3174 lines
136 KiB
Python
3174 lines
136 KiB
Python
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#!/usr/bin/env python
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"""
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Modified by Jay Johnson 2015, J Tech Photonics, Inc., jtechphotonics.com
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modified by Adam Polak 2014, polakiumengineering.org
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based on Copyright (C) 2009 Nick Drobchenko, nick@cnc-club.ru
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based on gcode.py (C) 2007 hugomatic...
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based on addnodes.py (C) 2005,2007 Aaron Spike, aaron@ekips.org
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based on dots.py (C) 2005 Aaron Spike, aaron@ekips.org
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based on interp.py (C) 2005 Aaron Spike, aaron@ekips.org
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based on bezmisc.py (C) 2005 Aaron Spike, aaron@ekips.org
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based on cubicsuperpath.py (C) 2005 Aaron Spike, aaron@ekips.org
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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"""
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import inkex, simplestyle, simplepath
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import cubicsuperpath, simpletransform, bezmisc
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import os
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import math
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import bezmisc
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import re
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import copy
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import sys
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import time
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import cmath
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import numpy
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import codecs
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import random
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import gettext
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_ = gettext.gettext
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### Check if inkex has errormsg (0.46 version doesnot have one.) Could be removed later.
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if "errormsg" not in dir(inkex):
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inkex.errormsg = lambda msg: sys.stderr.write((unicode(msg) + "\n").encode("UTF-8"))
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def bezierslopeatt(((bx0,by0),(bx1,by1),(bx2,by2),(bx3,by3)),t):
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ax,ay,bx,by,cx,cy,x0,y0=bezmisc.bezierparameterize(((bx0,by0),(bx1,by1),(bx2,by2),(bx3,by3)))
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dx=3*ax*(t**2)+2*bx*t+cx
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dy=3*ay*(t**2)+2*by*t+cy
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if dx==dy==0 :
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dx = 6*ax*t+2*bx
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dy = 6*ay*t+2*by
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if dx==dy==0 :
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dx = 6*ax
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dy = 6*ay
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if dx==dy==0 :
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print_("Slope error x = %s*t^3+%s*t^2+%s*t+%s, y = %s*t^3+%s*t^2+%s*t+%s, t = %s, dx==dy==0" % (ax,bx,cx,dx,ay,by,cy,dy,t))
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print_(((bx0,by0),(bx1,by1),(bx2,by2),(bx3,by3)))
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dx, dy = 1, 1
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return dx,dy
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bezmisc.bezierslopeatt = bezierslopeatt
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def ireplace(self,old,new,count=0):
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pattern = re.compile(re.escape(old),re.I)
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return re.sub(pattern,new,self,count)
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################################################################################
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###
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### Styles and additional parameters
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###
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################################################################################
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math.pi2 = math.pi*2
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straight_tolerance = 0.0001
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straight_distance_tolerance = 0.0001
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engraving_tolerance = 0.0001
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loft_lengths_tolerance = 0.0000001
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options = {}
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defaults = {
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'header': """
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G90
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""",
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'footer': """G1 X0 Y0
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"""
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}
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intersection_recursion_depth = 10
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intersection_tolerance = 0.00001
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styles = {
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"loft_style" : {
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'main curve': simplestyle.formatStyle({ 'stroke': '#88f', 'fill': 'none', 'stroke-width':'1', 'marker-end':'url(#Arrow2Mend)' }),
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},
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"biarc_style" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#88f', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#8f8', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'line': simplestyle.formatStyle({ 'stroke': '#f88', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'area': simplestyle.formatStyle({ 'stroke': '#777', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
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},
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"biarc_style_dark" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#33a', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#3a3', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'line': simplestyle.formatStyle({ 'stroke': '#a33', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'area': simplestyle.formatStyle({ 'stroke': '#222', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"biarc_style_dark_area" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#33a', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#3a3', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
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'line': simplestyle.formatStyle({ 'stroke': '#a33', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
