text: # -*- encoding: utf-8 -*-
  #
  #
  # Copyright (C) 2002-2011 Jörg Lehmann <joergl@users.sourceforge.net>
  # Copyright (C) 2002-2011 André Wobst <wobsta@users.sourceforge.net>
  #
  # This file is part of PyX (http://pyx.sourceforge.net/).
  #
  # PyX is free software; you can redistribute it and/or modify
  # it under the terms of the GNU General Public License as published by
  # the Free Software Foundation; either version 2 of the License, or
  # (at your option) any later version.
  #
  # PyX is distributed in the hope that it will be useful,
  # but WITHOUT ANY WARRANTY; without even the implied warranty of
  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  # GNU General Public License for more details.
  #
  # You should have received a copy of the GNU General Public License
  # along with PyX; if not, write to the Free Software
  # Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
  
  import math
  import attr, canvasitem, deformer, unit
  import bbox as bboxmodule
  
  # global epsilon (used to judge whether a matrix is singular)
  _epsilon = (1e-5)**2
  
  def set(epsilon=None):
      global _epsilon
      if epsilon is not None:
          _epsilon = epsilon
  
  
  # some helper routines
  
  def _rmatrix(angle):
      phi = math.pi*angle/180.0
  
      return  ((math.cos(phi), -math.sin(phi)), 
               (math.sin(phi),  math.cos(phi)))
  
  def _rvector(angle, x, y):
      phi = math.pi*angle/180.0
  
      return  ((1-math.cos(phi))*x + math.sin(phi)    *y,
                -math.sin(phi)   *x + (1-math.cos(phi))*y)
  
  
  def _mmatrix(angle):
      phi = math.pi*angle/180.0
  
      return ( (math.cos(phi)*math.cos(phi)-math.sin(phi)*math.sin(phi),
                -2*math.sin(phi)*math.cos(phi)                ),
               (-2*math.sin(phi)*math.cos(phi),
                math.sin(phi)*math.sin(phi)-math.cos(phi)*math.cos(phi) ) )
  
  class _marker: pass
  
  # Exception
  
  class TrafoException(Exception):
      pass
  
  # trafo: affine transformations
  
  class trafo_pt(canvasitem.canvasitem, deformer.deformer):
  
      """affine transformation (coordinates in constructor in pts)
  
      Note that though the coordinates in the constructor are in
      pts (which is useful for internal purposes), all other
      methods only accept units in the standard user notation.
  
      """
  
      def __init__(self, matrix=((1, 0), (0, 1)), vector=(0, 0), epsilon=_marker):
          """Return trafo with given transformation matrix and vector. If epsilon
          is passed it is used instead of the global epsilon defined in the module to
          check whether the matrix is singular or not. Use epsilon=None to turn of this
          checking.
          """
          if epsilon is _marker:
              epsilon = _epsilon
          self.epsilon = epsilon
          if epsilon is not None and abs(matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]) < epsilon:
              raise TrafoException("transformation matrix must not be singular")
          else:
              self.matrix = matrix
          self.vector = vector
  
      def __mul__(self, other):
          if isinstance(other, trafo_pt):
              if self.epsilon is None or other.epsilon is None:
                  epsilon = None
              elif self.epsilon <= other.epsilon:
                  epsilon = self.epsilon
              else:
                  epsilon = other.epsilon
              matrix = ( ( self.matrix[0][0]*other.matrix[0][0] +
                           self.matrix[0][1]*other.matrix[1][0],
                           self.matrix[0][0]*other.matrix[0][1] +
                           self.matrix[0][1]*other.matrix[1][1] ),
                         ( self.matrix[1][0]*other.matrix[0][0] +
                           self.matrix[1][1]*other.matrix[1][0],
                           self.matrix[1][0]*other.matrix[0][1] +
                           self.matrix[1][1]*other.matrix[1][1] )
                       )
  
              vector = ( self.matrix[0][0]*other.vector[0] +
                         self.matrix[0][1]*other.vector[1] +
                         self.vector[0],
                         self.matrix[1][0]*other.vector[0] +
                         self.matrix[1][1]*other.vector[1] +
                         self.vector[1] )
  
              return trafo_pt(matrix=matrix, vector=vector, epsilon=epsilon)
          else:
              raise NotImplementedError("can only multiply two transformations")
  
      def __str__(self):
          return "[%f %f %f %f %f %f]" % \
                 ( self.matrix[0][0], self.matrix[1][0],
                   self.matrix[0][1], self.matrix[1][1],
                   self.vector[0], self.vector[1] )
  
      def processPS(self, file, writer, context, registry, bbox):
          file.write("[%f %f %f %f %f %f] concat\n" % \
                      ( self.matrix[0][0], self.matrix[1][0],
                        self.matrix[0][1], self.matrix[1][1],
                        self.vector[0], self.vector[1] ) )
  
      def processPDF(self, file, writer, context, registry, bbox):
          file.write("%f %f %f %f %f %f cm\n" % \
                      ( self.matrix[0][0], self.matrix[1][0],
                        self.matrix[0][1], self.matrix[1][1],
                        self.vector[0], self.vector[1] ) )
  
      def bbox(self):
          return bboxmodule.empty()
  
      def apply_pt(self, x_pt, y_pt):
          """apply transformation to point (x_pt, y_pt) in pts"""
          return ( self.matrix[0][0]*x_pt + self.matrix[0][1]*y_pt + self.vector[0],
                   self.matrix[1][0]*x_pt + self.matrix[1][1]*y_pt + self.vector[1] )
  
