1, edge2) / mju_norm3(normal);
+}
+
+// area of a triangle
+mjtNum ComputeVolume(const mjtNum* x, const int v[kNumVerts]) {
+  mjtNum normal[3];
+  mjtNum edge1[3];
+  mjtNum edge2[3];
+
+  mju_sub3(edge1, x+3*v[1], x+3*v[0]);
+  mju_sub3(edge2, x+3*v[2], x+3*v[0]);
+  mju_cross(normal, edge1, edge2);
+
+  return mju_norm3(normal) / 2;
+}
+
+// reads numeric attributes
+bool CheckAttr(const char* name, const mjModel* m, int instance) {
+  char* end;
+  std::string value = mj_getPluginConfig(m, instance, name);
+  value.erase(std::remove_if(value.begin(), value.end(), isspace), value.end());
+  strtod(value.c_str(), &end);
+  return end == value.data() + value.size();
+}
+
+struct PairHash
+{
+    template <class T1, class T2>
+    std::size_t operator() (const std::pair<T1, T2>& pair) const {
+        return std::hash<T1>()(pair.first) ^ std::hash<T2>()(pair.second);
+    }
+};
+
+}  // namespace
+
+// factory function
+std::optional<Shell> Shell::Create(const mjModel* m, mjData* d, int instance) {
+    if (CheckAttr("face", m, instance) &&
+        CheckAttr("poisson", m, instance) &&
+        CheckAttr("young", m, instance) &&
+        CheckAttr("thickness", m, instance)) {
+      mjtNum nu = strtod(mj_getPluginConfig(m, instance, "poisson"), nullptr);
+      mjtNum E = strtod(mj_getPluginConfig(m, instance, "young"), nullptr);
+      mjtNum thick =
+          strtod(mj_getPluginConfig(m, instance, "thickness"), nullptr);
+      mjtNum damp =
+          strtod(mj_getPluginConfig(m, instance, "damping"), nullptr);
+      std::vector<int> face;
+      String2Vector(mj_getPluginConfig(m, instance, "face"), face);
+      return Shell(m, d, instance, nu, E, damp, thick, face);
+    } else {
+      mju_warning("Invalid parameter specification in shell plugin");
+      return std::nullopt;
+    }
+}
+
+// create map from triangles to vertices and edges and from edges to vertices
+void Shell::CreateStencils(const std::vector<int>& face) {
+  // populate stencil
+  nt = face.size() / kNumVerts;
+  elements.resize(nt);
+  for (int t = 0; t < nt; t++) {
+    for (int v = 0; v < kNumVerts; v++) {
+      elements[t].vertices[v] = face[kNumVerts*t+v]-1;
+    }
+  }
+
+  // map from edge vertices to their index in `edges` vector
+  std::unordered_map<std::pair<int, int>, int, PairHash> edge_indices;
+
+  // loop over all triangles
+  for (int t = 0; t < nt; t++) {
+    int* v = elements[t].vertices;
+
+    // compute edges to vertices map for fast computations
+    for (int e = 0; e < kNumEdges; e++) {
+      auto pair = std::pair(
+        std::min(v[edge[e][0]], v[edge[e][1]]),
+        std::max(v[edge[e][0]], v[edge[e][1]])
+      );
+
+      // if edge is already present in the vector only store its index
+      auto [it, inserted] = edge_indices.insert({pair, ne});
+
+      if (inserted) {
+        StencilFlap flap;
+        flap.vertices[0] = v[edge[e][0]];
+        flap.vertices[1] = v[edge[e][1]];
+        flap.vertices[2] = v[(edge[e][1]+1) % 3];
+        flap.vertices[3] = -1;
+        flaps.push_back(flap);
+        elements[t].edges[e] = ne++;
+      } else {
+        elements[t].edges[e] = it->second;
+        flaps[it->second].vertices[3] = v[(edge[e][1]+1) % 3];
+      }
+    }
+  }
+}
+
+// plugin constructor
