Inkscape extension that randomly places an object along a path

randompathalongpath.inx

<?xml version="1.0" encoding="UTF-8"?>
<inkscape-extension xmlns="http://www.inkscape.org/namespace/inkscape/extension">
    <_name>Pattern randomly along Path</_name>
    <id>math.univ-lille1.barraud.pathdeformrandomly</id>
    <dependency type="executable" location="extensions">pathmodifier.py</dependency>
    <dependency type="executable" location="extensions">randompathalongpath.py</dependency>
    <dependency type="executable" location="extensions">inkex.py</dependency>
	<param name="tab" type="notebook">
        <page name="Options" _gui-text="Options">
        <param name="copymode" type="enum" _gui-text="Copies of the pattern:">
            <_item value="Single">Single</_item>
            <_item value="Single, stretched">Single, stretched</_item>
            <_item value="Repeated">Repeated</_item>
            <_item value="Repeated, stretched">Repeated, stretched</_item>
        </param>
        <param name="kind" type="enum" _gui-text="Deformation type:">
            <_item value="Snake">Snake</_item>
            <_item value="Ribbon">Ribbon</_item>
        </param>
        <param name="noffset" type="float" _gui-text="Normal offset:" min="-10000.0" max="10000.0">0.0</param>
        <param name="vertical" type="boolean" _gui-text="Pattern is vertical">false</param>
        <param name="duplicate" type="boolean" _gui-text="Duplicate the pattern before deformation">true</param>
        <param name="number_repetitions" type="int" _gui-text="Number of randomly picked points:" min="1" max="10000">0</param>
        <param name="random_toffset_min" type="float" _gui-text="Minimal random tangential offset (%):" min="-10000.0" max="10000.0">0.0</param>
        <param name="random_toffset_max" type="float" _gui-text="Maximum random tangential offset (%):" min="-10000.0" max="10000.0">100.0</param>
        </page>
        <page name="Help" _gui-text="Help">
            <_param name="title" type="description">This effect scatters or bends a pattern along arbitrary "skeleton" paths. The pattern is the topmost object in the selection. Groups of paths, shapes or clones are allowed.</_param>
        </page>
    </param>
    <effect>
    <object-type>all</object-type>
        <effects-menu>
            <submenu _name="Generate from Path"/>
        </effects-menu>
    </effect>
    <script>
        <command reldir="extensions" interpreter="python">randompathalongpath.py</command>
    </script>
</inkscape-extension>

randompathalongpath.py

#!/usr/bin/env python2
'''
Copyright (C) 2018 Philipp G. Haselwarter, philipp+inkscape@haselwarter.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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
barraud@math.univ-lille1.fr

Based on 'pathalongpath.py' by Jean-Francois Barraud.

Quick description:
This script randomly places and 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.
'''
# standard library
import copy
import random
# local library
import inkex
import cubicsuperpath
import bezmisc
import pathmodifier
import simpletransform


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 receives 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):
        random.seed(None)
        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("--random_toffset_min",
                        action="store", type="float",
                        dest="random_toffset_min", default=0.0, help="minimal random tangential offset")
        self.OptionParser.add_option("--random_toffset_max",
                        action="store", type="float",
                        dest="random_toffset_max", default=100.0, help="maximum random tangential offset")
        self.OptionParser.add_option("--number_repetitions",
                        action="store", type="int",
                        dest="number_repetitions", default=1, help="number of random repetitions")
        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("-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")
        self.OptionParser.add_option("--tab",
                        action="store", type="string",
                        dest="tab",
                        help="The selected UI-tab when OK was pressed")

    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 corresponding 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=="Single, stretched":
            self.options.repeat =False
            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]

        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 i in range(0, self.options.number_repetitions):

                    for skelnode in self.skeletons.itervalues():

                        self.curSkeleton = cubicsuperpath.parsePath(skelnode.get('d'))

                        if self.options.vertical:
                            flipxy(self.curSkeleton)

                        for comp in self.curSkeleton:
                            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)
                            tangential_offset = (random.uniform(self.options.random_toffset_min, self.options.random_toffset_max) / 100.0) * length

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

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

                            if self.options.stretch:
                                if not width:
                                    exit(_("The 'stretch' option requires that the pattern must have non-zero width :\nPlease edit the pattern width."))
                                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))
        return

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


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