diff --git a/.gitignore b/.gitignore
index 51efb17c..d3875662 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 # project/repo specific
+conf.py
 advanced/backends/*.bin
 scipy-tutorial/dask-report-large-chunk.html
 mydask.png
diff --git a/README.md b/README.md
index acf1078b..bca652ed 100644
--- a/README.md
+++ b/README.md
@@ -45,24 +45,20 @@ pixi run tutorial
 
 ### Building the Documentation Locally
 
-To build and serve the tutorial website locally as a development server:
-
-1. Build the Jupyter Book:
+To build and serve the tutorial website locally with live reload:
 
 ```bash
-pixi run build
+pixi run watch
 ```
 
-2. Serve the built site locally:
+This watches for changes, rebuilds, and serves at http://localhost:8000.
+
+To build without serving:
 
 ```bash
-pixi run python -m http.server --directory _build/html
+pixi run build
 ```
 
-Then visit http://localhost:8000 in your browser.
-
-Note: The `build` command does not have live rebuilding. You'll need to re-run `pixi run build` after making changes to see updates.
-
 ## Contributing
 
 Contributions are welcome and greatly appreciated! See our [CONTRIBUTING.md](./CONTRIBUTING.md) document.
diff --git a/_toc.yml b/_toc.yml
index 0a387442..793de3aa 100644
--- a/_toc.yml
+++ b/_toc.yml
@@ -66,6 +66,9 @@ parts:
 
   - caption: Advanced
     chapters:
+      - file: advanced/indexing/indexing.md
+        sections:
+          - file: advanced/indexing/why-trees.md
       - file: advanced/parallel-intro.md
       - file: advanced/apply_ufunc/apply_ufunc.md
         sections:
diff --git a/advanced/indexing/indexing.md b/advanced/indexing/indexing.md
new file mode 100644
index 00000000..72dae2a4
--- /dev/null
+++ b/advanced/indexing/indexing.md
@@ -0,0 +1,5 @@
+# Indexing
+
+```{tableofcontents}
+
+```
diff --git a/advanced/indexing/why-trees.md b/advanced/indexing/why-trees.md
new file mode 100644
index 00000000..18565713
--- /dev/null
+++ b/advanced/indexing/why-trees.md
@@ -0,0 +1,628 @@
+---
+jupytext:
+  formats: ipynb,md:myst
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.19.1
+kernelspec:
+  display_name: Python 3 (ipykernel)
+  language: python
+  name: python3
+---
+
+# Tree-Based Indexing
+
+```{seealso}
+[NDPointIndex](https://xarray-indexes.readthedocs.io/blocks/ndpoint.html) — use KD-trees and Ball trees with xarray's indexing system for efficient nearest-neighbor lookups on real datasets.
+```
+
+Imagine you have measurements at irregular locations and want to find the **nearest** data point to your query location.
+
+**In this notebook you'll learn:**
+
+- Why naive nearest-neighbor search is slow (O(n) comparisons)
+- How KD-trees speed this up dramatically (O(log n) comparisons)
+- Why KD-trees can give wrong answers for geographic lat/lon data
+- When to use a Ball tree instead
+
++++
+
+## The nearest neighbor problem in 1D
+
+Let's start with a simple 1D example:
+
+**The problem:** What temperature is it at 4.7 km? We need to find the nearest measurement.
+
+```{code-cell} ipython3
+---
+tags: [hide-input]
+---
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Temperature measurements at 7 locations along a transect
+locations = np.array([1, 3, 4, 7, 8, 9, 12])
+temperatures = np.array([15, 18, 17, 22, 24, 23, 19])
+
+# Plot the data
+fig, ax = plt.subplots(figsize=(10, 3))
+ax.scatter(locations, np.zeros_like(locations), s=100, c='blue', zorder=5)
+for loc, temp in zip(locations, temperatures):
+    ax.annotate(f'{temp}°', (loc, 0.15), ha='center', fontsize=10)
+ax.set_xlim(0, 14)
+ax.set_ylim(-0.5, 0.8)
+ax.set_xlabel('Location (km)')
+ax.set_yticks([])
+ax.set_title('Temperature measurements at 7 irregular locations')
+plt.tight_layout()
+plt.show()
+```
+
+The naive approach checks the distance to every point:
+
+```{code-cell} ipython3
+---
+tags: [hide-input]
+---
+# === Configuration: change this to explore different queries ===
+query = 4.7
+
+# Naive approach: check distance to EVERY point
+fig, ax = plt.subplots(figsize=(10, 4))
+
+# Draw the data points on the number line
+ax.scatter(locations, np.zeros_like(locations), s=100, c='blue', zorder=5)
+ax.scatter(query, 0, s=150, c='red', marker='x', zorder=10, lw=3)
+ax.axhline(0, color='black', lw=0.5, zorder=1)
+
+# Draw horizontal distance lines - stacked vertically for visibility
+for i, loc in enumerate(locations):
+    y_offset = 0.12 * (i + 1)
+    # Horizontal line showing the distance
+    ax.plot([query, loc], [y_offset, y_offset], 'gray', alpha=0.7, lw=2)
+    # Vertical ticks at endpoints
+    ax.plot([query, query], [y_offset - 0.03, y_offset + 0.03], 'gray', alpha=0.7, lw=1)
+    ax.plot([loc, loc], [y_offset - 0.03, y_offset + 0.03], 'gray', alpha=0.7, lw=1)
+    # Label
+    ax.annotate(f'{abs(loc - query):.1f} km', ((query + loc)/2, y_offset + 0.04),
+                ha='center', fontsize=8, color='gray')
+
+ax.set_xlim(0, 14)
+ax.set_ylim(-0.2, 1.1)
+ax.set_xlabel('Location (km)')
+ax.set_yticks([])
+ax.set_title(f'Naive search: compute distance to ALL {len(locations)} points (query={query})')
+plt.tight_layout()
+plt.show()
+
+print(f"Query: {query} km")
+print(f"Nearest point: {locations[np.argmin(np.abs(locations - query))]} km (distance = {np.min(np.abs(locations - query)):.1f} km)")
+print(f"Comparisons needed: {len(locations)}")
+```
+
+With 7 points this is fine, but with millions of points this becomes slow.