      def apply(self, x, y):
          # for the transformation we have to convert to points
          tx, ty = self.apply_pt(unit.topt(x), unit.topt(y))
          return tx * unit.t_pt, ty * unit.t_pt
  
      def deform(self, path):
          return path.transformed(self)
  
      def inverse(self):
          det = 1.0*(self.matrix[0][0]*self.matrix[1][1] - self.matrix[0][1]*self.matrix[1][0])
          matrix = ( ( self.matrix[1][1]/det, -self.matrix[0][1]/det),
                     (-self.matrix[1][0]/det,  self.matrix[0][0]/det) )
          return ( trafo_pt(matrix=matrix, epsilon=self.epsilon) *
                   trafo_pt(vector=(-self.vector[0], -self.vector[1]), epsilon=self.epsilon) )
  
      def mirrored(self, angle):
          return mirror(angle, epsilon=self.epsilon) * self
  
      def rotated_pt(self, angle, x=None, y=None):
          return rotate_pt(angle, x, y, epsilon=self.epsilon) * self
  
      def rotated(self, angle, x=None, y=None):
          return rotate(angle, x, y, epsilon=self.epsilon) * self
  
      def scaled_pt(self, sx, sy=None, x=None, y=None):
          return scale_pt(sx, sy, x, y, epsilon=self.epsilon) * self
  
      def scaled(self, sx, sy=None, x=None, y=None):
          return scale(sx, sy, x, y, epsilon=self.epsilon) * self
  
      def slanted_pt(self, a, angle=0, x=None, y=None):
          return slant_pt(a, angle, x, y, epsilon=self.epsilon) * self
  
      def slanted(self, a, angle=0, x=None, y=None):
          return slant(a, angle, x, y, epsilon=self.epsilon) * self
  
      def translated_pt(self, x, y):
          return translate_pt(x, y, epsilon=self.epsilon) * self
  
      def translated(self, x, y):
          return translate(x, y, epsilon=self.epsilon) * self
  
  
  class trafo(trafo_pt):
  
      """affine transformation"""
  
      def __init__(self, matrix=((1,0), (0,1)), vector=(0, 0), epsilon=_marker):
          trafo_pt.__init__(self,
                            matrix, (unit.topt(vector[0]), unit.topt(vector[1])),
                            epsilon=epsilon)
  
  #
  # some standard transformations 
  #
  
  class mirror(trafo):
      def __init__(self, angle=0, epsilon=_marker):
          trafo.__init__(self, matrix=_mmatrix(angle), epsilon=epsilon)
  
  
  class rotate_pt(trafo_pt):
      def __init__(self, angle, x=None, y=None, epsilon=_marker):
          vector = 0, 0
          if x is not None or y is not None:
              if x is None or y is None:
                  raise TrafoException("either specify both x and y or none of them")
              vector=_rvector(angle, x, y)
  
          trafo_pt.__init__(self, matrix=_rmatrix(angle), vector=vector, epsilon=epsilon)
  
  
  class rotate(trafo_pt):
      def __init__(self, angle, x=None, y=None, epsilon=_marker):
          vector = 0, 0 
          if x is not None or y is not None:
              if x is None or y is None:
                  raise TrafoException("either specify both x and y or none of them")
              vector=_rvector(angle, unit.topt(x), unit.topt(y))
  
          trafo_pt.__init__(self, matrix=_rmatrix(angle), vector=vector, epsilon=epsilon)
  
  
  class scale_pt(trafo_pt):
      def __init__(self, sx, sy=None, x=None, y=None, epsilon=_marker):
          if sy is None:
              sy = sx
          vector = 0, 0
          if x is not None or y is not None:
              if x is None or y is None:
                  raise TrafoException("either specify both x and y or none of them")
              vector = (1-sx)*x, (1-sy)*y
          trafo_pt.__init__(self, matrix=((sx, 0), (0, sy)), vector=vector, epsilon=epsilon)
  
  
  class scale(trafo):
      def __init__(self, sx, sy=None, x=None, y=None, epsilon=_marker):
          if sy is None:
              sy = sx
          vector = 0, 0
          if x is not None or y is not None:
              if x is None or y is None:
                  raise TrafoException("either specify both x and y or none of them")
              vector = (1-sx)*x, (1-sy)*y
          trafo.__init__(self, matrix=((sx, 0), (0, sy)), vector=vector, epsilon=epsilon)
  
  
  class slant_pt(trafo_pt):
      def __init__(self, a, angle=0, x=None, y=None, epsilon=_marker):
          t = ( rotate_pt(-angle, x, y, epsilon=epsilon) *
                trafo(matrix=((1, a), (0, 1)), epsilon=epsilon) *
                rotate_pt(angle, x, y, epsilon=epsilon) )
          trafo_pt.__init__(self, t.matrix, t.vector, epsilon=epsilon)
  
  
  class slant(trafo):
      def __init__(self, a, angle=0, x=None, y=None, epsilon=_marker):
          t = ( rotate(-angle, x, y, epsilon=epsilon) *
                trafo(matrix=((1, a), (0, 1)), epsilon=epsilon) *
                rotate(angle, x, y, epsilon=epsilon) )
          trafo.__init__(self, t.matrix, t.vector, epsilon=epsilon)
  
  
  class translate_pt(trafo_pt):
      def __init__(self, x, y, epsilon=_marker):
          trafo_pt.__init__(self, vector=(x, y), epsilon=epsilon)
  
  
  class translate(trafo):
      def __init__(self, x, y, epsilon=_marker):
          trafo.__init__(self, vector=(x, y), epsilon=epsilon)
  