+Shell::Shell(const mjModel* m, mjData* d, int instance, mjtNum nu, mjtNum E,
+             mjtNum damp, mjtNum thick, const std::vector<int>& face)
+    : damping(damp), thickness(thick) {
+  // count plugin bodies
+  nv = ne = 0;
+  for (int i = 1; i < m->nbody; i++) {
+    if (m->body_plugin[i] == instance) {
+      if (!nv++) {
+        i0 = i;
+      }
+    }
+  }
+
+  // generate triangles from the vertices
+  CreateStencils(face);
+
+  // material parameters
+  mjtNum mu = E / (2*(1+nu));
+
+  // loop over all triangles
+  for (int t = 0; t < nt; t++) {
+    int* v = elements[t].vertices;
+    for (int i = 0; i < kNumVerts; i++) {
+      if (m->body_plugin[i0+v[i]] != instance) {
+        mju_error("This body does not have the requested plugin instance");
+      }
+    }
+  }
+
+  // allocate array
+  position.assign(nv*3, 0);
+  bending.assign(ne*16, 0);
+
+  // store previous positions
+  mju_copy(position.data(), m->body_pos+3*i0, 3*nv);
+
+  // assemble bending Hessian
+  for (int e = 0; e < ne; e++)  {
+    int* v = flaps[e].vertices;
+    int vadj[3] = {v[1], v[0], v[3]};
+
+    if (v[3]== -1) {
+      // skip boundary edges
+      continue;
+    }
+
+    // cotangent operator from Wardetzky at al., "Discrete Quadratic Curvature
+    // Energies", https://cims.nyu.edu/gcl/papers/wardetzky2007dqb.pdf
+
+    mjtNum a01 = cot(m->body_pos+3*i0, v[0], v[1], v[2]);
+    mjtNum a02 = cot(m->body_pos+3*i0, v[0], v[3], v[1]);
+    mjtNum a03 = cot(m->body_pos+3*i0, v[1], v[2], v[0]);
+    mjtNum a04 = cot(m->body_pos+3*i0, v[1], v[0], v[3]);
+    mjtNum c[4] = {a03 + a04, a01 + a02, -(a01 + a03), -(a02 + a04)};
+    mjtNum volume = ComputeVolume(m->body_pos+3*i0, v) +
+                    ComputeVolume(m->body_pos+3*i0, vadj);
+
+    for (int v1 = 0; v1 < StencilFlap::kNumVerts; v1++) {
+      for (int v2 = 0; v2 < StencilFlap::kNumVerts; v2++) {
+        bending[16 * e + 4 * v1 + v2] +=
+            1.5 * c[v1] * c[v2] / volume * mu * pow(thickness, 3) / 12;
+      }
+    }
+  }
+}
+
+void Shell::Compute(const mjModel* m, mjData* d, int instance) {
+  mjtNum kD = damping / m->opt.timestep;
+
+  // compute bending contribution
+  mjtNum embedding;
+  for (int e = 0; e < ne; e++) {
+    int* v = flaps[e].vertices;
+    mjtNum force[12] = {0};
+    if (v[3] == -1) {
+      // skip boundary edges
+      continue;
+    }
+    for (int i = 0; i < StencilFlap::kNumVerts; i++) {
+      for (int j = 0; j < StencilFlap::kNumVerts; j++) {
+        for (int x = 0; x < 3; x++) {
+          embedding = d->xpos[3*(i0+v[j])+x]*(kD+1) - position[3*v[j]+x]*kD;
+          force[3*i+x] += bending[16*e+4*i+j] * embedding;
+        }
+      }
+    }
+
+    // update stored positions
+    mju_copy(position.data(), d->xpos+3*i0, 3*nv);
+
+    // insert into global force
+    for (int i = 0; i < StencilFlap::kNumVerts; i++) {
+      for (int x = 0; x < 3; x++) {
+        d->qfrc_passive[m->body_dofadr[i0]+3*v[i]+x] -= force[3*i+x];
+      }
+    }
+  }
+}
+
+
+
+void Shell::RegisterPlugin() {
+  mjpPlugin plugin;
+  mjp_defaultPlugin(&plugin);
+
+  plugin.name = "mujoco.elasticity.shell";
+  plugin.capabilityflags |= mjPLUGIN_PASSIVE;
+
+  const char* attributes[] = {"face", "young", "poisson", "damping",
+                              "thickness"};