+
+**The solution:** Pre-compute a tree structure that partitions the space. In 1D, this is essentially a binary search tree - each split divides the remaining points in half:
+
+```{code-cell} ipython3
+---
+tags: [hide-input]
+---
+from scipy.spatial import KDTree
+from matplotlib.patches import Rectangle
+
+# === Configuration ===
+
+# Build the tree (this is the pre-computation step)
+tree = KDTree(locations.reshape(-1, 1))
+
+# Query the tree first to get the result
+dist, idx = tree.query([[query]])
+nearest = locations[idx[0]]
+
+# Map from value to node name for finding the result node
+value_to_node = {1: 'LL', 3: 'L1', 4: 'LR', 7: 'root', 8: 'RL', 9: 'R1', 12: 'RR'}
+found_node = value_to_node[nearest]
+
+# Determine the search path based on query value
+if query < 7:
+    if query < 3:
+        path_nodes = ['root', 'L1', 'LL']
+        regions = [(0, 14), (0, 7), (0, 3)]
+    else:
+        path_nodes = ['root', 'L1', 'LR']
+        regions = [(0, 14), (0, 7), (3, 7)]
+else:
+    if query < 9:
+        path_nodes = ['root', 'R1', 'RL']
+        regions = [(0, 14), (7, 14), (7, 9)]
+    else:
+        path_nodes = ['root', 'R1', 'RR']
+        regions = [(0, 14), (7, 14), (9, 14)]
+
+# Create visualization: tree on left, 3 narrowing steps on right
+fig = plt.figure(figsize=(16, 9))
+
+# Left side: Tree diagram with spatial ranges
+ax_tree = fig.add_subplot(1, 2, 1)
+ax_tree.set_xlim(0, 16)
+ax_tree.set_ylim(-0.5, 5.5)
+ax_tree.axis('off')
+ax_tree.set_title('KD-tree structure\n(each node shows the spatial range it covers)', fontsize=12, fontweight='bold')
+
+# Tree node positions - now includes spatial range for each node
+nodes = {
+    'root': {'pos': (8, 4.5), 'value': 7, 'color': 'steelblue', 'label': 'split=7', 'range': '[0, 14]'},
+    'L1': {'pos': (4, 2.6), 'value': 3, 'color': 'coral', 'label': 'split=3', 'range': '[0, 7)'},
+    'R1': {'pos': (12, 2.6), 'value': 9, 'color': 'seagreen', 'label': 'split=9', 'range': '[7, 14]'},
+    'LL': {'pos': (2, 0.8), 'value': 1, 'color': 'gray', 'label': '1', 'range': '[0, 3)'},
+    'LR': {'pos': (6, 0.8), 'value': 4, 'color': 'gray', 'label': '4', 'range': '[3, 7)'},
+    'RL': {'pos': (10, 0.8), 'value': 8, 'color': 'gray', 'label': '8', 'range': '[7, 9)'},
+    'RR': {'pos': (14, 0.8), 'value': 12, 'color': 'gray', 'label': '12', 'range': '[9, 14]'},
+}
+
+# Draw edges
+edges = [('root', 'L1'), ('root', 'R1'), ('L1', 'LL'), ('L1', 'LR'), ('R1', 'RL'), ('R1', 'RR')]
+for parent, child in edges:
+    px, py = nodes[parent]['pos']
+    cx, cy = nodes[child]['pos']
+    ax_tree.plot([px, cx], [py, cy], 'k-', lw=2, zorder=1)
+
+# Draw nodes with spatial range labels
+for name, node in nodes.items():
+    x, y = node['pos']
+    is_split = 'split' in node['label']
+    size = 2200 if is_split else 1500
+    ax_tree.scatter(x, y, s=size, c=node['color'], zorder=5, edgecolors='black', linewidths=2)
+    ax_tree.annotate(node['label'], (x, y), ha='center', va='center',
+                     fontsize=11 if is_split else 10, fontweight='bold', color='white')
+    # Add range label below each node
+    ax_tree.annotate(node['range'], (x, y - 0.55), ha='center', va='top',
+                     fontsize=9, color='black', style='italic',
+                     bbox=dict(boxstyle='round,pad=0.2', facecolor='white', edgecolor='gray', alpha=0.8))
+
+# Highlight the path taken
+for i in range(len(path_nodes) - 1):
+    px, py = nodes[path_nodes[i]]['pos']
+    cx, cy = nodes[path_nodes[i+1]]['pos']
+    ax_tree.plot([px, cx], [py, cy], 'r-', lw=5, alpha=0.4, zorder=2)
+
+# Add query annotation
+ax_tree.annotate(f'query={query}', (8, 4.5), xytext=(11, 5.2),