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'area': simplestyle.formatStyle({ 'stroke': '#222', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"biarc_style_i" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#880', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#808', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'line': simplestyle.formatStyle({ 'stroke': '#088', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'area': simplestyle.formatStyle({ 'stroke': '#999', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"biarc_style_dark_i" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#dd5', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#d5d', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'line': simplestyle.formatStyle({ 'stroke': '#5dd', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
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'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"biarc_style_lathe_feed" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#07f', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#0f7', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'line': simplestyle.formatStyle({ 'stroke': '#f44', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"biarc_style_lathe_passing feed" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#07f', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#0f7', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'line': simplestyle.formatStyle({ 'stroke': '#f44', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"biarc_style_lathe_fine feed" : {
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'biarc0': simplestyle.formatStyle({ 'stroke': '#7f0', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'biarc1': simplestyle.formatStyle({ 'stroke': '#f70', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'line': simplestyle.formatStyle({ 'stroke': '#744', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
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'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
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},
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"area artefact": simplestyle.formatStyle({ 'stroke': '#ff0000', 'fill': '#ffff00', 'stroke-width':'1' }),
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"area artefact arrow": simplestyle.formatStyle({ 'stroke': '#ff0000', 'fill': '#ffff00', 'stroke-width':'1' }),
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"dxf_points": simplestyle.formatStyle({ "stroke": "#ff0000", "fill": "#ff0000"}),
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}
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################################################################################
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### Cubic Super Path additional functions
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################################################################################
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def csp_simple_bound(csp):
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minx,miny,maxx,maxy = None,None,None,None
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for subpath in csp:
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for sp in subpath :
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for p in sp:
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minx = min(minx,p[0]) if minx!=None else p[0]
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miny = min(miny,p[1]) if miny!=None else p[1]
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maxx = max(maxx,p[0]) if maxx!=None else p[0]
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maxy = max(maxy,p[1]) if maxy!=None else p[1]
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return minx,miny,maxx,maxy
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def csp_segment_to_bez(sp1,sp2) :
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return sp1[1:]+sp2[:2]
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def bound_to_bound_distance(sp1,sp2,sp3,sp4) :
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min_dist = 1e100
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max_dist = 0
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points1 = csp_segment_to_bez(sp1,sp2)
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points2 = csp_segment_to_bez(sp3,sp4)
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for i in range(4) :
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for j in range(4) :
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min_, max_ = line_to_line_min_max_distance_2(points1[i-1], points1[i], points2[j-1], points2[j])
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min_dist = min(min_dist,min_)
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max_dist = max(max_dist,max_)
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print_("bound_to_bound", min_dist, max_dist)
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return min_dist, max_dist
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def csp_to_point_distance(csp, p, dist_bounds = [0,1e100], tolerance=.01) :
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min_dist = [1e100,0,0,0]
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for j in range(len(csp)) :
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for i in range(1,len(csp[j])) :
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d = csp_seg_to_point_distance(csp[j][i-1],csp[j][i],p,sample_points = 5, tolerance = .01)
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if d[0] < dist_bounds[0] :
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# draw_pointer( list(csp_at_t(subpath[dist[2]-1],subpath[dist[2]],dist[3]))
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# +list(csp_at_t(csp[dist[4]][dist[5]-1],csp[dist[4]][dist[5]],dist[6])),"red","line", comment = math.sqrt(dist[0]))
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return [d[0],j,i,d[1]]
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else :
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if d[0] < min_dist[0] : min_dist = [d[0],j,i,d[1]]
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return min_dist
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def csp_seg_to_point_distance(sp1,sp2,p,sample_points = 5, tolerance = .01) :
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ax,ay,bx,by,cx,cy,dx,dy = csp_parameterize(sp1,sp2)
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dx, dy = dx-p[0], dy-p[1]
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if sample_points < 2 : sample_points = 2
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d = min( [(p[0]-sp1[1][0])**2 + (p[1]-sp1[1][1])**2,0.], [(p[0]-sp2[1][0])**2 + (p[1]-sp2[1][1])**2,1.] )
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for k in range(sample_points) :
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t = float(k)/(sample_points-1)
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i = 0
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while i==0 or abs(f)>0.000001 and i<20 :
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t2,t3 = t**2,t**3
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f = (ax*t3+bx*t2+cx*t+dx)*(3*ax*t2+2*bx*t+cx) + (ay*t3+by*t2+cy*t+dy)*(3*ay*t2+2*by*t+cy)
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df = (6*ax*t+2*bx)*(ax*t3+bx*t2+cx*t+dx) + (3*ax*t2+2*bx*t+cx)**2 + (6*ay*t+2*by)*(ay*t3+by*t2+cy*t+dy) + (3*ay*t2+2*by*t+cy)**2
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if df!=0 :
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t = t - f/df
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else :
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break
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i += 1
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if 0<=t<=1 :
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p1 = csp_at_t(sp1,sp2,t)
