Class: StraightSkeleton::Nodes

Inherits:
Object
  • Object
show all
Defined in:
lib/nswtopo/geometry/straight_skeleton/nodes.rb

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(data) ⇒ Nodes

Returns a new instance of Nodes.



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 10

def initialize(data)
  @active, @indices = Set[], Hash.new.compare_by_identity
  data.to_d.map do |points|
    next points unless points.length > 2
    points.each.with_object [] do |point, points|
      points << point unless points.last == point
    end
  end.map.with_index do |(*points, point), index|
    points.first == point ? [points, :ring, (index unless points.hole?)] : [points << point, :segments, nil]
  end.each do |points, pair, index|
    normals = points.send(pair).map(&:diff).map(&:normalised).map(&:perp)
    points.map do |point|
      Vertex.new self, point
    end.each do |node|
      @active << node
    end.send(pair).zip(normals).each do |edge, normal|
      Nodes.stitch normal, *edge
      @indices[normal] = index if index
    end
  end
end

Instance Attribute Details

#direction ⇒ Object (readonly)

Returns the value of attribute direction.



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 145

def direction
  @direction
end

Class Method Details

.solve(n0, n1, n2, x0, x1, x2) ⇒ Object

################################# solve for vector p and scalar t:

n0.p - t = x0
n1.p - t = x1
n2.p - t = x2

#################################



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 39

def self.solve(n0, n1, n2, x0, x1, x2)
  det = n2.cross(n1) + n1.cross(n0) + n0.cross(n2)
  return if det.zero?
  travel = (x0 * n1.cross(n2) + x1 * n2.cross(n0) + x2 * n0.cross(n1)) / det
  point = [n1.minus(n2).perp.times(x0), n2.minus(n0).perp.times(x1), n0.minus(n1).perp.times(x2)].inject(&:plus) / det
  [point, travel]
end

.solve_asym(n0, n1, n2, x0, x1, x2) ⇒ Object

################################# solve for vector p and scalar t:

n0.p - t = x0
n1.p - t = x1
n2 x p   = x2

#################################



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 54

def self.solve_asym(n0, n1, n2, x0, x1, x2)
  det = n0.minus(n1).dot(n2)
  return if det.zero?
  travel = (x0 * n1.dot(n2) - x1 * n2.dot(n0) + x2 * n0.cross(n1)) / det
  point = (n2.times(x0 - x1).plus n0.minus(n1).perp.times(x2)) / det
  [point, travel]
end

.stitch(normal, *edge) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 5

def self.stitch(normal, *edge)
  edge[1].neighbours[0], edge[0].neighbours[1] = edge
  edge[1].normals[0] = edge[0].normals[1] = normal
end

Instance Method Details

#collapse(edge) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 62

def collapse(edge)
  (n00, n01), (n10, n11) = edge.map(&:normals)
  p0, p1 = edge.map(&:point)
  t0, t1 = edge.map(&:travel)
  return if p0.equal? p1
  good = [n00 && !n00.cross(n01).zero?, n11 && !n11.cross(n10).zero?]
  point, travel = case
  when good.all? then Nodes::solve(n00, n01, n11, n00.dot(p0) - t0, n01.dot(p1) - t1, n11.dot(p1) - t1)
  when good[0] then Nodes::solve_asym(n00, n01, n10, n00.dot(p0) - t0, n01.dot(p0) - t0, n10.cross(p1))
  when good[1] then Nodes::solve_asym(n11, n10, n10, n11.dot(p1) - t1, n10.dot(p1) - t1, n01.cross(p0))
  end || return
  return if travel * direction < @travel * direction
  return if @limit && travel.abs > @limit.abs
  @candidates << Collapse.new(self, point, travel, edge)
end

#include?(node) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 104

def include?(node)
  @active.include? node
end

#index(node) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 290

def index(node)
  @indices.values_at(*node.normals).find(&:itself)
end

#insert(node) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 108

def insert(node)
  @active << node
  @track[node.normals[1]] << node if node.normals[1]
  2.times.inject [node] do |nodes|
    [nodes.first.prev, *nodes, nodes.last.next].compact
  end.segments.uniq.each do |edge|
    collapse edge
  end
  split node if node.splits?
end

#nodeset ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 125

def nodeset
  [].tap do |result|
    pending, processed = @active.dup, Set[]
    while pending.any?
      nodes = pending.take 1
      while node = nodes.last.next and !processed.include?(node)
        nodes.push node
        processed << node
      end
      while node = nodes.first.prev and !processed.include?(node)
        nodes.unshift node
        processed << node
      end
      pending.subtract nodes
      nodes << nodes.first if nodes.first == nodes.last.next
      result << nodes unless nodes.one?
    end
  end
end

#progress(limit: nil, rounding_angle: DEFAULT_ROUNDING_ANGLE, cutoff_angle: nil, interval: nil, splits: true, &block) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 147

def progress(limit: nil, rounding_angle: DEFAULT_ROUNDING_ANGLE, cutoff_angle: nil, interval: nil, splits: true, &block)
  return self if limit && limit.zero?

  nodeset.tap do
    @active.clear
    @indices = nil
  end.map do |*nodes, node|
    nodes.first == node ? [nodes, :ring] : [nodes << node, :segments]
  end.each.with_index do |(nodes, pair), index|
    normals = nodes.send(pair).map do |edge|
      edge[0].normals[1]
    end
    nodes.map do |node|
      Vertex.new self, node.project(@limit)
    end.each do |node|
      @active << node
    end.send(pair).zip(normals).each do |edge, normal|
      Nodes.stitch normal, *edge
    end
  end if @limit

  @candidates, @travel, @limit, @direction = AVLTree.new, 0, limit && limit.to_d, limit ? limit <=> 0 : 1

  rounding_angle *= Math::PI / 180
  cutoff_angle *= Math::PI / 180 if cutoff_angle