+                 fontsize=11, color='red', fontweight='bold',
+                 arrowprops=dict(arrowstyle='->', color='red', lw=2))
+
+# Mark the found node
+found_x, found_y = nodes[found_node]['pos']
+ax_tree.annotate(f'found {nearest}!', (found_x + 1.2, found_y + 0.3), fontsize=11, ha='left', color='red', fontweight='bold')
+
+# Right side: 3 subplots showing narrowing search space
+steps = [
+    ("Step 1: Start with all points", regions[0], 'steelblue', f'{query} < 7? → go left' if query < 7 else f'{query} > 7? → go right'),
+    ("Step 2: After first split", regions[1], 'coral', f'{query} < 3? → go left' if query < 3 else f'{query} > 3? → go right' if query < 7 else f'{query} < 9? → go left' if query < 9 else f'{query} > 9? → go right'),
+    (f"Step 3: Found nearest = {nearest}", regions[2], 'gold', None),
+]
+
+for i, (title, (region_start, region_end), color, annotation) in enumerate(steps):
+    ax = fig.add_subplot(3, 2, 2*(i+1))
+
+    # Draw all data points
+    for loc in locations:
+        in_region = region_start <= loc <= region_end
+        ax.scatter(loc, 0, s=100 if in_region else 60,
+                   c='blue' if in_region else 'lightgray',
+                   zorder=5, edgecolors='black' if in_region else 'gray', linewidths=1)
+        if in_region:
+            ax.annotate(f'{loc}', (loc, -0.25), ha='center', fontsize=9, fontweight='bold')
+
+    # Draw query point
+    ax.scatter(query, 0, s=150, c='red', marker='x', zorder=10, lw=3)
+
+    # Highlight the active region
+    rect = Rectangle((region_start, -0.15), region_end - region_start, 0.3,
+                      fill=True, facecolor=color, alpha=0.2, edgecolor=color, lw=2, zorder=2)
+    ax.add_patch(rect)
+
+    # Draw split lines
+    if i == 0:
+        ax.axvline(7, color='steelblue', lw=2, ls='--', alpha=0.8)
+        ax.annotate('split=7', (7, 0.25), ha='center', fontsize=9, color='steelblue', fontweight='bold')
+    elif i == 1:
+        if query < 7:
+            ax.axvline(3, color='coral', lw=2, ls='--', alpha=0.8)
+            ax.annotate('split=3', (3, 0.25), ha='center', fontsize=9, color='coral', fontweight='bold')
+        else:
+            ax.axvline(9, color='seagreen', lw=2, ls='--', alpha=0.8)
+            ax.annotate('split=9', (9, 0.25), ha='center', fontsize=9, color='seagreen', fontweight='bold')
+
+    # Add decision annotation
+    if annotation:
+        ax.annotate(annotation, (0.98, 0.95), xycoords='axes fraction', ha='right', va='top',
+                    fontsize=10, color='darkgreen', fontweight='bold',
+                    bbox=dict(boxstyle='round', facecolor='lightyellow', edgecolor='green', alpha=0.8))
+
+    ax.set_xlim(-0.5, 14.5)
+    ax.set_ylim(-0.4, 0.45)
+    ax.set_title(title, fontsize=11, fontweight='bold')
+    ax.set_yticks([])
+    if i == 2:
+        ax.set_xlabel('Location (km)', fontsize=10)
+
+plt.tight_layout()
+plt.show()
+
+print(f"Nearest point: {nearest} km")
+print(f"Comparisons needed: ~{len(path_nodes)} (log₂({len(locations)}) ≈ 3)")
+```
+
+## Extending to 2D
+
+The same idea works in higher dimensions. Now our measurements are scattered across a 2D area:
+
+```{code-cell} ipython3
+---
+tags: [hide-input]
+---
+# 2D example: temperature measurements scattered across an area
+from matplotlib.patches import Rectangle
+
+np.random.seed(42)
+points_2d = np.random.rand(20, 2) * 10  # 20 points in a 10x10 area
+
+# === Configuration ===
+query_2d = np.array([6.5, 4.0])  # Change this to query a different location
+
+# Build tree - using leafsize=2 to demonstrate meaningful subdivision
+# (default leafsize=10 would barely split with only 20 points!)