+  plugin.nattribute = sizeof(attributes) / sizeof(attributes[0]);
+  plugin.attributes = attributes;
+  plugin.nstate = +[](const mjModel* m, int instance) { return 0; };
+
+  plugin.init = +[](const mjModel* m, mjData* d, int instance) {
+    auto elasticity_or_null = Shell::Create(m, d, instance);
+    if (!elasticity_or_null.has_value()) {
+      return -1;
+    }
+    d->plugin_data[instance] = reinterpret_cast<uintptr_t>(
+        new Shell(std::move(*elasticity_or_null)));
+    return 0;
+  };
+  plugin.destroy = +[](mjData* d, int instance) {
+    delete reinterpret_cast<Shell*>(d->plugin_data[instance]);
+    d->plugin_data[instance] = 0;
+  };
+  plugin.compute = +[](const mjModel* m, mjData* d, int instance, int type) {
+    auto* elasticity = reinterpret_cast<Shell*>(d->plugin_data[instance]);
+    elasticity->Compute(m, d, instance);
+  };
+
+  mjp_registerPlugin(&plugin);
+}
+
+}  // namespace mujoco::plugin::elasticity
diff --git a/plugin/elasticity/shell.h b/plugin/elasticity/shell.h
new file mode 100644
index 00000000..16dc66a5
--- /dev/null
+++ b/plugin/elasticity/shell.h
@@ -0,0 +1,79 @@
+// Copyright 2023 DeepMind Technologies Limited
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef MUJOCO_PLUGIN_ELASTICITY_SHELL_H_
+#define MUJOCO_PLUGIN_ELASTICITY_SHELL_H_
+
+#include <optional>
+#include <vector>
+
+#include <mujoco/mjdata.h>
+#include <mujoco/mjmodel.h>
+#include <mujoco/mjtnum.h>
+
+
+namespace mujoco::plugin::elasticity {
+
+struct Stencil2D {
+  static constexpr int kNumEdges = 3;
+  static constexpr int kNumVerts = 3;
+  int vertices[kNumVerts];
+  int edges[kNumEdges];
+};
+
+struct StencilFlap {
+  static constexpr int kNumVerts = 4;
+  int vertices[kNumVerts];
+};
+
+class Shell {
+ public:
+  // Returns a new Shell instance or nullopt on failure.
+  static std::optional<Shell> Create(const mjModel* m, mjData* d,
+                                     int instance);
+  Shell(Shell&&) = default;
+
+  Shell& operator=(Shell&& other) = default;
+
+  void Compute(const mjModel* m, mjData* d, int instance);
+
+  static void RegisterPlugin();
+
+  int i0;  // index of first body
+  int nc;  // number of quads in the grid
+  int nv;  // number of vertices (bodies) in the Shell
+  int nt;  // number of area elements (triangles)
+  int ne;  // number of edges in the Shell
+
+  // connectivity info for mapping tetrahedra to edges and vertices
+  std::vector<Stencil2D> elements;          // triangles              (nt x 6)
+  std::vector<StencilFlap> flaps;           // adjacent triangles     (ne x 4)
+
+  // precomputed quantities
+  std::vector<mjtNum> position;             // previous-step positions (nv x 3)
+  std::vector<mjtNum> bending;              // bending Hessian         (ne x 16)
+
+  mjtNum damping;
+  mjtNum thickness;
+
+ private:
+  Shell(const mjModel* m, mjData* d, int instance, mjtNum nu, mjtNum E,
+        mjtNum damp, mjtNum thick, const std::vector<int>& face);
+
+  void CreateStencils(const std::vector<int>& face);
+};
+
+}  // namespace mujoco::plugin::elasticity
+
+#endif  // MUJOCO_PLUGIN_ELASTICITY_SHELL_H_
diff --git a/src/user/user_composite.cc b/src/user/user_composite.cc
index b150f27b..2becbc02 100644
--- a/src/user/user_composite.cc
+++ b/src/user/user_composite.cc
@@ -14,6 +14,7 @@
 
