#!/usr/bin/env python

import gtk, cairo
import math

class Values(object):
   pass

def key_press_event (win, event, val):
   if event.string in ['q', 'Q']:
      gtk.main_quit ()
   elif event.string in ['f', 'F']:
      val.full = not val.full
      if val.full:
         win.fullscreen ()
      else:
         win.unfullscreen ()
   elif event.string in ['z', 'Z']:
      val.zoom = (val.zoom + 1) % 3
      win.queue_draw ()
   elif event.string in ['+']:
      val.steps = min (val.steps * 2, 4096)
      win.queue_draw ()
   elif event.string in ['-']:
      val.steps = max (val.steps / 2, 2)
      win.queue_draw ()
   else:
      return False

   return True


def expose_event (win, event, val):
   w, h = win.get_size ()

   bez = [-0.8, 0.0, 0.6, 0.0, 0.8, 0.03, 0.8, 0.0]
   bez = [-0.8, -0.8, -0.7, -0.8, 0.7, 1.05, 0.7, 0.7]

   stroke_radius = 0.2

   cr = gtk.gdk.Drawable.cairo_create (win.window)
   cr.rectangle (*event.area)
   cr.clip ()

   cr.translate (w/2.0, h/2.0)
   cr.scale (min (w/2., h/2.), -min (w/2., h/2.))

   if val.zoom != 0:
      cr.scale (4, 4)

      if val.zoom == 1:
         cr.translate (-bez[0], -bez[1])
      else:
         cr.translate (-bez[6], -bez[7])

   pxl = cr.device_to_user_distance (1, 0)[0]

   # draw the black thick stroke
   cr.set_line_width (stroke_radius * 2)
   cr.move_to (*bez[0:2])
   cr.curve_to (*bez[2:8])
   cr.stroke ()

   cr.set_line_width (1 * pxl)

   for draw in [0, 1]:
      for t in xrange (val.steps + 1):
         dt = float (t) / val.steps

         # bezier curve
         x = bez[0] + 3*dt*(bez[2]-bez[0]) + 3*dt*dt*(bez[4]-2*bez[2]+bez[0]) + dt*dt*dt*(bez[6]-3*bez[4]+3*bez[2]-bez[0])
         y = bez[1] + 3*dt*(bez[3]-bez[1]) + 3*dt*dt*(bez[5]-2*bez[3]+bez[1]) + dt*dt*dt*(bez[7]-3*bez[5]+3*bez[3]-bez[1])

         # first derivative of bezier curve
         dx = 3*(bez[2]-bez[0]) + 6*dt*(bez[4]-2*bez[2]+bez[0]) + 3*dt*dt*(bez[6]-3*bez[4]+3*bez[2]-bez[0])
         dy = 3*(bez[3]-bez[1]) + 6*dt*(bez[5]-2*bez[3]+bez[1]) + 3*dt*dt*(bez[7]-3*bez[5]+3*bez[3]-bez[1])

         # second derivative of bezier curve
         ddx = 6*(bez[4]-2*bez[2]+bez[0]) + 6*dt*(bez[6]-3*bez[4]+3*bez[2]-bez[0])
         ddy = 6*(bez[5]-2*bez[3]+bez[1]) + 6*dt*(bez[7]-3*bez[5]+3*bez[3]-bez[1])

         # curvature = (dx**2 + dy**2)**1.5 / (dx*ddy - ddx*dy)

         # not exactly the curvature, but the factor necessary to calculate the
         # midpoint of the osculating circle

         curvnorm = (dx**2 + dy**2) / (dx*ddy - ddx*dy)

         l = (dx**2 + dy**2)**0.5

         # draw the blue dabs
         if draw == 0:
            cr.set_source_rgba (0.0, 0.0, 1.0, 1.0)
            cr.move_to (x - dy/l * stroke_radius, y + dx/l * stroke_radius)
            cr.line_to (x + dy/l * stroke_radius, y - dx/l * stroke_radius)
            cr.stroke ()

         # draw red dots at the centers of the osculating circles.
         else:
            cr.set_source_rgba (1.0, 0.0, 0.0, 1.0)
            cr.arc (x - dy * curvnorm, y + dx * curvnorm, 1.5*pxl, 0, 2*math.pi)
            cr.fill ()

   # draw green thin bezier curve plus its handles
   cr.set_line_width (1 * pxl)
   cr.set_source_rgba (0.0, 1.0, 0.0, 0.7)
   cr.move_to (*bez[0:2])
   cr.curve_to (*bez[2:8])
   cr.move_to (bez[0], bez[1])
   cr.line_to (bez[2], bez[3])
   cr.move_to (bez[4], bez[5])
   cr.line_to (bez[6], bez[7])
   cr.stroke ()

   cr.set_source_rgba (1.0, 0.0, 0.0, 0.7)
   cr.arc (bez[0], bez[1], 3*pxl, 0, 2*math.pi)
   cr.new_sub_path ()
   cr.arc (bez[2], bez[3], 3*pxl, 0, 2*math.pi)
   cr.new_sub_path ()
   cr.arc (bez[4], bez[5], 3*pxl, 0, 2*math.pi)
   cr.new_sub_path ()
   cr.arc (bez[6], bez[7], 3*pxl, 0, 2*math.pi)
   cr.fill ()

   return True


def setup_ui (val):
   win = gtk.Window ()
   win.set_default_size (500, 500)

   win.set_events (gtk.gdk.EXPOSURE_MASK | gtk.gdk.KEY_PRESS_MASK)

   win.connect ("expose-event", expose_event, val)
   win.connect ("key-press-event", key_press_event, val)
   win.connect ("delete-event", gtk.main_quit)

   win.show_all ()

   val.full = False
   val.zoom = 0
   val.steps = 128


if __name__=='__main__':
   val = Values ()
   setup_ui (val)
   gtk.main ()