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pathalongpath.py

#!/usr/bin/env python
'''
Copyright (C) 2006 Jean-Francois Barraud, barraud@math.univ-lille1.fr

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
barraud@math.univ-lille1.fr

Quick description:
This script deforms an object (the pattern) along other paths (skeletons)...
The first selected object is the pattern
the last selected ones are the skeletons.

Imagine a straight horizontal line L in the middle of the bounding box of the pattern.
Consider the normal bundle of L: the collection of all the vertical lines meeting L.
Consider this as the initial state of the plane; in particular, think of the pattern
as painted on these lines.

Now move and bend L to make it fit a skeleton, and see what happens to the normals:
they move and rotate, deforming the pattern.
'''

import inkex, cubicsuperpath, bezmisc
import pathmodifier,simpletransform
import copy, math, re, random
import gettext
_ = gettext.gettext

def flipxy(path):
    for pathcomp in path:
        for ctl in pathcomp:
            for pt in ctl:
                tmp=pt[0]
                pt[0]=-pt[1]
                pt[1]=-tmp

def offset(pathcomp,dx,dy):
    for ctl in pathcomp:
        for pt in ctl:
            pt[0]+=dx
            pt[1]+=dy

def stretch(pathcomp,xscale,yscale,org):
    for ctl in pathcomp:
        for pt in ctl:
            pt[0]=org[0]+(pt[0]-org[0])*xscale
            pt[1]=org[1]+(pt[1]-org[1])*yscale

def linearize(p,tolerance=0.001):
    '''
    This function recieves a component of a 'cubicsuperpath' and returns two things:
    The path subdivided in many straight segments, and an array containing the length of each segment.
    
    We could work with bezier path as well, but bezier arc lengths are (re)computed for each point 
    in the deformed object. For complex paths, this might take a while.
    '''
    zero=0.000001
    i=0
    d=0
    lengths=[]
    while i<len(p)-1:
        box  = bezmisc.pointdistance(p[i  ][1],p[i  ][2])
        box += bezmisc.pointdistance(p[i  ][2],p[i+1][0])
        box += bezmisc.pointdistance(p[i+1][0],p[i+1][1])
        chord = bezmisc.pointdistance(p[i][1], p[i+1][1])
        if (box - chord) > tolerance:
            b1, b2 = bezmisc.beziersplitatt([p[i][1],p[i][2],p[i+1][0],p[i+1][1]], 0.5)
            p[i  ][2][0],p[i  ][2][1]=b1[1]
            p[i+1][0][0],p[i+1][0][1]=b2[2]
            p.insert(i+1,[[b1[2][0],b1[2][1]],[b1[3][0],b1[3][1]],[b2[1][0],b2[1][1]]])
        else:
            d=(box+chord)/2
            lengths.append(d)
            i+=1
    new=[p[i][1] for i in range(0,len(p)-1) if lengths[i]>zero]
    new.append(p[-1][1])
    lengths=[l for l in lengths if l>zero]
    return(new,lengths)

class PathAlongPath(pathmodifier.Diffeo):
    def __init__(self):
        pathmodifier.Diffeo.__init__(self)
        self.OptionParser.add_option("--title")
        self.OptionParser.add_option("-n", "--noffset",
                        action="store", type="float", 
                        dest="noffset", default=0.0, help="normal offset")
        self.OptionParser.add_option("-t", "--toffset",
                        action="store", type="float", 
                        dest="toffset", default=0.0, help="tangential offset")
        self.OptionParser.add_option("-k", "--kind",
                        action="store", type="string", 
                        dest="kind", default=True,
                        help="choose between wave or snake effect")
        self.OptionParser.add_option("-c", "--copymode",
                        action="store", type="string", 
                        dest="copymode", default=True,
                        help="repeat the path to fit deformer's length")
        self.OptionParser.add_option("-p", "--space",
                        action="store", type="float", 
                        dest="space", default=0.0)
        self.OptionParser.add_option("-v", "--vertical",
                        action="store", type="inkbool", 
                        dest="vertical", default=False,
                        help="reference path is vertical")
        self.OptionParser.add_option("-d", "--duplicate",
                        action="store", type="inkbool", 
                        dest="duplicate", default=False,
                        help="duplicate pattern before deformation")

    def prepareSelectionList(self):

        idList=self.options.ids
        idList=pathmodifier.zSort(self.document.getroot(),idList)
        id = idList[-1]
        self.patterns={id:self.selected[id]}

##        ##first selected->pattern, all but first selected-> skeletons
##        id = self.options.ids[-1]
##        self.patterns={id:self.selected[id]}

        if self.options.duplicate:
            self.patterns=self.duplicateNodes(self.patterns)
        self.expandGroupsUnlinkClones(self.patterns, True, True)
        self.objectsToPaths(self.patterns)
        del self.selected[id]

        self.skeletons=self.selected
        self.expandGroupsUnlinkClones(self.skeletons, True, False)
        self.objectsToPaths(self.skeletons)

    def lengthtotime(self,l):
        '''
        Recieves an arc length l, and returns the index of the segment in self.skelcomp 
        containing the coresponding point, to gether with the position of the point on this segment.