+LEAFSIZE = 2
+tree_2d = KDTree(points_2d, leafsize=LEAFSIZE)
+dist, idx = tree_2d.query([query_2d])
+nearest_2d = points_2d[idx[0]]
+
+# With leafsize=2, we get ~4 levels of splits (log2(20/2) ≈ 3-4)
+# Let's show the first 2 splits conceptually, then the final leaf comparison
+
+# Approximate the splits (KD-tree alternates x, y, x, y...)
+x_split = np.median(points_2d[:, 0])  # ~4.0
+
+# Determine which half based on query x
+if query_2d[0] >= x_split:
+    # Right half
+    half_points = points_2d[points_2d[:, 0] >= x_split]
+    x_decision = f"x={query_2d[0]} > {x_split:.1f}? → go right"
+    x_region = (x_split, 0, 10, 10)  # (x_min, y_min, x_max, y_max)
+else:
+    # Left half
+    half_points = points_2d[points_2d[:, 0] < x_split]
+    x_decision = f"x={query_2d[0]} < {x_split:.1f}? → go left"
+    x_region = (0, 0, x_split, 10)
+
+y_split = np.median(half_points[:, 1])
+
+# Determine which quadrant based on query y
+if query_2d[1] >= y_split:
+    # Upper region
+    y_decision = f"y={query_2d[1]} > {y_split:.1f}? → go up"
+    if query_2d[0] >= x_split:
+        final_region = (x_split, y_split, 10, 10)  # top-right
+    else:
+        final_region = (0, y_split, x_split, 10)  # top-left
+else:
+    # Lower region
+    y_decision = f"y={query_2d[1]} < {y_split:.1f}? → go down"
+    if query_2d[0] >= x_split:
+        final_region = (x_split, 0, 10, y_split)  # bottom-right
+    else:
+        final_region = (0, 0, x_split, y_split)  # bottom-left
+
+# Define regions for visualization
+regions = [
+    (0, 0, 10, 10),      # Step 1: all points
+    x_region,             # Step 2: half based on x
+    final_region,         # Step 3: quadrant based on y
+]
+
+# Get actual points in final region (these are the leaf candidates)
+x_min, y_min, x_max, y_max = final_region
+final_candidates = [pt for pt in points_2d
+                    if x_min <= pt[0] <= x_max and y_min <= pt[1] <= y_max]
+
+# Create figure
+fig, axes = plt.subplots(2, 2, figsize=(12, 10))
+axes = axes.flatten()
+
+step_titles = [
+    "Step 1: Start with all 20 points",
+    f"Step 2: Split on x ≈ {x_split:.1f}",
+    f"Step 3: Split on y ≈ {y_split:.1f}",
+    f"Step 4: Compare {len(final_candidates)} candidates in leaf"
+]
+step_colors = ['steelblue', 'coral', 'gold', 'limegreen']
+decisions = [x_decision, y_decision, None, None]
+
+for i, ax in enumerate(axes):
+    x_min, y_min, x_max, y_max = regions[min(i, 2)]
+
+    # Get points in current region
+    points_in_region = [(pt, x_min <= pt[0] <= x_max and y_min <= pt[1] <= y_max) for pt in points_2d]
+
+    # Draw all points
+    for pt, in_region in points_in_region:
+        ax.scatter(pt[0], pt[1], s=80 if in_region else 40,
+                   c='blue' if in_region else 'lightgray',
+                   edgecolors='black' if in_region else 'gray',
+                   zorder=5, linewidths=1)
+
+    # Draw query point
+    ax.scatter(*query_2d, s=150, c='red', marker='x', zorder=10, lw=3)
+
+    # Draw the active region
+    rect = Rectangle((x_min, y_min), x_max - x_min, y_max - y_min,
+                      fill=True, facecolor=step_colors[i], alpha=0.15,
+                      edgecolor=step_colors[i], lw=2, zorder=2)
+    ax.add_patch(rect)
+
+    # Draw split lines
+    if i >= 1:
+        ax.axvline(x_split, color='steelblue', lw=2, ls='--', alpha=0.8)
+        ax.annotate(f'x={x_split:.1f}', (x_split, 9.7), ha='center', fontsize=9,
+                    color='steelblue', fontweight='bold')
+    if i >= 2:
+        # Only draw y split line in the relevant half
+        if query_2d[0] >= x_split:
+            ax.axhline(y_split, xmin=x_split/10, xmax=1, color='coral', lw=2, ls='--', alpha=0.8)
+        else:
+            ax.axhline(y_split, xmin=0, xmax=x_split/10, color='coral', lw=2, ls='--', alpha=0.8)
+        ax.annotate(f'y={y_split:.1f}', (9.7, y_split + 0.2),
+                    ha='right', va='bottom', fontsize=9, color='coral', fontweight='bold')
+
+    # Final step: draw lines to ALL candidates
