#!/usr/bin/env python 
'''
Copyright (C) 2007 Tavmjong Bah, tavmjong@free.fr
Copyright (C) 2006 Georg Wiora, xorx@quarkbox.de
Copyright (C) 2006 Johan Engelen, johan@shouraizou.nl
Copyright (C) 2005 Aaron Spike, aaron@ekips.org

This program 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.

This program 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 this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

Changes:
 * This program is a modified version of wavy.py by Aaron Spike.
 * 22-Dec-2006: Wiora : Added axis and isotropic scaling
 * 21-Jun-2007: Tavmjong: Added polar coordinates

'''
import inkex, simplepath, simplestyle
from math import *
from random import *

def drawfunction(xstart, xend, ybottom, ytop, samples, width, height, left, bottom, 
    fx = "sin(x)", fpx = "cos(x)", fponum = True, times2pi = False, polar = False, isoscale = True, drawaxis = True):

    if times2pi == True:
        xstart = 2 * pi * xstart
        xend   = 2 * pi * xend   
      
    # coords and scales based on the source rect
    scalex = width / (xend - xstart)
    xoff = left
    coordx = lambda x: (x - xstart) * scalex + xoff  #convert x-value to coordinate
    if polar :  # Set scale so that left side of rectangle is -1, right side is +1.
                # (We can't use xscale for both range and scale.)
        centerx = left + width/2.0
        polar_scalex = width/2.0
        coordx = lambda x: x * polar_scalex + centerx  #convert x-value to coordinate

    scaley = height / (ytop - ybottom)
    yoff = bottom
    coordy = lambda y: (ybottom - y) * scaley + yoff  #convert y-value to coordinate

    # Check for isotropic scaling and use smaller of the two scales, correct ranges
    if isoscale and not polar:
      if scaley<scalex:
        # compute zero location
        xzero = coordx(0)
        # set scale
        scalex = scaley
        # correct x-offset
        xstart = (left-xzero)/scalex
        xend = (left+width-xzero)/scalex
      else :
        # compute zero location
        yzero = coordy(0)
        # set scale
        scaley = scalex
        # correct x-offset
        ybottom = (yzero-bottom)/scaley
        ytop = (bottom+height-yzero)/scaley

    # functions specified by the user
    try:
        if fx != "":
            f = eval('lambda x: ' + fx.strip('"'))
        if fpx != "":
            fp = eval('lambda x: ' + fpx.strip('"'))
    # handle incomplete/invalid function gracefully
    except SyntaxError:
        return []

    # step is the distance between nodes on x
    step = (xend - xstart) / (samples-1)
    third = step / 3.0
    ds = step * 0.001 # Step used in calculating derivatives

    a = [] # path array 
    # add axis
    if drawaxis :
      # check for visibility of x-axis
      if ybottom<=0 and ytop>=0:
        # xaxis
        a.append(['M ',[left, coordy(0)]])
        a.append([' l ',[width, 0]])
      # check for visibility of y-axis
      if xstart<=0 and xend>=0:
        # xaxis
        a.append([' M ',[coordx(0),bottom]])
        a.append([' l ',[0, -height]])

    # initialize function and derivative for 0;
    # they are carried over from one iteration to the next, to avoid extra function calculations. 
    x0 =   xstart
    y0 = f(xstart)
    if polar :
        xp0 = y0 * cos( x0 )
        yp0 = y0 * sin( x0 )
        x0 = xp0
        y0 = yp0
    if fponum or polar: # numerical derivative, using 0.001*step as the small differential
        x1 = xstart + ds # Second point AFTER first point (Good for first point)
        y1 = f(x1)
        if polar :
            xp1 = y1 * cos( x1 )
            yp1 = y1 * sin( x1 )
            x1 = xp1
            y1 = yp1
        dx0 = (x1 - x0)/ds 
        dy0 = (y1 - y0)/ds
    else: # derivative given by the user
        dx0 = 1 # Only works for rectangular coordinates
        dy0 = fp(xstart)

    # Start curve
    a.append([' M ',[coordx(x0), coordy(y0)]]) # initial moveto

    for i in range(int(samples-1)):
        x1 = (i+1) * step + xstart
        x2 = x1 - ds # Second point BEFORE first point (Good for last point)
        y1 = f(x1)
        y2 = f(x2)
        if polar :
            xp1 = y1 * cos( x1 )
            yp1 = y1 * sin( x1 )
            xp2 = y2 * cos( x2 )
            yp2 = y2 * sin( x2 )
            x1 = xp1
            y1 = yp1
            x2 = xp2
            y2 = yp2
        if fponum or polar: # numerical derivative
            dx1 = (x1 - x2)/ds
            dy1 = (y1 - y2)/ds
        else: # derivative given by the user
            dx1 = 1 # Only works for rectangular coordinates
            dy1 = fp(x1)
        # create curve
        a.append([' C ',
                  [coordx(x0 + (dx0 * third)), coordy(y0 + (dy0 * third)), 
                   coordx(x1 - (dx1 * third)), coordy(y1 - (dy1 * third)),
                   coordx(x1),                 coordy(y1)]
                  ])
        x0  = x1  # Next segment's start is this segments end
        y0  = y1
        dx0 = dx1 # Assume the function is smooth everywhere, so carry over the derivative too
        dy0 = dy1    
    return a

