begin
public system

use math: pi, isnan, isinf

color_table = [
   "002080",
   "006000",
   "800060"
]

function fstr(x)
   str(x,"f",2)
end

function hline(s,y)
   s.a.push('<line x1="0" y1="{0}" x2="10" y2="{0}" stroke="#848480" stroke-width="0.02"/>\n' %
      [y].map(fstr))
end

function vline(s,x)
   s.a.push('<line x1="{0}" y1="0" x2="{0}" y2="10" stroke="#848480" stroke-width="0.02"/>\n' %
      [x].map(fstr))
end

function path_push(s,color,points)
   if len(points)!=0
      s.a.push('<polyline fill="none" stroke="#{}" stroke-width="0.06"\npoints="{}"/>\n' % [
         color, points.join(" ")
      ])
      points.clear()
   end
end

function path(s,a,color)
   mx = 5/s.wx; px = s.px
   my = 5/s.wy; py = s.py
   points = []
   for [x,y] in a
      if isnan(y) or isinf(y)
         path_push(s,color,points)
      else
         vx = 5+(x-px)*mx
         vy = 5-(y-py)*my
         if -1000<vy and vy<1000
            points.push([fstr(vx),fstr(vy)].join(","))
         else
            path_push(s,color,points)
         end
      end
   end
   path_push(s,color,points)
end

function vpath(s,a,color)
   mx = 5/s.wx; px = s.px
   my = 5/s.wy; py = s.py
   points = []
   for [x,y] in a
      if isnan(x) or isinf(x) or isnan(y) or isinf(y)
         path_push(s,color,points)
      else
         vx = 5+(x-px)*mx
         vy = 5-(y-py)*my
         if abs(x)<1000 and abs(y)<1000
            points.push([fstr(vx),fstr(vy)].join(","))
         else
            path_push(s,color,points)
         end
      end
   end
   path_push(s,color,points)
end

function getfx(s)
   mx = 5/s.wx; px = s.px
   return |x| fstr(5+(x-px)*mx)
end

function getfy(s)
   my = 5/s.wy; py = s.py
   return |y| fstr(5-(y-py)*my)
end

function scatter_circle(s,fx,fy,x,y,color)
   s.a.push('<circle cx="{}" cy="{}" r="0.12" fill="#{}"/>\n' % [fx(x),fy(y),color])
end

head = """\
<?xml version="1.0" encoding="UTF-8"?>
<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="{0}" height="{1}">
{4}<style><![CDATA[
text{{font-family: "DejaVu Sans", sans-serif;}}
]]></style>
<rect x="0" y="0" width="100%" height="100%" fill="#ffffff"/>

<g transform="scale({2},{3})">
"""

foot = """\
</g>
</svg>\
"""

defs = """\
<defs> 
  <pattern id="grid" x="0" y="0" width="1" height="1" patternUnits="userSpaceOnUse">
    <rect x="0" y="0" width="10" height="10" stroke="#dadad0" stroke-width="0.08" fill="none"/>
  </pattern>
</defs>
"""

function to_s(x)
   x = 0.01*int(100*x)
   if x == int(x)
      x = int(x)
   end
   if x<0
      return "\x{2212}{}"%[abs(x)]
   else
      return str(x)
   end
end

function text(s,x,y,txt)
   s.a.push('<text x="{}" y="{}" font-size="0.5" text-anchor="end">{}</text>\n' % [fstr(x),fstr(y),txt])
end

function scale(s)
   wx = s.wx; px = s.px
   wy = s.wy; py = s.py

   x_adjust = 5.2
   y_adjust = 5.5
   for x in 1..4
      text(s,x_adjust+x,y_adjust,to_s(px+x*wx/5))
   end
   for x in -4..-1
      text(s,x_adjust+x,y_adjust,to_s(px+x*wx/5))
   end

   x_adjust = 4.86
   y_adjust = 5.1
   for y in 1..4
      text(s,x_adjust,y_adjust-y,to_s(py+y*wy/5))
   end
   for y in -4..-1
      text(s,x_adjust,y_adjust-y,to_s(py+y*wy/5))
   end
end

function axes(s)
   hline(s,5)
   vline(s,5)
   scale(s)
end

function grid(s)
   s.defs = defs
   s.a.push('<rect fill="url(#grid)" stroke="#dadad0" stroke-width="0.1" x="0" y="0" width="10" height="10"/>\n')
end

Graphics = table{
   function string
      "system"
   end,

   function rect(x,y,h,w)
      self.a.push('<rect x="{}" y="{}" width="{}" height="{}" stroke-width="0.1"/>\n' %
         [x,y,h,w].map(fstr))
   end,

   function line(x1,y1,x2,y2)
      mx = 5/self.wx
      my = 5/self.wy
      self.a.push('<line x1="{}" y1="{}" x2="{}" y2="{}" stroke="black" stroke-width="0.1"/>\n' %
         [5+mx*x1,5-my*y1,5+mx*x2,5-my*y2].map(fstr))
   end,

   function plot(f)
      px = self.px
      py = self.py
      a = list(px-self.wx..px+self.wx: 1/self.n)
      if f: List
         for fk in f
            color = self.color_it()
            path(self,a.map(|x| [x,fk(x)]),color)
         end
      else
         color = self.color_it()
         path(self,a.map(|x| [x,f(x)]),color)
      end
   end,

   function vplot(f,argm={})
      {t0 = self.t0, t1 = self.t1, n = self.n} = argm
      a = list(t0..t1: 1/n)
      color = self.color_it()
      vpath(self,a.map(f),color)
   end,
   
   function scatter(a,m = null)
      fx = getfx(self)
      fy = getfy(self)
      if m is null
         color = "8080a0"
      else
         {color = "8080a0"} = m
      end
      for x,y in a
         scatter_circle(self,fx,fy,x,y,color)
      end
   end,

   function flush
      self.a.join("",head % [self.w,self.h,self.w//10,self.h//10,self.defs],foot)
   end
}

function system(d={})
   {w=400, h=400, wx=5, wy=5, px=0, py=0, n=10, t0=0, t1=2*pi} = d
   s = table Graphics{
      a=[], w=w, h=h,
      wx=wx, wy=wy, px=px, py=py,
      defs="", n=n, t0=t0, t1=t1,
      color_it = cycle(color_table)
   }
   grid(s)
   axes(s)
   return s
end

end