class Vec3
  def initialize(x = 0, y = 0, z = 0)
    @x = x.to_f
    @y = y.to_f
    @z = z.to_f
  end

  attr_reader :x, :y, :z

  def +(oth)
    self.class.new(@x + oth.x, @y + oth.y, @z + oth.z)
  end

  def -@
    self.class.new(-@x, -@y, -@z)
  end

  def -(oth)
    self + -oth
  end

  def *(oth)
    if oth.is_a?(Vec3)
      self.class.new(@x * oth.x, @y * oth.y, @z * oth.z)
    else
      self.class.new(@x * oth, @y * oth, @z * oth)
    end
  end

  def /(oth)
    self * (1.0 / oth)
  end

  def dot(oth)
    v = self * oth
    v.x + v.y + v.z
  end

  def cross(oth)
    self.class.new(
      @y * oth.z - @z * oth.y,
      @z * oth.x - @x * oth.z,
      @x * oth.y - @y * oth.x
    )
  end

  def mag_sqr
    @x ** 2 + @y ** 2 + @z ** 2
  end

  def mag
    mag_sqr ** 0.5
  end

  def unit
    self / mag
  end

  def to_s
    "{#{@x}, #{@y}, #{@z}}"
  end
end

class Point < Vec3; end

class Colour < Vec3
  def r; @x; end
  def g; @y; end
  def b; @z; end

  def to_ppm
    "%3d %3d %3d" % [(r * 255.999).to_i, (g * 255.999).to_i, (b * 255.999).to_i]
  end
end