        If the deformer is closed, do computations modulo the toal length.
        '''
        if self.skelcompIsClosed:
            l=l % sum(self.lengths)
        if l<=0:
            return 0,l/self.lengths[0]
        i=0
        while (i<len(self.lengths)) and (self.lengths[i]<=l):
            l-=self.lengths[i]
            i+=1
        t=l/self.lengths[min(i,len(self.lengths)-1)]
        return i, t

    def applyDiffeo(self,bpt,vects=()):
        '''
        The kernel of this stuff:
        bpt is a base point and for v in vectors, v'=v-p is a tangent vector at bpt.
        '''
        s=bpt[0]-self.skelcomp[0][0]
        i,t=self.lengthtotime(s)
        if i==len(self.skelcomp)-1:
            x,y=bezmisc.tpoint(self.skelcomp[i-1],self.skelcomp[i],1+t)
            dx=(self.skelcomp[i][0]-self.skelcomp[i-1][0])/self.lengths[-1]
            dy=(self.skelcomp[i][1]-self.skelcomp[i-1][1])/self.lengths[-1]
        else:
            x,y=bezmisc.tpoint(self.skelcomp[i],self.skelcomp[i+1],t)
            dx=(self.skelcomp[i+1][0]-self.skelcomp[i][0])/self.lengths[i]
            dy=(self.skelcomp[i+1][1]-self.skelcomp[i][1])/self.lengths[i]

        vx=0
        vy=bpt[1]-self.skelcomp[0][1]
        if self.options.wave:
            bpt[0]=x+vx*dx
            bpt[1]=y+vy+vx*dy
        else:
            bpt[0]=x+vx*dx-vy*dy
            bpt[1]=y+vx*dy+vy*dx

        for v in vects:
            vx=v[0]-self.skelcomp[0][0]-s
            vy=v[1]-self.skelcomp[0][1]
            if self.options.wave:
                v[0]=x+vx*dx
                v[1]=y+vy+vx*dy
            else:
                v[0]=x+vx*dx-vy*dy
                v[1]=y+vx*dy+vy*dx

    def effect(self):
        if len(self.options.ids)<2:
            inkex.errormsg(_("This extension requires two selected paths."))
            return
        self.prepareSelectionList()
        self.options.wave = (self.options.kind=="Ribbon")
        if self.options.copymode=="Single":
            self.options.repeat =False
            self.options.stretch=False
        elif self.options.copymode=="Repeated":
            self.options.repeat =True
            self.options.stretch=False
        elif self.options.copymode=="Single, stretched":
            self.options.repeat =False
            self.options.stretch=True
        elif self.options.copymode=="Repeated, stretched":
            self.options.repeat =True
            self.options.stretch=True

        bbox=simpletransform.computeBBox(self.patterns.values())
                    
        if self.options.vertical:
            #flipxy(bbox)...
            bbox=(-bbox[3],-bbox[2],-bbox[1],-bbox[0])
            
        width=bbox[1]-bbox[0]
        dx=width+self.options.space

        for id, node in self.patterns.iteritems():
            if node.tag == inkex.addNS('path','svg') or node.tag=='path':
                d = node.get('d')
                p0 = cubicsuperpath.parsePath(d)
                if self.options.vertical:
                    flipxy(p0)

                newp=[]
                for skelnode in self.skeletons.itervalues(): 
                    self.curSekeleton=cubicsuperpath.parsePath(skelnode.get('d'))
                    if self.options.vertical:
                        flipxy(self.curSekeleton)
                    for comp in self.curSekeleton:
                        p=copy.deepcopy(p0)
                        self.skelcomp,self.lengths=linearize(comp)
                        #!!!!>----> TODO: really test if path is closed! end point==start point is not enough!
                        self.skelcompIsClosed = (self.skelcomp[0]==self.skelcomp[-1])

                        length=sum(self.lengths)
                        xoffset=self.skelcomp[0][0]-bbox[0]+self.options.toffset
                        yoffset=self.skelcomp[0][1]-(bbox[2]+bbox[3])/2-self.options.noffset


                        if self.options.repeat:
                            NbCopies=max(1,int(round((length+self.options.space)/dx)))
                            width=dx*NbCopies
                            if not self.skelcompIsClosed:
                                width-=self.options.space
                            bbox=bbox[0],bbox[0]+width, bbox[2],bbox[3]
                            new=[]
                            for sub in p:
                                for i in range(0,NbCopies,1):
                                    new.append(copy.deepcopy(sub))
                                    offset(sub,dx,0)
                            p=new

                        for sub in p:
                            offset(sub,xoffset,yoffset)

                        if self.options.stretch:
                            for sub in p:
                                stretch(sub,length/width,1,self.skelcomp[0])

                        for sub in p:
                            for ctlpt in sub:
                                self.applyDiffeo(ctlpt[1],(ctlpt[0],ctlpt[2]))

                        if self.options.vertical:
                            flipxy(p)
                        newp+=p

                node.set('d', cubicsuperpath.formatPath(newp))

if __name__ == '__main__':
    e = PathAlongPath()
    e.affect()

                    
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