+    if i == 3:
+        for pt, in_region in points_in_region:
+            if in_region:
+                is_nearest = np.allclose(pt, nearest_2d)
+                ax.plot([query_2d[0], pt[0]], [query_2d[1], pt[1]],
+                        color='limegreen' if is_nearest else 'gray',
+                        lw=3 if is_nearest else 1.5,
+                        alpha=1.0 if is_nearest else 0.6,
+                        zorder=6 if is_nearest else 4)
+
+        ax.scatter(*nearest_2d, s=200, facecolors='none', edgecolors='limegreen', lw=3, zorder=15)
+        ax.annotate('nearest!', (nearest_2d[0] + 0.3, nearest_2d[1] + 0.3),
+                    ha='left', fontsize=10, color='green', fontweight='bold')
+
+    # Add decision annotation
+    if decisions[i]:
+        ax.annotate(decisions[i], (0.98, 0.98), xycoords='axes fraction',
+                    ha='right', va='top', fontsize=10, color='darkgreen', fontweight='bold',
+                    bbox=dict(boxstyle='round', facecolor='lightyellow', edgecolor='green', alpha=0.9))
+
+    ax.set_xlim(-0.5, 10.5)
+    ax.set_ylim(-0.5, 10.5)
+    ax.set_aspect('equal')
+    ax.set_xlabel('x')
+    ax.set_ylabel('y')
+    ax.set_title(step_titles[i], fontsize=11, fontweight='bold')
+
+plt.tight_layout()
+plt.show()
+
+print(f"Query: ({query_2d[0]}, {query_2d[1]})")
+print(f"KDTree built with leafsize={LEAFSIZE}")
+print(f"Started with {len(points_2d)} points")
+print(f"After 2 tree splits: narrowed to {len(final_candidates)} candidates")
+print(f"Final step: {len(final_candidates)} distance calculations")
+print(f"Total: 2 splits + {len(final_candidates)} comparisons = {2 + len(final_candidates)} operations (vs 20 naive)")
+```
+
+## How it scales
+
+The same principle extends to 3D, 4D, and beyond. Here's how the number of comparisons scales:
+
+```{code-cell} ipython3
+---
+tags: [hide-input]
+---
+# How comparisons scale with data size
+data_sizes = np.array([10, 100, 1000, 10000, 100000, 1000000])
+naive_comparisons = data_sizes  # O(n)
+kdtree_comparisons = np.log2(data_sizes).astype(int) + 1  # O(log n)
+
+fig, ax = plt.subplots(figsize=(10, 5))
+
+ax.plot(data_sizes, naive_comparisons, 'o-', color='gray', lw=2, markersize=8, label='Naive: O(n)')
+ax.plot(data_sizes, kdtree_comparisons, 's-', color='steelblue', lw=2, markersize=8, label='KD-tree: O(log n)')
+
+ax.set_xscale('log')
+ax.set_yscale('log')
+ax.set_xlabel('Number of data points')
+ax.set_ylabel('Comparisons per query')
+ax.set_title('Finding nearest neighbor: Naive vs KD-tree')
+ax.legend(fontsize=11)
+ax.grid(True, alpha=0.3)
+
+# Annotate key points
+for n, naive, kd in zip(data_sizes[::2], naive_comparisons[::2], kdtree_comparisons[::2]):
+    ax.annotate(f'{naive:,}', (n, naive), textcoords="offset points", xytext=(0,10), ha='center', fontsize=9, color='gray')
+    ax.annotate(f'{kd}', (n, kd), textcoords="offset points", xytext=(0,-15), ha='center', fontsize=9, color='steelblue')
+
+plt.tight_layout()
+plt.show()
+
+print("With 1 million points: naive needs 1,000,000 comparisons, KD-tree needs ~20")
+```
+
+(the-problem-with-geographic-coordinates)=
+
+## The problem with geographic coordinates
+
+KD-trees use **Euclidean distance**—they measure straight-line distance in whatever coordinate system you give them. This works perfectly for x/y coordinates in meters or kilometers.
+
+But for **latitude/longitude coordinates**, Euclidean distance over degrees is wrong! Here's why:
+
+- **Latitude degrees are constant**: 1° latitude ≈ 111 km everywhere on Earth
+- **Longitude degrees shrink toward the poles**: 1° longitude ≈ 111 km at the equator, but only ~19 km at 80°N
+
+This means a KD-tree treating lat/lon as flat coordinates will systematically pick the **wrong** nearest neighbor at high latitudes:
+
+```{code-cell} ipython3
+---
+tags: [hide-input]
+---
+# Visualize haversine vs Euclidean - 2D circle diagram
+from sklearn.neighbors import BallTree
+
+# At 80°N (near Arctic): longitude degrees are MUCH shorter!
