Ipelet that applies point-line duality

duality.lua

label = "Duality"

about = [[
Applies point-line duality to line segments and marks.
]]

function dualize(model,num)
  local t = { label = label,
        pno = model.pno,
        vno = model.vno,
        original = model:page():clone(),
        undo = _G.revertOriginal
      }

  -- scale factor for the slope value of lines
  -- in other words, if I put a mark at x-coordinate 1,
  -- then it'll get dualized to a line with slope slopeScale
  local slopeScale = 1.0 / 32

  t.redo = function (t, doc)
    -- get the current page
    local p = doc[t.pno]

    layer = p:addLayer(nil)
    p:setActive(1, layer)
    p:setVisible(1, layer, true)

    -- make sure to iterate over the copy
    for i,obj,sel,layer in t.original:objects() do
      if sel and obj:type() == "path" then
        shape = obj:shape()
        if #shape == 1 then
          curve = shape[1]
          if curve.type == 'curve' and #curve == 1 then
            segment = curve[1]
            if segment.type == 'segment' then
              startPoint = segment[1]
              endPoint = segment[2]
              dx = endPoint.x - startPoint.x
              dy = endPoint.y - startPoint.y
              if dx == 0 then
                model:warning('Vertical line detected; ignoring it')
              else
                a = dy / dx
                b = startPoint.y - a * startPoint.x

                -- create a mark at (a, -b)
                mark = ipe.Reference(model.attributes, 'mark/disk(sx)', ipe.Vector(a / slopeScale, -b))
                p:insert(nil, mark, 0, layer)
              end
            end
          end
        end
      end
      if sel and obj:type() == "reference" then
        local a = slopeScale * obj:position().x
        local b = -obj:position().y
        -- create a line
        local startPoint = ipe.Vector(-250, a * -250 + b)
        local endPoint = ipe.Vector(250, a * 250 + b)
        local segment = { type = 'curve', closed = false }
        segment[1] = { type = 'segment', startPoint, endPoint }
        mark = ipe.Path(model.attributes, {segment})
        p:insert(nil, mark, 0, layer)
      end
    end
  end

  model:register(t)
end

----------------------------------------------------------------------

methods = {
   { label = "Dualize", run=dualize }
}