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d1 = (p1[0]-p[0])**2 + (p1[1]-p[1])**2
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if d1 < d[0] :
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d = [d1,t]
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return d
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def csp_seg_to_csp_seg_distance(sp1,sp2,sp3,sp4, dist_bounds = [0,1e100], sample_points = 5, tolerance=.01) :
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# check the ending points first
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dist = csp_seg_to_point_distance(sp1,sp2,sp3[1],sample_points, tolerance)
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dist += [0.]
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if dist[0] <= dist_bounds[0] : return dist
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d = csp_seg_to_point_distance(sp1,sp2,sp4[1],sample_points, tolerance)
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if d[0]<dist[0] :
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dist = d+[1.]
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if dist[0] <= dist_bounds[0] : return dist
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d = csp_seg_to_point_distance(sp3,sp4,sp1[1],sample_points, tolerance)
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if d[0]<dist[0] :
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dist = [d[0],0.,d[1]]
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if dist[0] <= dist_bounds[0] : return dist
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d = csp_seg_to_point_distance(sp3,sp4,sp2[1],sample_points, tolerance)
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if d[0]<dist[0] :
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dist = [d[0],1.,d[1]]
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if dist[0] <= dist_bounds[0] : return dist
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sample_points -= 2
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if sample_points < 1 : sample_points = 1
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ax1,ay1,bx1,by1,cx1,cy1,dx1,dy1 = csp_parameterize(sp1,sp2)
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ax2,ay2,bx2,by2,cx2,cy2,dx2,dy2 = csp_parameterize(sp3,sp4)
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# try to find closes points using Newtons method
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for k in range(sample_points) :
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for j in range(sample_points) :
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t1,t2 = float(k+1)/(sample_points+1), float(j)/(sample_points+1)
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t12, t13, t22, t23 = t1*t1, t1*t1*t1, t2*t2, t2*t2*t2
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i = 0
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F1, F2, F = [0,0], [[0,0],[0,0]], 1e100
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x,y = ax1*t13+bx1*t12+cx1*t1+dx1 - (ax2*t23+bx2*t22+cx2*t2+dx2), ay1*t13+by1*t12+cy1*t1+dy1 - (ay2*t23+by2*t22+cy2*t2+dy2)
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while i<2 or abs(F-Flast)>tolerance and i<30 :
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#draw_pointer(csp_at_t(sp1,sp2,t1))
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f1x = 3*ax1*t12+2*bx1*t1+cx1
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f1y = 3*ay1*t12+2*by1*t1+cy1
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f2x = 3*ax2*t22+2*bx2*t2+cx2
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f2y = 3*ay2*t22+2*by2*t2+cy2
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F1[0] = 2*f1x*x + 2*f1y*y
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F1[1] = -2*f2x*x - 2*f2y*y
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|
|
F2[0][0] = 2*(6*ax1*t1+2*bx1)*x + 2*f1x*f1x + 2*(6*ay1*t1+2*by1)*y +2*f1y*f1y
|
||
|
|
F2[0][1] = -2*f1x*f2x - 2*f1y*f2y
|
||
|
|
F2[1][0] = -2*f2x*f1x - 2*f2y*f1y
|
||
|
|
F2[1][1] = -2*(6*ax2*t2+2*bx2)*x + 2*f2x*f2x - 2*(6*ay2*t2+2*by2)*y + 2*f2y*f2y
|
||
|
|
F2 = inv_2x2(F2)
|
||
|
|
if F2!=None :
|
||
|
|
t1 -= ( F2[0][0]*F1[0] + F2[0][1]*F1[1] )
|
||
|
|
t2 -= ( F2[1][0]*F1[0] + F2[1][1]*F1[1] )
|
||
|
|
t12, t13, t22, t23 = t1*t1, t1*t1*t1, t2*t2, t2*t2*t2
|
||
|
|
x,y = ax1*t13+bx1*t12+cx1*t1+dx1 - (ax2*t23+bx2*t22+cx2*t2+dx2), ay1*t13+by1*t12+cy1*t1+dy1 - (ay2*t23+by2*t22+cy2*t2+dy2)
|
||
|
|
Flast = F
|
||
|
|
F = x*x+y*y
|
||
|
|
else :
|
||
|
|
break
|
||
|
|
i += 1
|
||
|
|
if F < dist[0] and 0<=t1<=1 and 0<=t2<=1:
|
||
|
|
dist = [F,t1,t2]
|
||
|
|
if dist[0] <= dist_bounds[0] :
|
||
|
|
return dist
|
||
|
|
return dist
|
||
|
|
|
||
|
|
|
||
|
|
def csp_to_csp_distance(csp1,csp2, dist_bounds = [0,1e100], tolerance=.01) :
|
||
|
|
dist = [1e100,0,0,0,0,0,0]
|
||
|
|
for i1 in range(len(csp1)) :
|
||
|
|
for j1 in range(1,len(csp1[i1])) :
|
||
|
|
for i2 in range(len(csp2)) :
|
||
|
|
for j2 in range(1,len(csp2[i2])) :
|
||
|
|
d = csp_seg_bound_to_csp_seg_bound_max_min_distance(csp1[i1][j1-1],csp1[i1][j1],csp2[i2][j2-1],csp2[i2][j2])
|
||
|
|
if d[0] >= dist_bounds[1] : continue
|
||
|
|
if d[1] < dist_bounds[0] : return [d[1],i1,j1,1,i2,j2,1]
|
||
|
|
d = csp_seg_to_csp_seg_distance(csp1[i1][j1-1],csp1[i1][j1],csp2[i2][j2-1],csp2[i2][j2], dist_bounds, tolerance=tolerance)
|
||
|
|
if d[0] < dist[0] :
|
||
|
|
dist = [d[0], i1,j1,d[1], i2,j2,d[2]]
|
||
|
|
if dist[0] <= dist_bounds[0] :
|
||
|
|
return dist
|
||
|
|
if dist[0] >= dist_bounds[1] :
|
||
|
|
return dist
|
||
|
|
return dist
|
||
|
|
# draw_pointer( list(csp_at_t(csp1[dist[1]][dist[2]-1],csp1[dist[1]][dist[2]],dist[3]))
|
||
|
|
# + list(csp_at_t(csp2[dist[4]][dist[5]-1],csp2[dist[4]][dist[5]],dist[6])), "#507","line")
|
||
|
|
|
||
|
|
|
||
|
|
def csp_split(sp1,sp2,t=.5) :
|
||
|
|
[x1,y1],[x2,y2],[x3,y3],[x4,y4] = sp1[1], sp1[2], sp2[0], sp2[1]
|
||
|
|
x12 = x1+(x2-x1)*t
|
||
|
|
y12 = y1+(y2-y1)*t
|
||
|
|
x23 = x2+(x3-x2)*t
|
||
|
|
y23 = y2+(y3-y2)*t
|
||
|
|
x34 = x3+(x4-x3)*t
|
||
|
|
y34 = y3+(y4-y3)*t
|
||
|
|
x1223 = x12+(x23-x12)*t
|
||
|
|
y1223 = y12+(y23-y12)*t
|
||
|
|
x2334 = x23+(x34-x23)*t
|
||
|
|
y2334 = y23+(y34-y23)*t
|
||
|
|
x = x1223+(x2334-x1223)*t
|
||
|
|
y = y1223+(y2334-y1223)*t
|
||
|
|
return [sp1[0],sp1[1],[x12,y12]], [[x1223,y1223],[x,y],[x2334,y2334]], [[x34,y34],sp2[1],sp2[2]]
|
||
|
|
|
||
|
|
def csp_true_bounds(csp) :
|
||
|
|
# Finds minx,miny,maxx,maxy of the csp and return their (x,y,i,j,t)
|
||
|
|
minx = [float("inf"), 0, 0, 0]
|
||
|
|
maxx = [float("-inf"), 0, 0, 0]
|
||
|
|
miny = [float("inf"), 0, 0, 0]
|
||
|
|
maxy = [float("-inf"), 0, 0, 0]
|
||
|
|
for i in range(len(csp)):
|
||
|
|
for j in range(1,len(csp[i])):
|
||
|
|
ax,ay,bx,by,cx,cy,x0,y0 = bezmisc.bezierparameterize((csp[i][j-1][1],csp[i][j-1][2],csp[i][j][0],csp[i][j][1]))
|
||
|
|
roots = cubic_solver(0, 3*ax, 2*bx, cx) + [0,1]
|
||
|
|
for root in roots :
|
||
|
|
if type(root) is complex and abs(root.imag)<1e-10:
|
||
|
|
root = root.real
|
||
|
|
if type(root) is not complex and 0<=root<=1:
|
||
|
|
y = ay*(root**3)+by*(root**2)+cy*root+y0
|
||
|
|
x = ax*(root**3)+bx*(root**2)+cx*root+x0
|
||
|
|
maxx = max([x,y,i,j,root],maxx)
|
||
|
|
minx = min([x,y,i,j,root],minx)
|
||
|
|
|
||
|
|
roots = cubic_solver(0, 3*ay, 2*by, cy) + [0,1]
|
||
|
|
for root in roots :
|
||
|
|
if type(root) is complex and root.imag==0:
|
||
|
|
root = root.real
|
||
|
|
if type(root) is not complex and 0<=root<=1:
|
||
|
|
y = ay*(root**3)+by*(root**2)+cy*root+y0
|
||
|
|
x = ax*(root**3)+bx*(root**2)+cx*root+x0
|
||
|
|
maxy = max([y,x,i,j,root],maxy)
|
||
|
|
miny = min([y,x,i,j,root],miny)
|
||
|
|
maxy[0],maxy[1] = maxy[1],maxy[0]
|
||
|
|
miny[0],miny[1] = miny[1],miny[0]
