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Twists

Twist system

The twist system is a list of twists, sorted in alphabetical order by name. It can be accessed during puzzle construction as puzzle.twists.

Twists can be added to the twist system using puzzle.twists:add().

Twist indexing

The twist system can be indexed by the name or index of a twist.

Examples of twist indexing
-- Gets the twist with the name "L"
puzzle.twists.L

-- Gets the twist with the name "L'"
puzzle.twists["L'"]

-- Gets the first twist alphabetically
puzzle.twists[1]

Fields

The twist system has no fields.

Methods

puzzle.twists:add()

puzzle.twists:add() adds a twist to the twist system, along with (optionally) its inverses and multipliers. It takes three arguments: an axis whose layers bound the pieces affected by the twist, a transform to apply to pieces, and an optional table with extra data about the twist.

The table has the following keys:

Key Type Default value Description
multipliers boolean See note 1 whether to generate double/triple/etc. twists1
inverse boolean See note 1 whether to generate inverse twist2
prefix string axis name prefix before twist name
name string nil name for twist
suffix string nil suffix after twist name
inv_name string nil name for inverse twist
inv_suffix string See note 2 suffix after inverse twist name
name_fn function nil function from integer to string
qtm integer 1 value of the twist in the quantum turn metric
gizmo_pole_distance number nil distance of the gizmo pole facet

Notes

  1. true in 3D; false in 4D+
  2. If inv_name is nil or unspecified, then inv_suffix defaults to "'" (a string containing the ' character); if inv_name is non-nil, then inv_suffix defaults to an empty string

If name_fn is non-nil, then name and inv_name must both be nil.

name_fn takes a single argument: an integer corresponding to the twist multiplier (e.g., 1 for R, -1 for R', 2 for R2, -2 for R2', etc.). It returns a string, which is used in place of both name and inv_name.

Each twist is assigned a name by concatenating <prefix> .. <name> .. <suffix> .. <multiplier>, where: - <prefix> is prefix - <name> is either the output of name_fn (if name_fn is non-nil) or name/inv_name (selected using the sign of the multiplier). - <suffix> is suffix/inv_suffix (selected using the sign of the multiplier) - <multiplier> is tostring(multiplier)

puzzle.twists:rename()

puzzle.twists:rename() renames multiple twists at once. See :rename()

Operations

  • #puzzle.twists returns the number of twists that have been defined
  • type(puzzle.twists) returns 'twistsystem'
  • tostring(puzzle.twists)
  • ipairs(puzzle.twists)

Twist

A twist is a twist that can be applied to the puzzle.

Fields

  • .name is the string name of the color
  • .axis is the axis of the twist, which is typically fixed by its transform
  • .transform is the transform applied to pieces during the twist

Some fields can be written to:

  • Writing a new string to .name renames the twist

All other fields are read-only.

Methods

Axes have no methods.

Operations

  • twist == twist
  • twist ~= twist
  • twist * twist composes two twists, if there is a twist corresponding to their composition
  • twist ^ number returns the twist composed with itself some number of times (which may be negative), if there is such a twist
  • type(twist) returns 'twist'
  • tostring(twist)

Layer system

A layer system is an ordered list of the layers on an axis. It can be accessed during puzzle construction as axis.layers.

Layer system indexing

Indexing a layer system by a layer index returns a table with the following keys:

  • bottom is the hyperplane bounding the bottom of the layer
  • top is the hyperplane bounding the top of the layer, or nil if there is none

Fields

A layer system has no fields.

Methods

axis.layers:add()

axis.layers:add() adds a new layer to the layer system. It takes two arguments: a hyperplane bounding the bottom of the layer, and an optional hyperplane bounding the top of the layer. If the second hyperplane is omitted, then the layer is unbounded.

Operations

  • #axis.layers returns the number of layers in the layer system
  • type(axis.layers) returns 'layersystem'
  • ipairs(axis.layers)

Layer

A layer is a region along a twist axis where pieces may be affected by a twist. It is bounded below by a hyperplane, and optionally bounded above by another hyperplane.

  1. E.g., R2 from R ↩

  2. E.g., R' from R ↩