Delaunay Voronoi

Centroid Voronoi

Displays a Voronoi tessellation computed from the centroids of all US counties, using Observable Plot’s centroid transform on GeoJSON county features loaded from the us-atlas CDN. Each county’s polygon centroid becomes a Voronoi seed point, producing a map that shows how centroid-based nearest-neighbor regions differ from actual county boundaries. Voronoi cells are colored by census region (Northeast, Midwest, South, West) or by individual state, with a categorical color legend at the top. State borders are overlaid by default. Interactive controls include: projection type picker (Albers, Albers USA, Mercator, Equal Earth, Equirectangular), color-by picker (Region, State), color scheme selector (Tableau10, Observable10, Category10, Accent, Dark2, Paired, Set1, Set2), cell opacity slider (0.10–1.00), cell stroke width slider (0–2px), and toggles to independently show/hide the Voronoi cells, actual county borders, state borders, and centroid dots. When centroid dots are enabled, a dot radius slider (0.5–4px) appears. Hovering over the chart shows a tooltip with county FIPS code, state name, and region for the nearest centroid. The chart should render approximately 3,100 colored Voronoi cells covering the entire US, with state borders overlaid, on an Albers projection.

Delaunay Hull

Displays a Delaunay mesh triangulation with convex hulls overlaid, using Palmer Penguins data. The Delaunay mesh is computed per-group (using the z channel) so that triangulation edges only connect points within the same category. Convex hulls are drawn around each group with a configurable stroke width and a subtle fill. Data points are overlaid as dots. Interactive controls include: X-axis field picker (Culmen Depth, Culmen Length, Flipper Length, Body Mass), Y-axis field picker, Group By picker (Species, Island), color scheme selector (observable10, category10, accent, dark2, paired, set1, set2, tableau10), mesh opacity slider (0.05–1.00), hull width slider (0.5–6px), and toggles to show/hide the mesh, hull, and dots independently. Hovering over the chart shows a tooltip with species, island, and all numeric measurements for the nearest point. The chart should render colored Delaunay mesh lines connecting data points within each group, with convex hull outlines and 26 penguin data points, plus a categorical color legend at the top.

Planar vs Spherical Voronoi

Compares planar (Euclidean) and spherical (geodesic) Voronoi tessellations of 50 world airports on various map projections. In side-by-side mode, two charts are shown: the left uses Plot.voronoiMesh (planar, red lines) and the right uses d3-geo-voronoi cellMesh rendered with Plot.geo (spherical, blue lines). In overlay mode, both tessellations are drawn on a single chart with red for planar and blue for spherical, making the differences easily visible. Interactive controls include: projection picker (Equal Earth, Orthographic, Equirectangular, Stereographic, Azimuthal Equal-Area, Gnomonic), view mode toggle (Side by Side, Overlay), stroke width slider (0.2–3px), dot radius slider (0.5–5px), and a checkbox to show/hide the sphere outline. Hovering over the chart shows a tooltip with the airport name and coordinates for the nearest point. The chart should render Voronoi mesh lines clipped to the sphere with 50 airport dots, demonstrating how planar and spherical Voronoi partitions diverge at large scales.

Voronoi Map

Displays a Voronoi tessellation of US state capitals on an azimuthal projection, showing each capital’s nearest-neighbor geographic region. The chart uses a clipped spherical projection centered on the contiguous United States with a faint nation outline, Voronoi cell boundaries, and dots marking each capital. All 50 state capitals are included as seed data; those outside the clip radius (e.g., Alaska, Hawaii at default 24°) are clipped. Interactive controls include: projection type picker (Azimuthal Equal-Area, Azimuthal Equidistant, Orthographic, Stereographic, Gnomonic), clip radius slider (10°–60°), dot radius slider (0.5–8px), Voronoi stroke width slider (0.2–4px), nation fill opacity slider (0–0.60), and toggles to independently show/hide the Voronoi cells, capital dots, and nation outline. Hovering over the chart shows a tooltip with the capital name and state for the nearest point. The chart should render approximately 48 capital dots (contiguous US at default clip), Voronoi cell boundaries clipped to a sphere, and a faint US nation outline within a circular azimuthal projection.

Voronoi Scatterplot

Displays a Voronoi tessellation scatterplot using Palmer Penguins data. Each data point’s nearest-neighbor region is shown as a colored Voronoi cell, with dots overlaid on top to form a scatterplot. The chart defaults to culmen depth vs culmen length, colored by species. Interactive controls include: X-axis column picker (CulmenDepth, CulmenLength, FlipperLength, BodyMass), Y-axis column picker, color-by column picker (Species, Island), color scheme selector (observable10, category10, accent, dark2, paired, set1, set2, tableau10), Voronoi opacity slider (0.05–0.80), dot radius slider (1–8), and toggles to show/hide Voronoi cells and dots independently. Hovering over the chart shows a tooltip with species, island, and all numeric measurements for the nearest point. The chart should render 26 colored Voronoi cells with semi-transparent fill and 26 solid dots, with a categorical color legend at the top.

Walmart Store Voronoi

Displays a Voronoi mesh of Walmart store locations across the United States on a geographic projection, showing the territory nearest to each store. The chart uses an Albers projection by default and renders a US nation outline as a faint filled shape, small dots for each Walmart store location, and Voronoi mesh lines partitioning the map into nearest-store regions. Approximately 65 representative Walmart store locations are included as seed data, spread across the contiguous US. Interactive controls include: projection type picker (Albers, Albers USA, Mercator, Equal Earth, Equirectangular), dot radius slider (0.5–5px), mesh stroke width slider (0.2–3px), mesh opacity slider (0.05–1.00), nation fill opacity slider (0–0.50), and toggles to independently show/hide the Voronoi mesh, store dots, and nation outline. Hovering over the chart shows a tooltip with the city and state for the nearest store. The chart should render approximately 65 store dots connected by a Voronoi mesh network, with a faint US nation outline beneath, all on an Albers projection.