Specify direction of an arc in a curve containing many segments

label = "Fillet"

about = [[
Create fillets in a polyline or polygon
]]




function get_polysegments(obj)

   if obj:type() ~= "path" then return end

   local shape = obj:shape()
   if (#shape ~= 1 or shape[1].type ~= "curve" or #shape[1] < 2) then return end
   local m = obj:matrix()
   local v
   local seg = {}

   
   -- get all the line segments
   for i=1,#shape[1] do
      v = shape[1][i]
      if v.type ~= "segment" then return end
      seg[#seg+1] = ipe.Segment(m*v[1],m*v[2])
   end

   local closed = shape[1].closed

   if closed then
      local a,b = seg[#seg]:endpoints()
      local c,d = seg[1]:endpoints()
      seg[#seg+1] = ipe.Segment(b,c)
      seg[#seg+1] = seg[1]
   end
   
   return seg, closed
end



function run(model)

   local p = model:page()
   local prim = p:primarySelection()
   if not prim then model.ui:explain("no selection") return end
   local obj = p[prim]


   local seg, closed = get_polysegments(obj)

   if seg==nil then
      model:warning("Primary selection is not a polyline or polygon")
   end


   local str = model:getString("Enter fillet radius in pts")
   if not str or str:match("^%s*$") then return end
   local r = tonumber(str)

   local s11,s12,s21,s22
   local n1,n2,p11,p12,p21,p22
   local c
   local x1, x2
   local shape={type="curve", closed=closed}

   for i=1,#seg-1 do
      -- normals of line segments with length equal to r
      n1 = r*seg[i]:line():normal()
      n2 = r*seg[i+1]:line():normal()

      -- endpoints of line segments
      p11,p12 = seg[i]:endpoints()
      p21,p22 = seg[i+1]:endpoints()

      -- line segments translated by +/- the respective normals
      s11 = ipe.Segment(p11+n1,p12+n1)
      s12 = ipe.Segment(p11-n1,p12-n1)
      s21 = ipe.Segment(p21+n2,p22+n2)
      s22 = ipe.Segment(p21-n2,p22-n2)


      -- find center of the joing arc which is equal to the intersection
      -- of two of the translated line segments
      if s11:intersects(s21) then
	 c = s11:intersects(s21)
      elseif s11:intersects(s22) then
	 c = s11:intersects(s22)
      elseif s12:intersects(s21) then
	 c = s12:intersects(s21)
      elseif s12:intersects(s22) then
	 c = s12:intersects(s22)
      end

      -- start and end point of the arc
      x1 = seg[i]:project(c)
      x2 = seg[i+1]:project(c)


      -- append segments and arcs to form filleted shape
      if i>1 then
	 shape[#shape+1] = {type="segment", shape[#shape][2],x1}       
      elseif i==1 and closed==false then
	 shape[#shape+1] = {type="segment", p11,x1}
      end
      shape[#shape+1] = {type="arc", x1,x2,arc=ipe.Arc(ipe.Matrix(r, 0, 0, r, c.x, c.y),x1,x2)}
      if i==#seg-1 and closed==false then
	 shape[#shape+1] = {type="segment", x2,p22}
      end

   end

   
   local path = ipe.Path(model.attributes, { shape } )
   model:creation("create excircles of triangles", path)



end


----------------------------------------------------------------------
shortcuts.ipelet_1_fillet = "Shift+f"

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