  @track = Hash.new do |hash, normal|
    hash[normal] = Set[]
  end.compare_by_identity

  @active.group_by(&:point).reject do |point, nodes|
    case nodes.length
    when 1 then true
    when 2
      nodes[0].next&.point == nodes[1].prev&.point &&
      nodes[1].next&.point == nodes[0].prev&.point
    else false
    end
  end.each do |point, nodes|
    @active.subtract nodes
    nodes.each.with_object [] do |node, events|
      events << [:incoming, node.prev] if node.prev
      events << [:outgoing, node.next] if node.next
    end.sort_by do |event, node|
      case event
      when :incoming then [-@direction * node.normals[1].angle,        1]
      when :outgoing then [-@direction * node.normals[0].negate.angle, 0]
      end
    end.ring.map(&:transpose).each do |events, neighbours|
      node = Vertex.new self, point
      case events
      when [:outgoing, :incoming] then next
      when [:outgoing, :outgoing]
        Nodes.stitch neighbours[1].normals[0], node, neighbours[1]
      when [:incoming, :incoming]
        Nodes.stitch neighbours[0].normals[1], neighbours[0], node
      when [:incoming, :outgoing]
        Nodes.stitch neighbours[0].normals[1], neighbours[0], node
        Nodes.stitch neighbours[1].normals[0], node, neighbours[1]
      end
      @active << node
    end
  end

  @active.reject(&:terminal?).select do |node|
    direction * Math::atan2(node.normals.inject(&:cross), node.normals.inject(&:dot)) < -cutoff_angle
  end.each do |node|
    @active.delete node
    2.times.map do
      Vertex.new self, node.point
    end.each.with_index do |vertex, index|
      vertex.normals[index] = node.normals[index]
      vertex.neighbours[index] = node.neighbours[index]
      vertex.neighbours[index].neighbours[1-index] = vertex
      @active << vertex
    end
  end if cutoff_angle

  @active.reject(&:terminal?).select(&:reflex?).each do |node|
    angle = Math::atan2 node.normals.inject(&:cross).abs, node.normals.inject(&:dot)
    extras = (angle / rounding_angle).floor
    next unless extras > 0
    extra_normals = extras.times.map do |n|
      node.normals[0].rotate_by(angle * (n + 1) * -direction / (extras + 1))
    end.each do |normal|
      @indices[normal] = @indices[node.normals[0]] if @indices
    end
    extra_nodes = extras.times.map do
      Vertex.new self, node.point
    end.each do |extra_node|
      @active << extra_node
    end
    edges = [node.neighbours[0], node, *extra_nodes, node.neighbours[1]].segments
    normals = [node.normals[0], *extra_normals, node.normals[1]]
    edges.zip(normals).each do |edge, normal|
      Nodes.stitch normal, *edge
    end
  end

  @active.select(&:next).map do |node|
    [node, node.next]
  end.each do |edge|
    collapse edge
    @track[edge[0].normals[1]] << edge[0]
  end.map do |edge|
    [edge.map(&:point).transpose.map(&:minmax), edge]
  end.tap do |bounds_edges|
    @index = RTree.load bounds_edges
  end

  @active.select(&:splits?).each do |node|
    split node
  end if splits

  travel = 0
  while candidate = @candidates.pop
    next unless candidate.viable?
    @travel = candidate.travel
    while travel < @travel
      yield :interval, travel, readout(travel)
      travel += interval
    end if interval && block_given?
    candidate.replace! do |node, index = 0|
      @active.delete node
      yield :nodes, *[node, candidate].rotate(index).map(&:original) if block_given?
    end
  end

  self
end

#readout(travel = @limit) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 278

def readout(travel = @limit)
  nodeset.map do |nodes|
    nodes.map do |node|
      node.project(travel).to_f
    end
  end.map do |points|
    points.segments.reject do |segment|
      segment.inject(&:==)
    end.map(&:last).unshift(points.first)
  end.reject(&:one?)
end

#split(node) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 78

def split(node)
  bounds = node.project(@limit).zip(node.point).map do |centre, coord|
    [coord, centre - @limit, centre + @limit].minmax
  end if @limit
  @index.search(bounds).map do |edge|
    p0, p1, p2 = [*edge, node].map(&:point)
    t0, t1, t2 = [*edge, node].map(&:travel)
    (n00, n01), (n10, n11), (n20, n21) = [*edge, node].map(&:normals)
    next if p0 == p2 || p1 == p2
    next if node.terminal? and Split === node and node.source.normals[0].equal? n01
    next if node.terminal? and Split === node and node.source.normals[1].equal? n01
    next unless node.terminal? || [n20, n21].compact.inject(&:plus).dot(n01) < 0
    point, travel = case
    when n20 && n21 then Nodes::solve(n20, n21, n01, n20.dot(p2) - t2, n21.dot(p2) - t2, n01.dot(p0) - t0)
    when n20 then Nodes::solve_asym(n01, n20, n20, n01.dot(p0) - t0, n20.dot(p2) - t2, n20.cross(p2))
    when n21 then Nodes::solve_asym(n01, n21, n21, n01.dot(p0) - t0, n21.dot(p2) - t2, n21.cross(p2))
    end || next
    next if travel * @direction < node.travel
    next if @limit && travel.abs > @limit.abs
    next if point.minus(p0).dot(n01) * @direction < 0
    Split.new self, point, travel, node, edge[0]
  end.compact.each do |split|
    @candidates << split
  end
end

#track(normal) ⇒ Object 



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# File 'lib/nswtopo/geometry/straight_skeleton/nodes.rb', line 119

def track(normal)
  @track[normal].select(&:active?).map do |node|
    [node, node.next]
  end
end