function Drawing.convert_line(drawing, shape)
  -- Perhaps we should do a more sophisticated "simple linear regression"
  -- here:
  --   https://en.wikipedia.org/wiki/Linear_regression#Simple_and_multiple_linear_regression
  -- But this works well enough for close-to-linear strokes.
  assert(shape.mode == 'freehand')
  shape.mode = 'line'
  shape.p1 = insert_point(drawing.points, shape.points[1].x, shape.points[1].y)
  local n = #shape.points
  shape.p2 = insert_point(drawing.points, shape.points[n].x, shape.points[n].y)
end
-- turn a line either horizontal or vertical
function Drawing.convert_horvert(drawing, shape)
  if shape.mode == 'freehand' then
    Drawing.convert_line(shape)
  end
  assert(shape.mode == 'line')
  local p1 = drawing.points[shape.p1]
  local p2 = drawing.points[shape.p2]
  if math.abs(p1.x-p2.x) > math.abs(p1.y-p2.y) then
    p2.y = p1.y
  else
    p2.x = p1.x
  end
end
function Drawing.smoothen(shape)
  assert(shape.mode == 'freehand')
  for _=1,7 do
    for i=2,#shape.points-1 do
      local a = shape.points[i-1]
      local b = shape.points[i]
      local c = shape.points[i+1]
      b.x = (a.x + b.x + c.x)/3
      b.y = (a.y + b.y + c.y)/3
    end
  end
end