Can you explain << operator?

[barracuda]

Hello, I am studying code of TIG from his extension TextureTools. His function for rotate of texture:uses << operator often:

def process(face=nil, angle=0.0)
  return nil unless face && face.is_a?(Sketchup::Face)
  return nil unless mat=face.material
  return nil unless mat.texture
  ###
  tw=Sketchup.create_texture_writer
  samples=[face.outer_loop.vertices[0].position]  ### 0,0 | Origin
  samples << samples[0].offset(face.normal.axes.x)### 1,0 | Offset Origin in X
  samples << samples[1].offset(face.normal.axes.y)### 1,1 | Offset X in Y
  samples << samples[0].offset(face.normal.axes.y)### 0,1 | Offset Origin in Y
  pts=[]### Array containing 3D points.
  uvs=[]### Array containing UV points.
  uvh=face.get_UVHelper(true, false, tw)
  samples.each{|pt|
    pts << pt                                      ### XYZ 3D coordinates 
    uvs << self.normalizeUVQ(uvh.get_front_UVQ(pt))### UVQ 2D coordinates
  }
  ###
  tr=Geom::Transformation.rotation(pts[0], face.normal, angle.degrees)
  tpts=[pts[0], uvs[0]]
  (1..3).each{|i|
    tpts << pts[i].transform(tr)
    tpts << uvs[i]
  }
  face.position_material(mat, tpts, true)
  @model.active_view.refresh
end

I would appreciate very much if you can explain step by step what is happening there from line #8 to #10 and from #13 to #18.

Also the part

  tpts=[pts[0], uvs[0]]
  (1..3).each{|i|
    tpts << pts[i].transform(tr)
    tpts << uvs[i]
  }

is mysterious.

There is also normalization function

def normalizeUVQ(uvq)
    uvq[0] /= uvq[2]
    uvq[1] /= uvq[2]
    uvq[2] = 1.0
    return uvq
end

It’s not clear to me what does this do and why it is needed in the code.

[jim_foltz]

<< is being used an on Array - it is the append operator. It is the same as:

array.push(value)

See: Class: Array (Ruby 2.2.4)

/= is a shortcut for division and assignment. for example:

 a /= b

is the same as

a = a / b

Similarly:

a = a + 1 

is the same as:

a += 1

[barracuda]

I know the rest of operators, but the append operator is new to me. Thank you.