|
||
|
|
|
||
|
|
return minx,miny,maxx,maxy
|
||
|
|
|
||
|
|
|
||
|
|
############################################################################
|
||
|
|
### csp_segments_intersection(sp1,sp2,sp3,sp4)
|
||
|
|
###
|
||
|
|
### Returns array containig all intersections between two segmets of cubic
|
||
|
|
### super path. Results are [ta,tb], or [ta0, ta1, tb0, tb1, "Overlap"]
|
||
|
|
### where ta, tb are values of t for the intersection point.
|
||
|
|
############################################################################
|
||
|
|
def csp_segments_intersection(sp1,sp2,sp3,sp4) :
|
||
|
|
a, b = csp_segment_to_bez(sp1,sp2), csp_segment_to_bez(sp3,sp4)
|
||
|
|
|
||
|
|
def polish_intersection(a,b,ta,tb, tolerance = intersection_tolerance) :
|
||
|
|
ax,ay,bx,by,cx,cy,dx,dy = bezmisc.bezierparameterize(a)
|
||
|
|
ax1,ay1,bx1,by1,cx1,cy1,dx1,dy1 = bezmisc.bezierparameterize(b)
|
||
|
|
i = 0
|
||
|
|
F, F1 = [.0,.0], [[.0,.0],[.0,.0]]
|
||
|
|
while i==0 or (abs(F[0])**2+abs(F[1])**2 > tolerance and i<10):
|
||
|
|
ta3, ta2, tb3, tb2 = ta**3, ta**2, tb**3, tb**2
|
||
|
|
F[0] = ax*ta3+bx*ta2+cx*ta+dx-ax1*tb3-bx1*tb2-cx1*tb-dx1
|
||
|
|
F[1] = ay*ta3+by*ta2+cy*ta+dy-ay1*tb3-by1*tb2-cy1*tb-dy1
|
||
|
|
F1[0][0] = 3*ax *ta2 + 2*bx *ta + cx
|
||
|
|
F1[0][1] = -3*ax1*tb2 - 2*bx1*tb - cx1
|
||
|
|
F1[1][0] = 3*ay *ta2 + 2*by *ta + cy
|
||
|
|
F1[1][1] = -3*ay1*tb2 - 2*by1*tb - cy1
|
||
|
|
det = F1[0][0]*F1[1][1] - F1[0][1]*F1[1][0]
|
||
|
|
if det!=0 :
|
||
|
|
F1 = [ [ F1[1][1]/det, -F1[0][1]/det], [-F1[1][0]/det, F1[0][0]/det] ]
|
||
|
|
ta = ta - ( F1[0][0]*F[0] + F1[0][1]*F[1] )
|
||
|
|
tb = tb - ( F1[1][0]*F[0] + F1[1][1]*F[1] )
|
||
|
|
else: break
|
||
|
|
i += 1
|
||
|
|
|
||
|
|
return ta, tb
|
||
|
|
|
||
|
|
|
||
|
|
def recursion(a,b, ta0,ta1,tb0,tb1, depth_a,depth_b) :
|
||
|
|
global bezier_intersection_recursive_result
|
||
|
|
if a==b :
|
||
|
|
bezier_intersection_recursive_result += [[ta0,tb0,ta1,tb1,"Overlap"]]
|
||
|
|
return
|
||
|
|
tam, tbm = (ta0+ta1)/2, (tb0+tb1)/2
|
||
|
|
if depth_a>0 and depth_b>0 :
|
||
|
|
a1,a2 = bez_split(a,0.5)
|
||
|
|
b1,b2 = bez_split(b,0.5)
|
||
|
|
if bez_bounds_intersect(a1,b1) : recursion(a1,b1, ta0,tam,tb0,tbm, depth_a-1,depth_b-1)
|
||
|
|
if bez_bounds_intersect(a2,b1) : recursion(a2,b1, tam,ta1,tb0,tbm, depth_a-1,depth_b-1)
|
||
|
|
if bez_bounds_intersect(a1,b2) : recursion(a1,b2, ta0,tam,tbm,tb1, depth_a-1,depth_b-1)
|
||
|
|
if bez_bounds_intersect(a2,b2) : recursion(a2,b2, tam,ta1,tbm,tb1, depth_a-1,depth_b-1)
|
||
|
|
elif depth_a>0 :
|
||
|
|
a1,a2 = bez_split(a,0.5)
|
||
|
|
if bez_bounds_intersect(a1,b) : recursion(a1,b, ta0,tam,tb0,tb1, depth_a-1,depth_b)
|
||
|
|
if bez_bounds_intersect(a2,b) : recursion(a2,b, tam,ta1,tb0,tb1, depth_a-1,depth_b)
|
||
|
|
elif depth_b>0 :
|
||
|
|
b1,b2 = bez_split(b,0.5)
|
||
|
|
if bez_bounds_intersect(a,b1) : recursion(a,b1, ta0,ta1,tb0,tbm, depth_a,depth_b-1)
|
||
|
|
if bez_bounds_intersect(a,b2) : recursion(a,b2, ta0,ta1,tbm,tb1, depth_a,depth_b-1)
|
||
|
|
else : # Both segments have been subdevided enougth. Let's get some intersections :).
|
||
|
|
intersection, t1, t2 = straight_segments_intersection([a[0]]+[a[3]],[b[0]]+[b[3]])
|
||
|
|
if intersection :
|
||
|
|
if intersection == "Overlap" :
|
||
|
|
t1 = ( max(0,min(1,t1[0]))+max(0,min(1,t1[1])) )/2
|
||
|
|
t2 = ( max(0,min(1,t2[0]))+max(0,min(1,t2[1])) )/2
|
||
|
|
bezier_intersection_recursive_result += [[ta0+t1*(ta1-ta0),tb0+t2*(tb1-tb0)]]
|
||
|
|
|
||
|
|
global bezier_intersection_recursive_result
|
||
|
|
bezier_intersection_recursive_result = []
|
||
|
|
recursion(a,b,0.,1.,0.,1.,intersection_recursion_depth,intersection_recursion_depth)
|
||
|
|
intersections = bezier_intersection_recursive_result
|
||
|
|
for i in range(len(intersections)) :
|
||
|
|
if len(intersections[i])<5 or intersections[i][4] != "Overlap" :
|
||
|
|
intersections[i] = polish_intersection(a,b,intersections[i][0],intersections[i][1])
|
||
|
|
return intersections
|
||
|
|
|
||
|
|
|
||
|
|
def csp_segments_true_intersection(sp1,sp2,sp3,sp4) :
|
||
|
|
intersections = csp_segments_intersection(sp1,sp2,sp3,sp4)
|
||
|
|
res = []
|
||
|
|
for intersection in intersections :
|
||
|
|
if (
|
||
|
|
(len(intersection)==5 and intersection[4] == "Overlap" and (0<=intersection[0]<=1 or 0<=intersection[1]<=1) and (0<=intersection[2]<=1 or 0<=intersection[3]<=1) )
|
||
|
|
or ( 0<=intersection[0]<=1 and 0<=intersection[1]<=1 )
|
||
|
|
) :
|
||
|
|
res += [intersection]
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def csp_get_t_at_curvature(sp1,sp2,c, sample_points = 16):
|
||
|
|
# returns a list containning [t1,t2,t3,...,tn], 0<=ti<=1...
|
||
|
|
if sample_points < 2 : sample_points = 2
|
||
|
|
tolerance = .0000000001
|
||
|
|
res = []
|
||
|
|
ax,ay,bx,by,cx,cy,dx,dy = csp_parameterize(sp1,sp2)
|
||
|
|
for k in range(sample_points) :
|
||
|
|
t = float(k)/(sample_points-1)
|
||
|
|
i, F = 0, 1e100
|
||
|
|
while i<2 or abs(F)>tolerance and i<17 :
|
||
|
|
try : # some numerical calculation could exceed the limits
|
||
|
|
t2 = t*t
|
||
|
|
#slopes...
