APOLLON

knot design through circle packing

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Draw a polygon. Apollon detects crossings, runs a circle-packing solver on the planar graph, then traces smooth orthogonal arcs through the packing to produce a balanced knot diagram. Assign over/under crossings and export the result as a 3D polyline.

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Views & modes

Mode	What you see
Graph view	The full circle packing — nodes, edges, interior face circles, and the exterior boundary circle. A structural map of the planar graph.
Display view	Smooth orthogonal-arc splines tracing only the knot path. Clean, publication-quality output.
Knot view	The knot with z-ordering: over-crossings in red, under-crossings in blue. Click crossings to toggle assignment.

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3D viewer

Export your knot as a JSON polyline. Open viewer/index.html to see it rendered as a Three.js tube with orbit controls, perspective/orthographic toggle, adjustable z-scale, and drag-and-drop support.

 
_{Conway knot  ·  Kinoshita–Terasaka knot}

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Controls

Enter   Begin packing — convert polygon to planar graph
A       Auto-converge circle packing
B / N   Big / small Möbius balance step
V       Full balance + rotation
S       Single step + balance
D       Toggle graph view / display view
1 / 2   Circular arc splines / Quadratic Bézier
K       Enter knot mode
E       Export knot to JSON
T       Capture screenshot
R       Reset

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Run

cargo run --release

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Created using Rust, Nannou and ThreeJS