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Continuous Assembly Patterns

CAPs

A prop-spinning path assembled from pieces of simpler patterns, looped forever.

Extension + Antispin = one closed loop
Start with the path

What is a CAP?

A CAP is a cyclic path assembled in time from two or more elementary patterns, each used one or more times. One prop traces every fragment and returns to its starting point.

Damien coined the term and published the construction while posting as Zaltymbunk and French_Saltimbanque on Home of Poi in 2009.

How this CAP is built

  • Extension: the hand carries the prop through half a cycle while the prop stays pointed away from center.
  • Antispin: the hand returns while the prop rotates against the hand path, shaping the inner petals.
  • The join: the hand and prop tip meet at the shared endpoint.
  • The cycle: the final position and orientation match the start, so the curve can repeat.
The curve atlas

From elementary curves to assembled CAPs

Damien called the elementary families rosettes and cycloids. In standard curve language they belong to the centered trochoid family; his cycloid cases are the cusp-forming epicycloids or hypocycloids. The clean plots below are reconstructed from his published parameters.

The animated reference illustrations Damien linked were by Robert Ferréol, Encyclopédie des formes mathématiques remarquables. Those archival GIFs are credited here and not republished.

Elementary patterns

One equation, one uninterrupted curve

Rosettes share equal radii. Cycloids tune the radii until cusps appear.

Assembled CAPs

Fragments joined into a cycle

These are the three composite plots Damien published in the 2009 framework.

Focused construction

The Yuta CAP (half cycle)

An extension half-cycle joined to an antispin half-cycle.

1 0 ; 1 3/4 ; 1/2 & -1 4 ; 1 3/4 ; 1/2
Choose what to reveal
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Damien's original 2009 plot The Yuta CAP (half cycle), preserved from ImagesHotel.org
Damien's original 2009 plot of the Yuta CAP built from two half-cycles
The archived image is shown as provenance. The live construction above is rebuilt from the published parameters.
Original notation 1 0 ; 1 3/4 ; 1/2 & -1 4 ; 1 3/4 ; 1/2

An extension half-cycle joined to an antispin half-cycle.

Origin chronology

Named on a forum, built at a burn

  1. Ideas at Burning Man

    Alien Jon described the OMCC group pulling apart complex poi patterns with Noel, Greg, Jordan, and Zan. Damien joined them with his own CAP explorations.

  2. The name and the model

    In a Home of Poi thread about Yuta's spinning, Alien Jon wrote, “I got the term from Damien.” Damien then set out the O/M/E model, notation, feasibility rules, and worked CAP examples.

  3. Lessons spread the idea

    Drex documented the definition and C-CAP technique. Nick Woolsey taught Capped Antispin Patterns. Drex's eight-step lesson credited Charlie's 9-Square Theory.

  4. The sources still matter

    The forum discussion survives, but old playlists and image hosts have disappeared. This exhibit keeps the mathematics readable while sending visitors back to the remaining originals.

The people

Credit where it started

Term, notation, and mathematics

Damien

Posting as Zaltymbunk and French_Saltimbanque

Coined Continuous Assembly Patterns and published the elementary curves, O/M/E notation, rosettes, cycloids, wrap fractions, feasibility rules, and composite examples shown on this page.

Alien Jon

Carried Damien's term into wider use and framed CAPs as a way to think about movement rather than the name of one move.

Nick Woolsey PlayPoi

Taught CAPs to a broad learner audience in 2016 and used the expansion “Capped Antispin Patterns.”

PlayPoi lesson

Charlie

Developed 9-Square Theory and the eight-step CAP approach credited in Drex's double staff lesson.

Eight-step lesson

Drex DrexFactor

Documented CAPs across the Tech Poi Blog, tutorials, and the preserved copy of Damien's mathematical framework.

C-CAP lesson

Also in the room at Burning Man 2007: Noel, Greg, Jordan, and Zan of the OMCC crew.

Two ways to close a pattern

CAPs and LOOPs start from different units

CAPs

Compose trajectories

CAPs serially assemble elementary paths for one prop. Each hand's trajectory is defined independently, then two-hand movement can be overlaid.

LOOPs

Compose snapshots

Each TKA letter records both hands at one step. LOOP transformations combine those letters into speakable words that return to their start.

Both answer the desire for patterns that can repeat forever. They are parallel concepts, not parent and child. Neither contains the other.

See it in motion

CAPs on video, 2009 to now

Tech Poi Blog #213: What is a CAP? by DrexFactor Poi
Tech Poi Blog #213: What is a CAP? DrexFactor Poi · 2011 A direct explanation of the term and the debate around it.
Basic Poi Dancing Tutorial: C-CAPs by DrexFactor Poi
Basic Poi Dancing Tutorial: C-CAPs DrexFactor Poi · 2012 A lesson on the extension and antispin pattern commonly called a C-CAP.
Poi Flowers: Learning CAPs (Capped Antispin Patterns) by Nick Woolsey · PlayPoi
Poi Flowers: Learning CAPs (Capped Antispin Patterns) Nick Woolsey · PlayPoi · 2016 The PlayPoi lesson that uses the expansion Capped Antispin Patterns.
Charlie's 9-Square Theory for Poi #3 by Charlie
Charlie's 9-Square Theory for Poi #3 Charlie · ~2015 Part three of Charlie's 9-Square Theory video series.
How to do 8-Step CAPs for Poi: 1-minute tutorial by DrexFactor Poi
How to do 8-Step CAPs for Poi: 1-minute tutorial DrexFactor Poi · 2017 An eight-step CAP taught in one minute.
Poi CAPs Tutorial: Basic C-CAPs by DrexFactor Poi
Poi CAPs Tutorial: Basic C-CAPs DrexFactor Poi · 2020 A later lesson on the classic C-CAP pattern.

Charlie's series continues in the full 9-Square Theory playlist. Alien Jon's pattern playlist from the origin thread no longer resolves.

Sources

Read the originals

  1. Origin discussion “What are CAP's?”

    Home of Poi, ca. 2009. Coinage attribution, the OMCC account, Damien's framework, and the community debate.

  2. Mathematical framework The Math of CAPs

    Damien's model and notation, preserved by DrexFactor.

  3. Curve references Encyclopédie des formes mathématiques remarquables

    Robert Ferréol's mathematical curve encyclopedia supplied the animated illustrations Damien linked.

  4. C-CAP lesson Basic Poi Dancing Tutorial: C-CAPs

    DrexFactor, 2012.

  5. Learner lesson Learning CAPs (Capped Antispin Patterns)

    Nick Woolsey, PlayPoi, 2016.

  6. Print reference Encyclo-poi-dia Vol. 2

    A print-era CAP chapter referenced in the origin thread.

See how TKA turns complete two-hand steps into cycles through composable transformations.

Explore the LOOP algebra