|
||
|
|
f1x = 3*ax*t2+2*bx*t+cx
|
||
|
|
f1y = 3*ay*t2+2*by*t+cy
|
||
|
|
f2x = 6*ax*t+2*bx
|
||
|
|
f2y = 6*ay*t+2*by
|
||
|
|
f3x = 6*ax
|
||
|
|
f3y = 6*ay
|
||
|
|
d = (f1x**2+f1y**2)**1.5
|
||
|
|
F1 = (
|
||
|
|
( (f1x*f3y-f3x*f1y)*d - (f1x*f2y-f2x*f1y)*3.*(f2x*f1x+f2y*f1y)*((f1x**2+f1y**2)**.5) ) /
|
||
|
|
((f1x**2+f1y**2)**3)
|
||
|
|
)
|
||
|
|
F = (f1x*f2y-f1y*f2x)/d - c
|
||
|
|
t -= F/F1
|
||
|
|
except:
|
||
|
|
break
|
||
|
|
i += 1
|
||
|
|
if 0<=t<=1 and F<=tolerance:
|
||
|
|
if len(res) == 0 :
|
||
|
|
res.append(t)
|
||
|
|
for i in res :
|
||
|
|
if abs(t-i)<=0.001 :
|
||
|
|
break
|
||
|
|
if not abs(t-i)<=0.001 :
|
||
|
|
res.append(t)
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def csp_max_curvature(sp1,sp2):
|
||
|
|
ax,ay,bx,by,cx,cy,dx,dy = csp_parameterize(sp1,sp2)
|
||
|
|
tolerance = .0001
|
||
|
|
F = 0.
|
||
|
|
i = 0
|
||
|
|
while i<2 or F-Flast<tolerance and i<10 :
|
||
|
|
t = .5
|
||
|
|
f1x = 3*ax*t**2 + 2*bx*t + cx
|
||
|
|
f1y = 3*ay*t**2 + 2*by*t + cy
|
||
|
|
f2x = 6*ax*t + 2*bx
|
||
|
|
f2y = 6*ay*t + 2*by
|
||
|
|
f3x = 6*ax
|
||
|
|
f3y = 6*ay
|
||
|
|
d = pow(f1x**2+f1y**2,1.5)
|
||
|
|
if d != 0 :
|
||
|
|
Flast = F
|
||
|
|
F = (f1x*f2y-f1y*f2x)/d
|
||
|
|
F1 = (
|
||
|
|
( d*(f1x*f3y-f3x*f1y) - (f1x*f2y-f2x*f1y)*3.*(f2x*f1x+f2y*f1y)*pow(f1x**2+f1y**2,.5) ) /
|
||
|
|
(f1x**2+f1y**2)**3
|
||
|
|
)
|
||
|
|
i+=1
|
||
|
|
if F1!=0:
|
||
|
|
t -= F/F1
|
||
|
|
else:
|
||
|
|
break
|
||
|
|
else: break
|
||
|
|
return t
|
||
|
|
|
||
|
|
|
||
|
|
def csp_curvature_at_t(sp1,sp2,t, depth = 3) :
|
||
|
|
ax,ay,bx,by,cx,cy,dx,dy = bezmisc.bezierparameterize(csp_segment_to_bez(sp1,sp2))
|
||
|
|
|
||
|
|
#curvature = (x'y''-y'x'') / (x'^2+y'^2)^1.5
|
||
|
|
|
||
|
|
f1x = 3*ax*t**2 + 2*bx*t + cx
|
||
|
|
f1y = 3*ay*t**2 + 2*by*t + cy
|
||
|
|
f2x = 6*ax*t + 2*bx
|
||
|
|
f2y = 6*ay*t + 2*by
|
||
|
|
d = (f1x**2+f1y**2)**1.5
|
||
|
|
if d != 0 :
|
||
|
|
return (f1x*f2y-f1y*f2x)/d
|
||
|
|
else :
|
||
|
|
t1 = f1x*f2y-f1y*f2x
|
||
|
|
if t1 > 0 : return 1e100
|
||
|
|
if t1 < 0 : return -1e100
|
||
|
|
# Use the Lapitals rule to solve 0/0 problem for 2 times...
|
||
|
|
t1 = 2*(bx*ay-ax*by)*t+(ay*cx-ax*cy)
|
||
|
|
if t1 > 0 : return 1e100
|
||
|
|
if t1 < 0 : return -1e100
|
||
|
|
t1 = bx*ay-ax*by
|
||
|
|
if t1 > 0 : return 1e100
|
||
|
|
if t1 < 0 : return -1e100
|
||
|
|
if depth>0 :
|
||
|
|
# little hack ;^) hope it wont influence anything...
|
||
|
|
return csp_curvature_at_t(sp1,sp2,t*1.004, depth-1)
|
||
|
|
return 1e100
|
||
|
|
|
||
|
|
|
||
|
|
def csp_curvature_radius_at_t(sp1,sp2,t) :
|
||
|
|
c = csp_curvature_at_t(sp1,sp2,t)
|
||
|
|
if c == 0 : return 1e100
|
||
|
|
else: return 1/c
|
||
|
|
|
||
|
|
|
||
|
|
def csp_special_points(sp1,sp2) :
|
||
|
|
# special points = curvature == 0
|
||
|
|
ax,ay,bx,by,cx,cy,dx,dy = bezmisc.bezierparameterize((sp1[1],sp1[2],sp2[0],sp2[1]))
|
||
|
|
a = 3*ax*by-3*ay*bx
|
||
|
|
b = 3*ax*cy-3*cx*ay
|
||
|
|
c = bx*cy-cx*by
|
||
|
|
roots = cubic_solver(0, a, b, c)
|
||
|
|
res = []
|
||
|
|
for i in roots :
|
||
|
|
if type(i) is complex and i.imag==0:
|
||
|
|
i = i.real
|
||
|
|
if type(i) is not complex and 0<=i<=1:
|
||
|
|
res.append(i)
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
def csp_subpath_ccw(subpath):
|
||
|
|
# Remove all zerro length segments
|
||
|
|
s = 0
|
||
|
|
#subpath = subpath[:]
|
||
|
|
if (P(subpath[-1][1])-P(subpath[0][1])).l2() > 1e-10 :
|
||
|
|
subpath[-1][2] = subpath[-1][1]
|
||
|
|
subpath[0][0] = subpath[0][1]
|
||
|
|
subpath += [ [subpath[0][1],subpath[0][1],subpath[0][1]] ]
|
||
|
|
pl = subpath[-1][2]
|
||
|
|
for sp1 in subpath:
|
||
|
|
for p in sp1 :
|
||
|
|
s += (p[0]-pl[0])*(p[1]+pl[1])
|
||
|
|
pl = p
|
||
|
|
return s<0
|
||
|
|
|
||
|
|
|
||
|
|
def csp_at_t(sp1,sp2,t):
|
||
|
|
ax,bx,cx,dx = sp1[1][0], sp1[2][0], sp2[0][0], sp2[1][0]
|
||
|
|
ay,by,cy,dy = sp1[1][1], sp1[2][1], sp2[0][1], sp2[1][1]
|
||
|
|
|
||
|
|
x1, y1 = ax+(bx-ax)*t, ay+(by-ay)*t