+lat = 80
+km_per_deg_lon = 111 * np.cos(np.radians(lat))  # ~19 km at 80°N!
+km_per_deg_lat = 111  # always ~111 km
+
+# Query point and two candidates (in lat/lon degrees)
+query_latlon = np.array([[lat, 0]])
+point_a_latlon = np.array([[lat, 2.0]])
+point_b_latlon = np.array([[lat + 0.5, 0]])
+points_latlon = np.vstack([point_a_latlon, point_b_latlon])
+
+# Test both trees
+kd_tree = KDTree(points_latlon)
+kd_dist, kd_idx = kd_tree.query(query_latlon)
+kd_picked = "A" if kd_idx[0] == 0 else "B"
+
+ball_tree = BallTree(np.radians(points_latlon), metric='haversine')
+ball_dist, ball_idx = ball_tree.query(np.radians(query_latlon))
+ball_picked = "A" if ball_idx[0] == 0 else "B"
+
+km_to_a = 2.0 * km_per_deg_lon
+km_to_b = 0.5 * km_per_deg_lat
+
+# Create figure
+fig = plt.figure(figsize=(14, 10), constrained_layout=True)
+
+# === Top: Circle diagram showing arc vs chord ===
+ax_circle = fig.add_subplot(211)
+ax_circle.set_aspect('equal')
+ax_circle.axis('off')
+
+# Draw circle
+radius = 1
+theta_full = np.linspace(0, 2*np.pi, 100)
+ax_circle.plot(radius * np.cos(theta_full), radius * np.sin(theta_full), 'k-', lw=2.5)
+
+# Two points on the circle
+theta_p = np.radians(120)  # Point P
+theta_q = np.radians(60)   # Point Q
+
+p_x, p_y = radius * np.cos(theta_p), radius * np.sin(theta_p)
+q_x, q_y = radius * np.cos(theta_q), radius * np.sin(theta_q)
+
+# Draw the ARC (haversine distance) - along the circle surface
+arc_theta = np.linspace(theta_q, theta_p, 50)
+arc_x = radius * np.cos(arc_theta)
+arc_y = radius * np.sin(arc_theta)
+ax_circle.plot(arc_x, arc_y, 'r-', lw=6, solid_capstyle='round', label='Arc length (haversine)', zorder=5)
+
+# Draw the CHORD (Euclidean distance) - straight line
+ax_circle.plot([p_x, q_x], [p_y, q_y], 'b--', lw=4, label='Chord length (Euclidean)', zorder=4)
+
+# Draw points
+ax_circle.scatter([p_x, q_x], [p_y, q_y], s=250, c='dodgerblue', edgecolors='black', lw=2, zorder=10)
+
+# Labels
+ax_circle.annotate('P', (p_x - 0.18, p_y + 0.08), fontsize=24, fontweight='bold')
+ax_circle.annotate('Q', (q_x + 0.1, q_y + 0.08), fontsize=24, fontweight='bold')
+
+# Distance annotations - positioned to avoid overlap
+# Arc annotation (above the arc)
+arc_mid_theta = (theta_p + theta_q) / 2
+arc_mid_x = 1.22 * np.cos(arc_mid_theta)
+arc_mid_y = 1.22 * np.sin(arc_mid_theta)
+ax_circle.annotate('arc length\n(along surface)', (arc_mid_x, arc_mid_y + 0.05),
+                   fontsize=13, color='darkred', fontweight='bold', ha='center',
+                   bbox=dict(boxstyle='round,pad=0.3', facecolor='mistyrose', edgecolor='red', alpha=0.9))
+
+# Chord annotation (below the chord)
+chord_mid_x = (p_x + q_x) / 2
+chord_mid_y = (p_y + q_y) / 2
+ax_circle.annotate('chord\n(straight line)', (chord_mid_x, chord_mid_y - 0.25),
+                   fontsize=13, color='darkblue', fontweight='bold', ha='center',
+                   bbox=dict(boxstyle='round,pad=0.3', facecolor='lightblue', edgecolor='blue', alpha=0.9))
+
+# Calculate actual distances for display
+arc_length = radius * abs(theta_p - theta_q)  # s = r * theta
+chord_length = np.sqrt((q_x - p_x)**2 + (q_y - p_y)**2)
+
+ax_circle.set_xlim(-1.5, 1.5)
+ax_circle.set_ylim(-1.0, 1.7)
+ax_circle.set_title('Haversine vs Euclidean: arc length ≠ chord length',
+                    fontsize=16, fontweight='bold', pad=15)
+
+# Legend on the left side
+ax_circle.legend(loc='center left', fontsize=11, bbox_to_anchor=(-0.15, 0.3))
+
+# Formula box on the right side
