Merge pull request #2041 from borglab/update-rot3

Update Rot3 doc

gtsam/geometry/doc/Rot3.ipynb

@@ -26,7 +26,7 @@
     {
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-        "A `gtsam.Rot3` represents a rotation in 3D space. It can be manipulated and presented as a rotation matrix, a quaternion, roll-pitch-yaw angles (Euler angles), or as an axis-angle combination. It models a 3D rotation in the [Special Orthogonal Group $\\text{SO}(3)$](https://en.wikipedia.org/wiki/SO(3)), which is a [Lie group](https://en.wikipedia.org/wiki/Lie_group)."
+        "A `gtsam.Rot3` represents an orientation or attitude in 3D space. It can be manipulated and presented as a rotation matrix $ R \\in \\mathbb{R}^{3 \\times 3} $, a unit quaternion, roll-pitch-yaw (Euler) angles $ (\\phi, \\theta, \\psi) $, or as an axis-angle representation $ (\\hat{\\omega}, \\theta) $ with $ \\hat{\\omega} \\in \\mathbb{R}^3 $ and $ \\theta \\in \\mathbb{R} $. It models a 3D orientation as both a manifold in $ \\mathcal{SO}(3) $ and as a Lie group in $ \\text{SO}(3) $. Internally, it is stored as a $ 3 \\times 3 $ rotation matrix but can be configured to use quaternions at build time for efficiency."
       ],
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@@ -43,30 +43,11 @@
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+      "outputs": [],
-        {
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-          "name": "stdout",
-          "text": [
-            "Collecting gtsam\n",
-            "  Downloading gtsam-4.2-cp311-cp311-manylinux2014_x86_64.whl.metadata (7.6 kB)\n",
-            "Requirement already satisfied: numpy>=1.11.0 in /usr/local/lib/python3.11/dist-packages (from gtsam) (1.26.4)\n",
-            "Requirement already satisfied: pyparsing>=2.4.2 in /usr/local/lib/python3.11/dist-packages (from gtsam) (3.2.1)\n",
-            "Downloading gtsam-4.2-cp311-cp311-manylinux2014_x86_64.whl (22.4 MB)\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m22.4/22.4 MB\u001b[0m \u001b[31m10.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25hInstalling collected packages: gtsam\n",
-            "Successfully installed gtsam-4.2\n"
-          ]
-        }
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       "source": [
         "%pip install gtsam"
       ]
@@ -81,7 +62,7 @@
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@@ -96,7 +77,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "A `Rot3` can be initialized in many different ways, which are detailed in this section. Note that printing a `Rot3` displays its 3x3 rotation matrix representation, which in general is a 3x3 matrix where the columns are unit vectors that define a coordinate frame."
+        "A `Rot3` can be initialized in many different ways, which are detailed in this section. Note that printing a `Rot3` displays its 3x3 rotation matrix representation, which in general is a 3x3 matrix where the columns are unit vectors that define the orientation's coordinate frame."
       ],
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@@ -1125,7 +1106,7 @@
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