|
||
|
|
x2, y2 = bx+(cx-bx)*t, by+(cy-by)*t
|
||
|
|
x3, y3 = cx+(dx-cx)*t, cy+(dy-cy)*t
|
||
|
|
|
||
|
|
x4,y4 = x1+(x2-x1)*t, y1+(y2-y1)*t
|
||
|
|
x5,y5 = x2+(x3-x2)*t, y2+(y3-y2)*t
|
||
|
|
|
||
|
|
x,y = x4+(x5-x4)*t, y4+(y5-y4)*t
|
||
|
|
return [x,y]
|
||
|
|
|
||
|
|
|
||
|
|
def csp_splitatlength(sp1, sp2, l = 0.5, tolerance = 0.01):
|
||
|
|
bez = (sp1[1][:],sp1[2][:],sp2[0][:],sp2[1][:])
|
||
|
|
t = bezmisc.beziertatlength(bez, l, tolerance)
|
||
|
|
return csp_split(sp1, sp2, t)
|
||
|
|
|
||
|
|
|
||
|
|
def cspseglength(sp1,sp2, tolerance = 0.001):
|
||
|
|
bez = (sp1[1][:],sp1[2][:],sp2[0][:],sp2[1][:])
|
||
|
|
return bezmisc.bezierlength(bez, tolerance)
|
||
|
|
|
||
|
|
|
||
|
|
def csplength(csp):
|
||
|
|
total = 0
|
||
|
|
lengths = []
|
||
|
|
for sp in csp:
|
||
|
|
for i in xrange(1,len(sp)):
|
||
|
|
l = cspseglength(sp[i-1],sp[i])
|
||
|
|
lengths.append(l)
|
||
|
|
total += l
|
||
|
|
return lengths, total
|
||
|
|
|
||
|
|
|
||
|
|
def csp_segments(csp):
|
||
|
|
l, seg = 0, [0]
|
||
|
|
for sp in csp:
|
||
|
|
for i in xrange(1,len(sp)):
|
||
|
|
l += cspseglength(sp[i-1],sp[i])
|
||
|
|
seg += [ l ]
|
||
|
|
|
||
|
|
if l>0 :
|
||
|
|
seg = [seg[i]/l for i in xrange(len(seg))]
|
||
|
|
return seg,l
|
||
|
|
|
||
|
|
|
||
|
|
def rebuild_csp (csp, segs, s=None):
|
||
|
|
# rebuild_csp() adds to csp control points making it's segments looks like segs
|
||
|
|
if s==None : s, l = csp_segments(csp)
|
||
|
|
|
||
|
|
if len(s)>len(segs) : return None
|
||
|
|
segs = segs[:]
|
||
|
|
segs.sort()
|
||
|
|
for i in xrange(len(s)):
|
||
|
|
d = None
|
||
|
|
for j in xrange(len(segs)):
|
||
|
|
d = min( [abs(s[i]-segs[j]),j], d) if d!=None else [abs(s[i]-segs[j]),j]
|
||
|
|
del segs[d[1]]
|
||
|
|
for i in xrange(len(segs)):
|
||
|
|
for j in xrange(0,len(s)):
|
||
|
|
if segs[i]<s[j] : break
|
||
|
|
if s[j]-s[j-1] != 0 :
|
||
|
|
t = (segs[i] - s[j-1])/(s[j]-s[j-1])
|
||
|
|
sp1,sp2,sp3 = csp_split(csp[j-1],csp[j], t)
|
||
|
|
csp = csp[:j-1] + [sp1,sp2,sp3] + csp[j+1:]
|
||
|
|
s = s[:j] + [ s[j-1]*(1-t)+s[j]*t ] + s[j:]
|
||
|
|
return csp, s
|
||
|
|
|
||
|
|
|
||
|
|
def csp_slope(sp1,sp2,t):
|
||
|
|
bez = (sp1[1][:],sp1[2][:],sp2[0][:],sp2[1][:])
|
||
|
|
return bezmisc.bezierslopeatt(bez,t)
|
||
|
|
|
||
|
|
|
||
|
|
def csp_line_intersection(l1,l2,sp1,sp2):
|
||
|
|
dd=l1[0]
|
||
|
|
cc=l2[0]-l1[0]
|
||
|
|
bb=l1[1]
|
||
|
|
aa=l2[1]-l1[1]
|
||
|
|
if aa==cc==0 : return []
|
||
|
|
if aa:
|
||
|
|
coef1=cc/aa
|
||
|
|
coef2=1
|
||
|
|
else:
|
||
|
|
coef1=1
|
||
|
|
coef2=aa/cc
|
||
|
|
bez = (sp1[1][:],sp1[2][:],sp2[0][:],sp2[1][:])
|
||
|
|
ax,ay,bx,by,cx,cy,x0,y0=bezmisc.bezierparameterize(bez)
|
||
|
|
a=coef1*ay-coef2*ax
|
||
|
|
b=coef1*by-coef2*bx
|
||
|
|
c=coef1*cy-coef2*cx
|
||
|
|
d=coef1*(y0-bb)-coef2*(x0-dd)
|
||
|
|
roots = cubic_solver(a,b,c,d)
|
||
|
|
retval = []
|
||
|
|
for i in roots :
|
||
|
|
if type(i) is complex and abs(i.imag)<1e-7:
|
||
|
|
i = i.real
|
||
|
|
if type(i) is not complex and -1e-10<=i<=1.+1e-10:
|
||
|
|
retval.append(i)
|
||
|
|
return retval
|
||
|
|
|
||
|
|
|
||
|
|
def csp_split_by_two_points(sp1,sp2,t1,t2) :
|
||
|
|
if t1>t2 : t1, t2 = t2, t1
|
||
|
|
if t1 == t2 :
|
||
|
|
sp1,sp2,sp3 = csp_split(sp1,sp2,t)
|
||
|
|
return [sp1,sp2,sp2,sp3]
|
||
|
|
elif t1 <= 1e-10 and t2 >= 1.-1e-10 :
|
||
|
|
return [sp1,sp1,sp2,sp2]
|
||
|
|
elif t1 <= 1e-10:
|
||
|
|
sp1,sp2,sp3 = csp_split(sp1,sp2,t2)
|
||
|
|
return [sp1,sp1,sp2,sp3]
|
||
|
|
elif t2 >= 1.-1e-10 :
|
||
|
|
sp1,sp2,sp3 = csp_split(sp1,sp2,t1)
|
||
|
|
return [sp1,sp2,sp3,sp3]
|
||
|
|
else:
|
||
|
|
sp1,sp2,sp3 = csp_split(sp1,sp2,t1)
|
||
|
|
sp2,sp3,sp4 = csp_split(sp2,sp3,(t2-t1)/(1-t1) )
|
||
|
|
return [sp1,sp2,sp3,sp4]
|
||
|
|
|
||
|
|
|
||
|
|
def csp_subpath_split_by_points(subpath, points) :
|
||
|
|
# points are [[i,t]...] where i-segment's number
|
||
|
|
points.sort()
|
||
|
|
points = [[1,0.]] + points + [[len(subpath)-1,1.]]