+formula_text = f"Arc length > Chord length\n(arc = {arc_length:.2f},  chord = {chord_length:.2f})"
+ax_circle.text(1.15, 0.3, formula_text, fontsize=12, ha='center',
+               bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.9))
+
+# === Bottom row: Side-by-side comparison ===
+# Bottom-left: KD-tree view (flat degrees)
+ax_kd = fig.add_subplot(223)
+ax_kd.scatter(0, 0, s=200, c='red', marker='x', zorder=10, lw=3, label='Query')
+ax_kd.scatter(2.0, 0, s=140, c='green', zorder=5, label='Point A (2° east)')
+ax_kd.scatter(0, 0.5, s=140, c='orange', zorder=5, label='Point B (0.5° north)')
+ax_kd.plot([0, 2.0], [0, 0], 'g-', lw=2.5, alpha=0.7)
+ax_kd.plot([0, 0], [0, 0.5], color='orange', lw=2.5, alpha=0.7)
+
+circle_kd = plt.Circle((0, 0.5), 0.15, fill=False, color='black', lw=3, linestyle='--', zorder=15)
+ax_kd.add_patch(circle_kd)
+ax_kd.annotate('KD-tree picks B\n(smaller in degrees)', (0.3, 0.75), fontsize=12, fontweight='bold')
+
+ax_kd.set_xlabel('Longitude offset (°)', fontsize=13)
+ax_kd.set_ylabel('Latitude offset (°)', fontsize=13)
+ax_kd.set_title(f'KD-tree: Euclidean on degrees\n(at {lat}°N latitude)', fontsize=13, fontweight='bold')
+ax_kd.legend(loc='upper right', fontsize=10)
+ax_kd.set_xlim(-0.5, 2.5)
+ax_kd.set_ylim(-0.5, 1.2)
+ax_kd.set_aspect('equal')
+ax_kd.grid(True, alpha=0.3)
+ax_kd.annotate('2.0°', (1.0, -0.15), ha='center', fontsize=14, color='green', fontweight='bold')
+ax_kd.annotate('0.5°', (-0.25, 0.25), ha='center', fontsize=14, color='orange', fontweight='bold', rotation=90)
+
+# Bottom-right: Reality in kilometers
+ax_real = fig.add_subplot(224)
+ax_real.scatter(0, 0, s=200, c='red', marker='x', zorder=10, lw=3, label=f'Query ({lat}°N)')
+ax_real.scatter(km_to_a, 0, s=140, c='green', zorder=5, label='Point A')
+ax_real.scatter(0, km_to_b, s=140, c='orange', zorder=5, label='Point B')
+ax_real.plot([0, km_to_a], [0, 0], 'g-', lw=2.5, alpha=0.7)
+ax_real.plot([0, 0], [0, km_to_b], color='orange', lw=2.5, alpha=0.7)
+
+circle_ball = plt.Circle((km_to_a, 0), 6, fill=False, color='black', lw=3, linestyle='--', zorder=15)
+ax_real.add_patch(circle_ball)
+ax_real.annotate('Ball tree picks A\n(smaller in km)', (5, 55), fontsize=12, fontweight='bold')
+
+ax_real.set_xlabel('East-West distance (km)', fontsize=13)
+ax_real.set_ylabel('North-South distance (km)', fontsize=13)
+ax_real.set_title(f'Ball tree: haversine (true distance)\n1° longitude = only {km_per_deg_lon:.0f} km at {lat}°N!',
+                  fontsize=13, fontweight='bold')
+ax_real.legend(loc='upper right', fontsize=10)
+ax_real.set_xlim(-10, 70)
+ax_real.set_ylim(-10, 70)
+ax_real.set_aspect('equal')
+ax_real.grid(True, alpha=0.3)
+ax_real.annotate(f'{km_to_a:.0f} km', (km_to_a/2, -6), ha='center', fontsize=14, color='green', fontweight='bold')
+ax_real.annotate(f'{km_to_b:.0f} km', (-7, km_to_b/2), ha='center', fontsize=14, color='orange', fontweight='bold', rotation=90)
+
+plt.show()
+
+print(f"At {lat}°N: 1° longitude = {km_per_deg_lon:.0f} km, 1° latitude = {km_per_deg_lat} km")
+print(f"\nPoint A: 2° east = {km_to_a:.0f} km  (along surface)")
+print(f"Point B: 0.5° north = {km_to_b:.0f} km")
+print(f"\nKD-tree picked: Point {kd_picked} {'✗ WRONG!' if kd_picked == 'B' else '✓'}")
+print(f"Ball tree picked: Point {ball_picked} {'✓ CORRECT!' if ball_picked == 'A' else '✗'}")
+```
+
+## Next steps
+
+Ready to use tree-based indexing with xarray? See [NDPointIndex](https://xarray-indexes.readthedocs.io/blocks/ndpoint.html) for how to integrate KD-trees and Ball trees with xarray's indexing system.
