diff --git a/examples/notebook_egocentric.py b/examples/notebook_egocentric.py
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+++ b/examples/notebook_egocentric.py
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+# %%
+import matplotlib.pyplot as plt
+import numpy as np
+import xarray as xr
+from scipy.spatial.transform import Rotation as R
+
+from movement import sample_data
+from movement.io import load_poses
+from movement.utils.vector import cart2pol, convert_to_unit, pol2cart
+
+# For interactive images; requires `pip install ipympl`
+# %matplotlib widget
+
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Import sample data
+# one individual, 6 keypoints
+
+ds_path = sample_data.fetch_dataset_paths(
+    "SLEAP_single-mouse_EPM.analysis.h5"
+)["poses"]
+ds = load_poses.from_sleap_file(ds_path, fps=None)  # force time_unit = frames
+
+
+print(ds)
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Define anterior and posterior keypoints
+
+anterior_keypoints = ["snout", "left_ear", "right_ear"]
+posterior_keypoints = ["centre", "tail_base"]
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Compute centroids
+
+# get position data array
+position = ds.position
+
+# Compute centroid per individual
+centroid = position.mean(dim="keypoints")  # v
+
+# Compute centroid for anterior and posterior keypoints
+centroid_anterior = position.sel(keypoints=anterior_keypoints).mean(
+    dim="keypoints", skipna=True
+)
+centroid_posterior = position.sel(keypoints=posterior_keypoints).mean(
+    dim="keypoints", skipna=True
+)
+
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Compute posterior2anterior vector per individual
+
+# Compute vector from posterior to anterior centroid
+posterior2anterior = centroid_anterior - centroid_posterior
+
+# Compute polar angle of posterior2anterior vector
+# the angle theta is positive going from the positive x-axis to the positive y-axis
+posterior2anterior_pol = cart2pol(posterior2anterior)
+# theta = posterior2anterior_pol.sel(space_pol="phi")  # h
+
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Compute coordinates in ego-centric coordinate system
+
+# Compute position in image coord system translated
+position_translated = position - centroid  # Y_centered
+position_translated_pol = cart2pol(position_translated)  # Y_centered_pol
+
+
+# Compute position in ego-centric coordinate system
+# for every frame, x-axis == anterior-posterior vector
+position_egocentric_pol = position_translated_pol.copy()
+
+# rho is the same as in the translated image coordinate system
+# phi angle is measured relative to the phi angle of the posterior2anterior vector
+position_egocentric_pol.loc[{"space_pol": "phi"}] = (
+    position_translated_pol.sel(space_pol="phi")
+    - posterior2anterior_pol.sel(
+        space_pol="phi"
+    )  # angle_relative_to_posterior2anterior
+)
+
+# Convert rotated position coordinates to cartesian
+position_egocentric = pol2cart(position_egocentric_pol)
+
+# Create a dataset with the `position` data array holding the egocentric coordinates
+# of the keypoints
+ds_egocentric = ds.copy()
+ds_egocentric["position"] = (
+    position_egocentric  # keypoint positions in egocentric coord system
+)
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Check by plotting the keypoint trajectories in the egocentric coordinate system
+
+fig, ax = plt.subplots(1, 1)
+for kpt in ds_egocentric.coords["keypoints"].data:
+    ax.scatter(
+        x=ds_egocentric.position.sel(keypoints=kpt, space="x"),
+        y=ds_egocentric.position.sel(keypoints=kpt, space="y"),
+        label=kpt,
+        alpha=0.5,
+    )
+    # add axis of egocentric coordinate system
+    ax.quiver(
+        [0],  # x
+        [0],  # y
+        [100],  # u
+        [0],  # v
+        color="r",
+        angles="xy",
+        scale=1,
+        scale_units="xy",
+    )
+    ax.quiver(
+        [0],  # x
+        [0],  # y
+        [0],  # u
+        [100],  # v
+        color="g",
+        angles="xy",
+        scale=1,
+        scale_units="xy",
+    )
+
+
+ax.legend()
+ax.invert_yaxis()
+ax.axis("equal")
+ax.set_xlim(-200, 200)
+ax.set_xlabel("x (pixels)")
+ax.set_ylabel("y (pixels)")
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Check that posterior2anterior vector in the egocentric coordinate system
+# is parallel to the x-axis
+
+# Compute centroid for anterior and posterior keypoints
+# in egocentric coordinate system
+centroid_anterior_rotated = position_egocentric.sel(
+    keypoints=anterior_keypoints
+).mean(dim="keypoints", skipna=True)
+centroid_posterior_rotated = position_egocentric.sel(
+    keypoints=posterior_keypoints
+).mean(dim="keypoints", skipna=True)
+
+# Compute posterior2anterior vector in egocentric coordinate system
+posterior2anterior_rotated = (
+    centroid_anterior_rotated - centroid_posterior_rotated
+)
+
+# Check that the y-component of the vector is close to zero
+print(np.nanmax(posterior2anterior_rotated.sel(space="y").data))
+print(np.nanmin(posterior2anterior_rotated.sel(space="y").data))
+
+# Check that the unit posterior2anterior vector is parallel to the x-axis
+posterior2anterior_rotated_unit = convert_to_unit(posterior2anterior_rotated)
+posterior2anterior_rotated_unit.plot.line(x="time", row="individuals")
+
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Compare to alternative approach using scipy Rotation objects
+
+# expand posterior2anterior data array to 3d space
+# ideally, reference vector defined everywhere -- interpolate with slerp?
+posterior2anterior_3d = posterior2anterior.pad(
+    {"space": (0, 1)}, constant_values={"space": (0)}
+)
+posterior2anterior_3d.coords["space"] = ["x", "y", "z"]
+
+
+# compute array of rotation matrices from ICS to ECS
+def compute_rotation_to_align_x_axis(vec):
+    if np.isnan(vec).any():
+        return R.from_matrix(np.eye(3))  # ---> identity, maybe not the best?
+    else:
+        rrot, rssd = R.align_vectors(
+            np.array([[1, 0, 0]]), vec, return_sensitivity=False
+        )
+        return rrot
+
+
+rotation2egocentric = xr.apply_ufunc(
+    lambda v: compute_rotation_to_align_x_axis(v),
+    posterior2anterior_3d,
+    input_core_dims=[["space"]],
+    vectorize=True,
+)
+
+# add to dataset
+ds["rotation2egocentric"] = rotation2egocentric
+
+# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+# Compute rotated keypoints
+
+# expand position data array to 3d space
+position_3d = position.pad({"space": (0, 1)}, constant_values={"space": (0)})
+position_3d.coords["space"] = ["x", "y", "z"]
+
+# compute translation from ICS to ECS
+centroid_3d = position_3d.mean(dim="keypoints")
+
+# compute keypoints in ECS (translated and rotated)
+position_ego_3d = xr.apply_ufunc(
+    lambda rot, trans, vec: rot.apply(vec - trans),
+    rotation2egocentric,  # rot
+    centroid_3d,  # trans
+    position_3d,  # vec
+    input_core_dims=[[], ["space"], ["space"]],
+    output_core_dims=[["space"]],
+    vectorize=True,
+)
+
+# compare to other approach
+print(position_3d.sel(keypoints="snout").data[-3:, :, :])  # ICS
+print("-----")
+print(position_ego_3d.sel(keypoints="snout").data[-3:, :, :])  # ECS
+print("-----")
+print(ds_egocentric.position.sel(keypoints="snout").data[-3:, :, :])  # ECS-2D
+
+# %%