|
||
|
|
parts = []
|
||
|
|
for int1,int2 in zip(points,points[1:]) :
|
||
|
|
if int1==int2 :
|
||
|
|
continue
|
||
|
|
if int1[1] == 1. :
|
||
|
|
int1[0] += 1
|
||
|
|
int1[1] = 0.
|
||
|
|
if int1==int2 :
|
||
|
|
continue
|
||
|
|
if int2[1] == 0. :
|
||
|
|
int2[0] -= 1
|
||
|
|
int2[1] = 1.
|
||
|
|
if int1[0] == 0 and int2[0]==len(subpath)-1:# and small(int1[1]) and small(int2[1]-1) :
|
||
|
|
continue
|
||
|
|
if int1[0]==int2[0] : # same segment
|
||
|
|
sp = csp_split_by_two_points(subpath[int1[0]-1],subpath[int1[0]],int1[1], int2[1])
|
||
|
|
if sp[1]!=sp[2] :
|
||
|
|
parts += [ [sp[1],sp[2]] ]
|
||
|
|
else :
|
||
|
|
sp5,sp1,sp2 = csp_split(subpath[int1[0]-1],subpath[int1[0]],int1[1])
|
||
|
|
sp3,sp4,sp5 = csp_split(subpath[int2[0]-1],subpath[int2[0]],int2[1])
|
||
|
|
if int1[0]==int2[0]-1 :
|
||
|
|
parts += [ [sp1, [sp2[0],sp2[1],sp3[2]], sp4] ]
|
||
|
|
else :
|
||
|
|
parts += [ [sp1,sp2]+subpath[int1[0]+1:int2[0]-1]+[sp3,sp4] ]
|
||
|
|
return parts
|
||
|
|
|
||
|
|
|
||
|
|
def csp_from_arc(start, end, center, r, slope_st) :
|
||
|
|
# Creates csp that approximise specified arc
|
||
|
|
r = abs(r)
|
||
|
|
alpha = (atan2(end[0]-center[0],end[1]-center[1]) - atan2(start[0]-center[0],start[1]-center[1])) % math.pi2
|
||
|
|
|
||
|
|
sectors = int(abs(alpha)*2/math.pi)+1
|
||
|
|
alpha_start = atan2(start[0]-center[0],start[1]-center[1])
|
||
|
|
cos_,sin_ = math.cos(alpha_start), math.sin(alpha_start)
|
||
|
|
k = (4.*math.tan(alpha/sectors/4.)/3.)
|
||
|
|
if dot(slope_st , [- sin_*k*r, cos_*k*r]) < 0 :
|
||
|
|
if alpha>0 : alpha -= math.pi2
|
||
|
|
else: alpha += math.pi2
|
||
|
|
if abs(alpha*r)<0.001 :
|
||
|
|
return []
|
||
|
|
|
||
|
|
sectors = int(abs(alpha)*2/math.pi)+1
|
||
|
|
k = (4.*math.tan(alpha/sectors/4.)/3.)
|
||
|
|
result = []
|
||
|
|
for i in range(sectors+1) :
|
||
|
|
cos_,sin_ = math.cos(alpha_start + alpha*i/sectors), math.sin(alpha_start + alpha*i/sectors)
|
||
|
|
sp = [ [], [center[0] + cos_*r, center[1] + sin_*r], [] ]
|
||
|
|
sp[0] = [sp[1][0] + sin_*k*r, sp[1][1] - cos_*k*r ]
|
||
|
|
sp[2] = [sp[1][0] - sin_*k*r, sp[1][1] + cos_*k*r ]
|
||
|
|
result += [sp]
|
||
|
|
result[0][0] = result[0][1][:]
|
||
|
|
result[-1][2] = result[-1][1]
|
||
|
|
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def point_to_arc_distance(p, arc):
|
||
|
|
### Distance calculattion from point to arc
|
||
|
|
P0,P2,c,a = arc
|
||
|
|
dist = None
|
||
|
|
p = P(p)
|
||
|
|
r = (P0-c).mag()
|
||
|
|
if r>0 :
|
||
|
|
i = c + (p-c).unit()*r
|
||
|
|
alpha = ((i-c).angle() - (P0-c).angle())
|
||
|
|
if a*alpha<0:
|
||
|
|
if alpha>0: alpha = alpha-math.pi2
|
||
|
|
else: alpha = math.pi2+alpha
|
||
|
|
if between(alpha,0,a) or min(abs(alpha),abs(alpha-a))<straight_tolerance :
|
||
|
|
return (p-i).mag(), [i.x, i.y]
|
||
|
|
else :
|
||
|
|
d1, d2 = (p-P0).mag(), (p-P2).mag()
|
||
|
|
if d1<d2 :
|
||
|
|
return (d1, [P0.x,P0.y])
|
||
|
|
else :
|
||
|
|
return (d2, [P2.x,P2.y])
|
||
|
|
|
||
|
|
|
||
|
|
def csp_to_arc_distance(sp1,sp2, arc1, arc2, tolerance = 0.01 ): # arc = [start,end,center,alpha]
|
||
|
|
n, i = 10, 0
|
||
|
|
d, d1, dl = (0,(0,0)), (0,(0,0)), 0
|
||
|
|
while i<1 or (abs(d1[0]-dl[0])>tolerance and i<4):
|
||
|
|
i += 1
|
||
|
|
dl = d1*1
|
||
|
|
for j in range(n+1):
|
||
|
|
t = float(j)/n
|
||
|
|
p = csp_at_t(sp1,sp2,t)
|
||
|
|
d = min(point_to_arc_distance(p,arc1), point_to_arc_distance(p,arc2))
|
||
|
|
d1 = max(d1,d)
|
||
|
|
n=n*2
|
||
|
|
return d1[0]
|
||
|
|
|
||
|
|
|
||
|
|
def csp_simple_bound_to_point_distance(p, csp):
|
||
|
|
minx,miny,maxx,maxy = None,None,None,None
|
||
|
|
for subpath in csp:
|
||
|
|
for sp in subpath:
|
||
|
|
for p_ in sp:
|
||
|
|
minx = min(minx,p_[0]) if minx!=None else p_[0]
|
||
|
|
miny = min(miny,p_[1]) if miny!=None else p_[1]
|
||
|
|
maxx = max(maxx,p_[0]) if maxx!=None else p_[0]
|
||
|
|
maxy = max(maxy,p_[1]) if maxy!=None else p_[1]
|
||
|
|
return math.sqrt(max(minx-p[0],p[0]-maxx,0)**2+max(miny-p[1],p[1]-maxy,0)**2)
|
||
|
|
|
||
|
|
|
||
|
|
def csp_point_inside_bound(sp1, sp2, p):
|
||
|
|
bez = [sp1[1],sp1[2],sp2[0],sp2[1]]
|
||
|
|
x,y = p
|
||
|
|
c = 0
|
||
|
|
for i in range(4):
|
||
|
|
[x0,y0], [x1,y1] = bez[i-1], bez[i]
|
||
|
|
if x0-x1!=0 and (y-y0)*(x1-x0)>=(x-x0)*(y1-y0) and x>min(x0,x1) and x<=max(x0,x1) :
|
||
|
|
c +=1
|
||
|
|
return c%2==0
|
||
|
|
|
||
|
|
|
||
|
|
def csp_bound_to_point_distance(sp1, sp2, p):
|
||
|
|
if csp_point_inside_bound(sp1, sp2, p) :
|
||
|
|
return 0.