class FuncPlot(inkex.Effect):
    def __init__(self):
        inkex.Effect.__init__(self)
        self.OptionParser.add_option("--xstart",
                        action="store", type="float", 
                        dest="xstart", default=0.0,
                        help="Start x-value")
        self.OptionParser.add_option("--xend",
                        action="store", type="float", 
                        dest="xend", default=1.0,
                        help="End x-value")
        self.OptionParser.add_option("--times2pi",
                        action="store", type="inkbool", 
                        dest="times2pi", default=True,
                        help="Multiply x-range by 2*pi")    
        self.OptionParser.add_option("--polar",
                        action="store", type="inkbool", 
                        dest="polar", default=False,
                        help="Plot using polar coordinates")    
        self.OptionParser.add_option("--ybottom",
                        action="store", type="float", 
                        dest="ybottom", default=-1.0,
                        help="y-value of rectangle's bottom")
        self.OptionParser.add_option("--ytop",
                        action="store", type="float", 
                        dest="ytop", default=1.0,
                        help="y-value of rectangle's top")
        self.OptionParser.add_option("-s", "--samples",
                        action="store", type="int", 
                        dest="samples", default=8,
                        help="Samples")    
        self.OptionParser.add_option("--fofx",
                        action="store", type="string", 
                        dest="fofx", default="sin(x)",
                        help="f(x) for plotting")    
        self.OptionParser.add_option("--fponum",
                        action="store", type="inkbool", 
                        dest="fponum", default=True,
                        help="Calculate the first derivative numerically")    
        self.OptionParser.add_option("--fpofx",
                        action="store", type="string", 
                        dest="fpofx", default="cos(x)",
                        help="f'(x) for plotting") 
        self.OptionParser.add_option("--remove",
                        action="store", type="inkbool", 
                        dest="remove", default=True,
                        help="If True, source rectangle is removed") 
        self.OptionParser.add_option("--isoscale",
                        action="store", type="inkbool", 
                        dest="isoscale", default=True,
                        help="If True, isotropic scaling is used") 
        self.OptionParser.add_option("--drawaxis",
                        action="store", type="inkbool", 
                        dest="drawaxis", default=True,
                        help="If True, axis are drawn") 
        self.OptionParser.add_option("--tab",
                        action="store", type="string", 
                        dest="tab", default="sampling",
                        help="The selected UI-tab when OK was pressed") 
        self.OptionParser.add_option("--funcplotuse",
                        action="store", type="string", 
                        dest="funcplotuse", default="",
                        help="dummy") 
        self.OptionParser.add_option("--pythonfunctions",
                        action="store", type="string", 
                        dest="pythonfunctions", default="",
                        help="dummy") 

    def effect(self):
        for id, node in self.selected.iteritems():
            if node.tag == inkex.addNS('rect','svg'):
                # create new path with basic dimensions of selected rectangle
                newpath = inkex.etree.Element(inkex.addNS('path','svg'))
                x = float(node.get('x'))
                y = float(node.get('y'))
                w = float(node.get('width'))
                h = float(node.get('height'))

                #copy attributes of rect
                s = node.get('style')
                if s:
                    newpath.set('style', s)
                
                t = node.get('transform')
                if t:
                    newpath.set('transform', t)
                    
                # top and bottom were exchanged
                newpath.set('d', simplepath.formatPath(
                            drawfunction(self.options.xstart,
                                self.options.xend,
                                self.options.ybottom,
                                self.options.ytop,
                                self.options.samples, 
                                w,h,x,y+h,
                                self.options.fofx, 
                                self.options.fpofx,
                                self.options.fponum,
                                self.options.times2pi,
                                self.options.polar,
                                self.options.isoscale,
                                self.options.drawaxis)))
                newpath.set('title', self.options.fofx)
                
                #newpath.setAttribute('desc', '!func;' + self.options.fofx + ';' 
                #                                      + self.options.fpofx + ';'
                #                                      + `self.options.fponum` + ';'
                #                                      + `self.options.xstart` + ';'
                #                                      + `self.options.xend` + ';'
                #                                      + `self.options.samples`)
                                
                # add path into SVG structure
                node.getparent().append(newpath)
                # option wether to remove the rectangle or not.
                if self.options.remove:
                    node.getparent().remove(node)
                
if __name__ == '__main__':
    e = FuncPlot()
    e.affect()


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