Method: Geometry::Polygon#union

Defined in:
lib/geometry/polygon.rb

#union(other) ⇒ Polygon Also known as: +

Create a new Geometry::Polygon that’s the union of the receiver and a passed Geometry::Polygon

This is a simplified implementation of the alogrithm outlined in the
paper {http://gvu.gatech.edu/people/official/jarek/graphics/papers/04PolygonBooleansMargalit.pdf An algorithm for computing the union, intersection or difference of two polygons}.
In particular, this method assumes the receiver and passed {Polygon}s are "island" type and that the desired output is "regular", as those terms are described in the paper.

Parameters:

Returns:



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# File 'lib/geometry/polygon.rb', line 99

def union(other)
    # Table 1: Both polygons are islands and the operation is union, so both must have the same orientation
    # Reverse the other polygon if the orientations are different
    other = other.reverse if self.clockwise? != other.clockwise?

    # Receiver's vertex ring
    ringA = VertexRing.new
    self.vertices.each {|v| ringA.push v, (other <=> v)}

    # The other vertex ring
    ringB = VertexRing.new
    other.vertices.each {|v| ringB.push v, (self <=> v)}

    # Find intersections
    offsetA = 0
    edgesB = other.edges.dup
    self.edges.each_with_index do |a, indexA|
  offsetB = 0
  ringB.edges_with_index do |b, indexB|
      intersection = a.intersection(b)
      if intersection === true
    if (a.first == b.first) and (a.last == b.last)      # Equal edges
    elsif (a.first == b.last) and (a.last == b.first)   # Ignore equal but opposite edges
    else
        if a.vector.normalize == b.vector.normalize # Same direction?
      offsetA += 1 if ringA.insert_boundary(indexA + 1 + offsetA, b.first)
      offsetB += 1 if ringB.insert_boundary(indexB + 1 + offsetB, a.last)
        else    # Opposite direction
      offsetA += 1 if ringA.insert_boundary(indexA + 1 + offsetA, b.last)
      offsetB += 1 if ringB.insert_boundary(indexB + 1 + offsetB, a.first)
        end
    end
      elsif intersection.is_a?(Point)
    offsetA += 1 if ringA.insert_boundary(indexA + 1 + offsetA, intersection)
    offsetB += 1 if ringB.insert_boundary(indexB + 1 + offsetB, intersection)
      end
  end
    end

    # Table 2: Both polygons are islands and the operation is union, so select outside from both polygons
    edgeFragments = []
    [[ringA, other], [ringB, self]].each do |ring, other_polygon|
  ring.edges do |v1,v2|
      if (v1[:type] == -1) or (v2[:type] == -1)
    edgeFragments.push :first => v1[:vertex], :last => v2[:vertex]
      elsif (v1[:type] == 0) and (v2[:type] == 0)
    if (other_polygon <=> Point[(v1[:vertex] + v2[:vertex])/2]) <= 0
        edgeFragments.push :first => v1[:vertex], :last => v2[:vertex]
    end
      end
  end
    end

    # Delete any duplicated edges. Array#uniq doesn't do the right thing, so using inject instead.
    edgeFragments = edgeFragments.inject([]) {|result,h| result << h unless result.include?(h); result}

    # Delete any equal-and-opposite edges
    edgeFragments = edgeFragments.reject {|f| edgeFragments.find {|f2| (f[:first] == f2[:last]) and (f[:last] == f2[:first])} }

    # Construct the output polygons
    output = edgeFragments.reduce([Array.new]) do |output, fragment|
  next output if fragment.empty?
  polygon = output.last
  polygon.push fragment[:first], fragment[:last] if polygon.empty?
  while 1 do
      adjacent_fragment = edgeFragments.find {|f| fragment[:last] == f[:first]}
      break unless adjacent_fragment

      polygon.push adjacent_fragment[:first], adjacent_fragment[:last]
      fragment = adjacent_fragment.dup
      adjacent_fragment.clear

      break if polygon.first == polygon.last # closed?
  end
  output << Array.new
    end

    # If everything worked properly there should be only one output Polygon
    output.reject! {|a| a.empty?}
    output = Polygon.new *(output[0])

    # Table 4: Both input polygons are "island" type and the operation
    #  is union, so the output polygon's orientation should be the same
    #  as the input polygon's orientation
    (self.clockwise? != output.clockwise?) ? output.reverse : output
end