Partitions · Convex Hulls · Intersection

Number of points

Number of parts (k)

Plot range 4

Points

Drag a point to recompute everything

Tverberg partition graph

nodes = intersecting partitions

Convex hulls of a selected partition

Partition #

The selector only lists partitions whose convex hulls have a non-empty intersection. Edge exists if two partitions differ by moving exactly one element from one part to another (k fixed).

Graph Statistics

Plot 2 analysis

Click a button to display graph statistics.

Visualization of Tverberg Partition Graphs

What this tool shows:
Given a set of points (first plot), this visualization generates the graph of Tverberg partitions, as described in the paper "Tverberg Partition Graphs" (https://epubs.siam.org/doi/10.1137/23M1610938).

How it works:
1. First plot: Shows the initial set of points. Drag points to modify configurations.
2. Second plot: Displays the Tverberg partition graph.
3. Third plot: Shows convex hulls of each part for a selected Tverberg partition.

Tverberg partition:
A partition of points into k parts such that the convex hulls of all parts have non-empty intersection.

Controls:
• Number of points: Total points to partition (n ≤ 9)
• Number of parts (k): Partition size (k ≤ 5)
• RANGE: Coordinate bounds (±range)
• Partition #: Select specific Tverberg partition to visualize

Interaction:
• Drag points in first plot to update all partitions
• Drag nodes in graph view to rearrange layout
• Use selector to view different partitions' convex hulls

Technical details:
• Self-contained HTML file (no server needed)
• Intersection test uses Helly-based check + candidate points
• Edge = partitions differ by moving exactly one element between parts
• PDF export: 4 hull plots per page
• Text export: Coordinates of all Tverberg partitions