Interactive application Experimental
Interactive Video
Overview · selected highlights

Fortune’s Loom

Follow Fortune and Apollonius geometry through the events, search structures and arithmetic decisions that create the diagram. Degenerate cases and precision policies remain visible; the 3D sweep extension is explicitly an unfinished exploration.

Events → beachline → diagram
EventStructureEdge
Brochure →Open project ↗
  1. y↓

    Move the sweep

    Site and circle events change the geometric frontier.

  2. ⌘

    Maintain the state

    Inspect beachline trees, queue contents and invalidated events.

  3. ∿

    Construct the edges

    Follow moving breakpoints into the evolving diagram.

  4. Δ

    Check the evidence

    Compare raw construction, reference edges and supported precision policies.

The browser port includes a subset of the desktop studies and arithmetic representations; some difficult cases behave differently.

Current C++ browser workbench: a recorded sweep event connects the geometric beachline to its tree and timeline.
Current C++ browser workbench: a recorded sweep event connects the geometric beachline to its tree and timeline.
The beachline, circle events, final edges and underlying tree evolve together during the native sweep.
Earlier Crystal prototype: an arc disappears at its predicted circle event.
Earlier Crystal prototype: an arc disappears at its predicted circle event.
Earlier Crystal prototype: beachline arcs and their tree nodes.
Earlier Crystal prototype: beachline arcs and their tree nodes.