def star_points(point, options)
      x, y = point
      radius = options[:radius]
      y = y + radius * 0.05
      points = []
      points << [x,                 y + radius * 0.9]
      points << [x + 0.25 * radius, y + 0.2 * radius]
      points << [x + radius,        y + 0.2 * radius]
      points << [x + 0.4 * radius,  y - 0.2 * radius]
      points << [x + 0.7 * radius,  y - 1.0 * radius]
      points << [x,                 y - 0.5 * radius]
      points << [x - 0.7 * radius,  y - 1.0 * radius]
      points << [x - 0.4 * radius,  y - 0.2 * radius]
      points << [x - radius,        y + 0.2 * radius]
      points << [x - 0.25 * radius, y + 0.2 * radius]
      points
    end
def star_points(point, options)
      x, y = point
      radius = options[:radius]
      y = y + radius * 0.05
      points = []
      points << [x,                 y + radius * 0.9]
      points << [x + 0.25 * radius, y + 0.2 * radius]
      points << [x + radius,        y + 0.2 * radius]
      points << [x + 0.4 * radius,  y - 0.2 * radius]
      points << [x + 0.7 * radius,  y - 1.0 * radius]
      points << [x,                 y - 0.5 * radius]
      points << [x - 0.7 * radius,  y - 1.0 * radius]
      points << [x - 0.4 * radius,  y - 0.2 * radius]
      points << [x - radius,        y + 0.2 * radius]
      points << [x - 0.25 * radius, y + 0.2 * radius]
      points
    end
radius is the horizontal half-width of the star (the star is the hand-drawn type that looks more natural to the eye, so it does not fit perfectly into a circle)