diff --git a/pixi.lock b/pixi.lock
index 6f1e3b5b..119d418f 100644
--- a/pixi.lock
+++ b/pixi.lock
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+      - python_abi 3.12.* *_cp312
+      - ucrt >=10.0.20348.0
+      - vc >=14.3,<15
+      - vc14_runtime >=14.44.35208
+    license: MIT
+    license_family: MIT
+    size: 303368
+    timestamp: 1760457029394
   - conda: https://conda.anaconda.org/conda-forge/linux-64/wayland-1.23.1-h3e06ad9_0.conda
     sha256: 0884b2023a32d2620192cf2e2fc6784b8d1e31cf9f137e49e00802d4daf7d1c1
     md5: 0a732427643ae5e0486a727927791da1
@@ -12351,6 +12565,43 @@ packages:
     license_family: APACHE
     size: 46718
     timestamp: 1733157432924
+  - conda: https://conda.anaconda.org/conda-forge/linux-64/websockets-16.0-py312h5253ce2_1.conda
+    sha256: dd598cab9175a9ab11c8a1798c49ccabe923263d12aababa84a296cb18206464
+    md5: e35ffb48178b20ee1a43fbe7abc93746
+    depends:
+      - python
+      - __glibc >=2.17,<3.0.a0
+      - libgcc >=14
+      - python_abi 3.12.* *_cp312
+    license: BSD-3-Clause
+    license_family: BSD
+    size: 358659
+    timestamp: 1768087389177
+  - conda: https://conda.anaconda.org/conda-forge/osx-arm64/websockets-16.0-py312hb3ab3e3_1.conda
+    sha256: 4b15497f3cbc40c6fc9e0f155e9cd31aa13e8d2cb1930355da934af22816a73a
+    md5: 3da07548ed0e08634abf2b3b878eabc1
+    depends:
+      - python
+      - python 3.12.* *_cpython
+      - __osx >=11.0
+      - python_abi 3.12.* *_cp312
+    license: BSD-3-Clause
+    license_family: BSD
+    size: 362390
+    timestamp: 1768087403337
+  - conda: https://conda.anaconda.org/conda-forge/win-64/websockets-16.0-py312he5662c2_1.conda
+    sha256: fda4ece1e956169d8c7fed231c52c53fbdb2dc36105d6a1a083174dda804ac0a
+    md5: 65db5c23f67c34d2ecbd6ede2c8b253e
+    depends:
+      - python
+      - vc >=14.3,<15
+      - vc14_runtime >=14.44.35208
+      - ucrt >=10.0.20348.0
+      - python_abi 3.12.* *_cp312
+    license: BSD-3-Clause
+    license_family: BSD
+    size: 414775
+    timestamp: 1768087427139
   - conda: https://conda.anaconda.org/conda-forge/noarch/widgetsnbextension-4.0.13-pyhd8ed1ab_1.conda
     sha256: a750202ae2a31d8e5ee5a5c127fcc7fa783cd0fbedbc0bf1ab549a109881fa9f
     md5: 237db148cc37a466e4222d589029b53e
diff --git a/pyproject.toml b/pyproject.toml
index 2115462c..e45b1274 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -46,7 +46,7 @@ line_length=100
 ignore-words-list="nd"
 skip="pixi.lock,.pixi,qaqc.yaml"
 
-[tool.pixi.project]
+[tool.pixi.workspace]
 name = "xarray-tutorial"
 channels = ["conda-forge"]
 platforms = ["osx-arm64", "linux-64", "win-64"]
@@ -61,6 +61,7 @@ checklinks = "jupyter-book build ./ --builder linkcheck"
 clear-cache = "jupyter-book clean ."
 # To clear a specific notebook pass ID number: jcache cache -p _build/.jupyter_cache remove 28
 # To clear all cached notebooks: jupyter-book clean . --all"
+watch = { cmd = "jupyter-book config sphinx ./ && sphinx-autobuild ./ _build/html -b html --re-ignore '_build/.*'", description = "Build and serve with live reload" }
 list-cache = "jcache cache -p _build/.jupyter_cache list"
 
 [tool.pixi.dependencies]
@@ -90,10 +91,12 @@ pydap = ">=3.5.5,<4"
 python-graphviz = ">=0.21,<0.22"
 pooch = ">=1.8.2,<2"
 rioxarray = ">=0.19.0,<0.20"
+scikit-learn = ">=1.6.0,<2"
 scipy = ">=1.16.0,<2"
 sphinx-codeautolink = ">=0.17.4,<0.18"
 sphinxcontrib-mermaid = ">=1.0.0,<2"
 sphinx-notfound-page = ">=1.1.0,<2"
+sphinx-autobuild = ">=2024.10.3,<2026"
 sphinxext-rediraffe = ">=0.2.7,<0.3"
 s3fs = ">=2025.5.1,<2026"
 xarray = ">=2025.7.0,<2026"
@@ -101,3 +104,4 @@ zarr = ">=3.0.10,<4"
 flox = ">=0.10.4,<0.11"
 numbagg = ">=0.9.0,<0.10"
 rich = ">=14.0.0,<15"
+jupyterlab_vim = ">=4.1.4,<5"