Formation Choreography: Dancer Spacing & Symmetry

Formations

From

Dancers 12

Tempo 100 BPM

Transition length 8 beats

Live Readouts

Min. spacing—

Mirror symmetry—

Total travel dist.—

Transition0%

How it works

Each formation is a set of target points in the stage plane. Moving from formation A to formation B is a bipartite assignment problem: which dancer goes to which target point? A naive index-order mapping (dancer i → target i) often forces long, crossing paths. This sim instead offers a greedy nearest-neighbor assignment:

for each dancer i (in order):
  find the closest still-unclaimed target j
  assign dancer i → target j, mark j claimed

This is the same heuristic real drill-writing software uses to shorten and de-cross marching paths — it is not globally optimal (that needs the Hungarian algorithm, O(n³)) but it is fast and removes most of the obvious crossing.

Position during a transition follows an eased interpolation:

p(t) = lerp(A_i, B_mapping[i], ease(t))
ease(t) = t<0.5 ? 4t³ : 1-(-2t+2)³/2   (cubic ease-in-out)

The three readouts are computed every frame from the current interpolated positions:

Min. spacing — smallest pairwise distance between any two dancers; a real stage manager keeps this above a safety margin to avoid collisions.
Mirror symmetry — for each dancer at (x, z), how close a matching dancer sits to the mirrored point (−x, z); expressed as 0–100%.
Total travel distance — sum of every dancer's straight-line path length for the current A→B assignment; compare it with "Optimize paths" toggled on vs off.

The spiral formation uses the golden-angle phyllotaxis rule (r = c·√i, θ = i·137.5°) — the same packing rule sunflower seeds and pinecone scales follow, repurposed here as a dense, evenly-spaced stage arrangement.

Dancer (colored by start position) Stage grid

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