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Axes

Axis system

The axis system is an ordered list of twist axes. It can be accessed during puzzle construction as puzzle.axes.

Axes can be added to the axis system using puzzle.axes:add().

Axis indexing

The axis system can be indexed by the name or index of a axis, or by its vector.

Examples of axis indexing
-- Gets the axis with the name "L"
puzzle.axes.L

-- Gets the first axis in the list
puzzle.axes[1]

-- Gets the axis with the vector (1,0,0)
puzzle.axes[vec('x')]

Fields

The axis system has no fields.

Methods

puzzle.axes:add()

puzzle.axes:add() adds a twist axis to the axis system, optionally adding layers to it and slicing the puzzle on each layer boundary. It takes two arguments: a vector for the new twist axis, and an optional table containing additional arguments. The new axis is returned.

If the vector is an orbit of vectors instead of just a single one, then puzzle.axes:add() will add an axis for each vector, all with the same layers. If the orbit has names assigned, then the new axes created by the cut will be assigned those names. An orbit of the new axes is returned.

The table may contain two optional keys:

  • layers is an optional sequential table of distances from the origin at which to add layer boundaries
  • slice is an optional boolean which defaults to true

If the table contains a sequence, then that sequence is used in place of layers. In this case the slice key is still used as normal.

If layers is specified, then add_axes() will automatically add layers to each axis it creates.

If slice is true, then add_axes() will automatically slice all pieces at the layer boundaries specified by layers.

Examples using puzzle.axes:add()
local sym = cd'bc3'

-- Add cubic axes with no layers
puzzle.axes:add(sym:orbit(sym.oox.unit))

-- Add cubic axes with a single cut through the origin
puzzle.axes:add(sym:orbit(sym.oox.unit), {0})

-- Add cubic axes with 3x3x3-like cuts
puzzle.axes:add(sym:orbit(sym.oox.unit), {1/3})

puzzle.axes:autoname()

puzzle.axes:autoname() assigns alphabetic names to all twist axes. It takes no arguments.

puzzle.axes:rename()

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

puzzle.axes:swap()

puzzle.axes:swap() swaps two axes in the ordering. See :swap()

puzzle.axes:reorder()

puzzle.axes:reorder() changes the ordering of all axes. See :reorder()

Operations

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

Axis

An axis is a twist axis around which twists can be defined.

Fields

  • .name is the string name of the color
  • .index is the integer index of the color in the color system
  • .vector is the vector of the axis, which typically stays fixed during any of its twists
  • .layers is the layer system of the axis
  • .opposite is the axis with the opposite vector, or nil if there is none

Some fields can be written to:

  • Writing a new string to .name renames the axis
  • Writing to .index reorders the axis to that index, shifting the axes in between

All other fields are read-only.

Methods

Axes have no methods.

Operations

  • axis == axis
  • axis ~= axis
  • type(axis) returns 'axis'
  • tostring(axis)

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.