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Region

A region is a subset of a space bounded by hyperplanes. They are most commonly used to identify pieces.

Constructors

axis()

Calling an axis as a function returns a region. It can be called in any of several ways:

  • Single layer. Calling an axis with a single layer index constructs a region bounding that layer.
  • Two layers. Calling an axis with two layer indices constructs a region bounding that layer range.
  • Layer list. Calling an axis with a sequential table of layer indices constructs a region bounding the union of all of those layers.
  • Layer mask string. Calling an axis with a layer mask string constructs a region bounding the union of the layers specified by the string. If the string is a single asterisk * then all layers are included.
Examples using axis()
-- Add 2 axes, each with 5 layers.
self.axes:add(vec('x'), {1/2, 1/4, 0, -1/2, -1/4})
self.axes:add(vec('y'), {1/2, 1/4, 0, -1/2, -1/4})
self.axes:autoname()

local region1 = self.axes.A(1) -- first layer of axis A
local region2 = self.axes.B('*') -- all 3 layers of axis B
local region3 = self.axes.B(1, 3) -- layers 1 to 3 of axis B
local region4 = self.axes.A({1, 3, 5}) -- layers 1, 3, and 5 of axis A
local region5 = self.axes.A('1..-2') -- layers 1 to 4 of axis A

hyperplane.region

hyperplane.region returns the region bounded by a hyperplane, on the side its normal vector is pointing away from.

Examples of hyperplane.region
local region1 = plane('x').region -- X <= 1
local region2 = plane('x').flip.region -- X >= 1
local region3 = ~plane('x').region -- X >= 1

orbit:intersection()

orbit:intersection() returns the intersection of all regions in an orbit. Each element of the orbit must be a single region. Names are ignored.

Examples of orbit:intersection()
-- region inside a unit cube
local region1 = cd'bc3':orbit(plane('x').region):intersection()

orbit:union()

orbit:union() returns the union of all regions in an orbit. Each element of the orbit must be a single region. Names are ignored.

Examples of orbit:union()
-- region outside a unit cube
local region1 = cd'bc3':orbit(plane('x').flip.region):union()

Fields

Regions have no fields.

Methods

Regions have the following methods:

  • :contains(point) returns whether the region contains a point

Operations

Regions support the following operations:

  • region & region (intersection)
  • region | region (union)
  • region ~ region (symmetric difference)
  • ~region (complement)
  • type(region) returns 'region'
  • tostring(region)