 #include "user/user_composite.h"
 
+#include <algorithm>
 #include <cmath>
 #include <cstddef>
 #include <cstdio>
@@ -25,9 +26,9 @@
 
 #include <mujoco/mjmacro.h>
 #include <mujoco/mjmodel.h>
+#include <mujoco/mujoco.h>
 #include "cc/array_safety.h"
 #include "engine/engine_io.h"
-#include "engine/engine_macro.h"
 #include "engine/engine_util_blas.h"
 #include "engine/engine_util_errmem.h"
 #include "engine/engine_util_misc.h"
@@ -394,7 +395,7 @@ bool mjCComposite::MakeParticle(mjCModel* model, mjCBody* body, char* error, int
   std::vector<mjtNum> volume(uservert.size()/3);
   mjtNum t = 1;
   if (dim == 2 && plugin_instance) {
-    // do nothing for now (until new passive forces are supported)
+    t = stod(plugin_instance->config_attribs["thickness"], nullptr);
   }
   if (!userface.empty()) {
     mjXUtil::String2Vector(userface, face);
@@ -487,6 +488,49 @@ bool mjCComposite::MakeParticle(mjCModel* model, mjCBody* body, char* error, int
     }
   }
 
+  // add isometry constraints
+  if (dim==2) {
+    char txt0[100], txt1[100], txt2[100];
+    std::vector<std::pair<int, int>> edge;
+
+    // create edges
+    for (int i=0; i<face.size()/3; i++) {
+      for (int j=0; j<3; j++) {
+        int v0 = face[3*i+(j+0)%3]-1;
+        int v1 = face[3*i+(j+1)%3]-1;
+        edge.push_back(v0 < v1 ? std::pair(v0, v1) : std::pair(v1, v0));
+      }
+    }
+
+    std::sort(edge.begin(), edge.end());
+    auto last = std::unique(edge.begin(), edge.end());
+    edge.erase(last, edge.end());
+
+    // create constraints
+    for (int i=0; i<edge.size(); i++) {
+      int v0 = edge[i].first;
+      int v1 = edge[i].second;
+
+      mju::sprintf_arr(txt0, "%sT%d_%d", prefix.c_str(), v0, v1);
+      mju::sprintf_arr(txt1, "%sS%d", prefix.c_str(), v0);
+      mju::sprintf_arr(txt2, "%sS%d", prefix.c_str(), v1);
+
+      // create tendon
+      mjCTendon* ten = model->AddTendon(def + mjCOMPKIND_TENDON);
+      ten->def = model->defaults[0];
+      ten->name = txt0;
+      ten->group = 4;
+      ten->WrapSite(txt1);
+      ten->WrapSite(txt2);
+
+      // add equality constraint
+      mjCEquality* eq = model->AddEquality(def + mjCOMPKIND_TENDON);
+      eq->def = model->defaults[0];
+      eq->type = mjEQ_TENDON;
+      eq->name1 = ten->name;
+    }
+  }
+
   if (skin) {
     MakeSkin3(model);
   }
diff --git a/test/engine/engine_plugin_test.cc b/test/engine/engine_plugin_test.cc
index abc69e82..8e1bc9e0 100644
--- a/test/engine/engine_plugin_test.cc
+++ b/test/engine/engine_plugin_test.cc
@@ -32,7 +32,7 @@ namespace {
 using ::testing::HasSubstr;
 using ::testing::NotNull;
 
-constexpr int kNumTruePlugins = 9;
+constexpr int kNumTruePlugins = 10;
 constexpr int kNumFakePlugins = 30;
 constexpr int kNumTestPlugins = 3;
 
diff --git a/test/plugin/elasticity/elasticity_test.cc b/test/plugin/elasticity/elasticity_test.cc
index d2e36025..614026f4 100644
--- a/test/plugin/elasticity/elasticity_test.cc
+++ b/test/plugin/elasticity/elasticity_test.cc
@@ -14,23 +14,77 @@
 
 // Tests for plugin-related functionalities.
 
-#include <array>
-#include <cstdint>
-#include <cstring>
-#include <sstream>
+#include <cmath>
+#include <limits>
 #include <vector>
 
 #include <gmock/gmock.h>
 #include <gtest/gtest.h>
 #include <mujoco/mujoco.h>
 #include "test/fixture.h"
+#include "plugin/elasticity/shell.h"
 #include "plugin/elasticity/solid.h"
 
 namespace mujoco {
 namespace {
 
+
+// -------------------------------- shell -----------------------------------
+TEST_F(PluginTest, ElasticEnergyShell) {
+  static constexpr char cantilever_xml[] = R"(
+  <mujoco>
+  <extension>
+    <plugin plugin="mujoco.elasticity.shell"/>
+  </extension>
+
+  <worldbody>
+    <composite type="particle" count="8 8 1" spacing="1">
+      <geom size=".025" group="4"/>
+      <plugin plugin="mujoco.elasticity.shell">
+        <config key="poisson" value="0"/>
+        <config key="young" value="2"/>
+        <config key="thickness" value="1"/>
+      </plugin>
+    </composite>
+  </worldbody>
+  </mujoco>
+  )";
+
+  char error[1024] = {0};
+  mjModel* m = LoadModelFromString(cantilever_xml, error, sizeof(error));
+  ASSERT_THAT(m, testing::NotNull()) << error;
+  mjData* d = mj_makeData(m);
+  auto* shell = reinterpret_cast<plugin::elasticity::Shell*>(d->plugin_data[0]);
+
+  // check that a plane is in the kernel of the energy
+  for (mjtNum scale = 1; scale < 4; scale++) {
+    for (int e = 0; e < shell->ne; e++) {
+      int* v = shell->flaps[e].vertices;
+      if (v[3]== -1) {
+        continue;
+      }
+      mjtNum energy = 0;
+      mjtNum volume = 1./2.;
+      for (int i = 0; i < 4; i++) {
+        for (int j = 0; j < 4; j++) {
+          for (int x = 0; x < 3; x++) {
+            mjtNum elongation1 = scale * shell->position[3*v[i]+x];
+            mjtNum elongation2 = scale * shell->position[3*v[j]+x];
+            energy += shell->bending[16*e+4*i+j] * elongation1 * elongation2;
+          }
+        }
+      }
+      EXPECT_NEAR(
+        4*energy/volume, 0, std::numeric_limits<float>::epsilon());
+    }
+  }
+
+  mj_deleteData(d);
+  mj_deleteModel(m);
+}
+
 // -------------------------------- solid -----------------------------------
-TEST_F(PluginTest, ElasticEnergy) {
+TEST_F(PluginTest, ElasticEnergySolid) {
   static constexpr char cantilever_xml[] = R"(
   <mujoco>
   <extension>