|
||
|
|
bez = csp_segment_to_bez(sp1,sp2)
|
||
|
|
min_dist = 1e100
|
||
|
|
for i in range(0,4):
|
||
|
|
d = point_to_line_segment_distance_2(p, bez[i-1],bez[i])
|
||
|
|
if d <= min_dist : min_dist = d
|
||
|
|
return min_dist
|
||
|
|
|
||
|
|
|
||
|
|
def line_line_intersect(p1,p2,p3,p4) : # Return only true intersection.
|
||
|
|
if (p1[0]==p2[0] and p1[1]==p2[1]) or (p3[0]==p4[0] and p3[1]==p4[1]) : return False
|
||
|
|
x = (p2[0]-p1[0])*(p4[1]-p3[1]) - (p2[1]-p1[1])*(p4[0]-p3[0])
|
||
|
|
if x==0 : # Lines are parallel
|
||
|
|
if (p3[0]-p1[0])*(p2[1]-p1[1]) == (p3[1]-p1[1])*(p2[0]-p1[0]) :
|
||
|
|
if p3[0]!=p4[0] :
|
||
|
|
t11 = (p1[0]-p3[0])/(p4[0]-p3[0])
|
||
|
|
t12 = (p2[0]-p3[0])/(p4[0]-p3[0])
|
||
|
|
t21 = (p3[0]-p1[0])/(p2[0]-p1[0])
|
||
|
|
t22 = (p4[0]-p1[0])/(p2[0]-p1[0])
|
||
|
|
else:
|
||
|
|
t11 = (p1[1]-p3[1])/(p4[1]-p3[1])
|
||
|
|
t12 = (p2[1]-p3[1])/(p4[1]-p3[1])
|
||
|
|
t21 = (p3[1]-p1[1])/(p2[1]-p1[1])
|
||
|
|
t22 = (p4[1]-p1[1])/(p2[1]-p1[1])
|
||
|
|
return ("Overlap" if (0<=t11<=1 or 0<=t12<=1) and (0<=t21<=1 or 0<=t22<=1) else False)
|
||
|
|
else: return False
|
||
|
|
else :
|
||
|
|
return (
|
||
|
|
0<=((p4[0]-p3[0])*(p1[1]-p3[1]) - (p4[1]-p3[1])*(p1[0]-p3[0]))/x<=1 and
|
||
|
|
0<=((p2[0]-p1[0])*(p1[1]-p3[1]) - (p2[1]-p1[1])*(p1[0]-p3[0]))/x<=1 )
|
||
|
|
|
||
|
|
|
||
|
|
def line_line_intersection_points(p1,p2,p3,p4) : # Return only points [ (x,y) ]
|
||
|
|
if (p1[0]==p2[0] and p1[1]==p2[1]) or (p3[0]==p4[0] and p3[1]==p4[1]) : return []
|
||
|
|
x = (p2[0]-p1[0])*(p4[1]-p3[1]) - (p2[1]-p1[1])*(p4[0]-p3[0])
|
||
|
|
if x==0 : # Lines are parallel
|
||
|
|
if (p3[0]-p1[0])*(p2[1]-p1[1]) == (p3[1]-p1[1])*(p2[0]-p1[0]) :
|
||
|
|
if p3[0]!=p4[0] :
|
||
|
|
t11 = (p1[0]-p3[0])/(p4[0]-p3[0])
|
||
|
|
t12 = (p2[0]-p3[0])/(p4[0]-p3[0])
|
||
|
|
t21 = (p3[0]-p1[0])/(p2[0]-p1[0])
|
||
|
|
t22 = (p4[0]-p1[0])/(p2[0]-p1[0])
|
||
|
|
else:
|
||
|
|
t11 = (p1[1]-p3[1])/(p4[1]-p3[1])
|
||
|
|
t12 = (p2[1]-p3[1])/(p4[1]-p3[1])
|
||
|
|
t21 = (p3[1]-p1[1])/(p2[1]-p1[1])
|
||
|
|
t22 = (p4[1]-p1[1])/(p2[1]-p1[1])
|
||
|
|
res = []
|
||
|
|
if (0<=t11<=1 or 0<=t12<=1) and (0<=t21<=1 or 0<=t22<=1) :
|
||
|
|
if 0<=t11<=1 : res += [p1]
|
||
|
|
if 0<=t12<=1 : res += [p2]
|
||
|
|
if 0<=t21<=1 : res += [p3]
|
||
|
|
if 0<=t22<=1 : res += [p4]
|
||
|
|
return res
|
||
|
|
else: return []
|
||
|
|
else :
|
||
|
|
t1 = ((p4[0]-p3[0])*(p1[1]-p3[1]) - (p4[1]-p3[1])*(p1[0]-p3[0]))/x
|
||
|
|
t2 = ((p2[0]-p1[0])*(p1[1]-p3[1]) - (p2[1]-p1[1])*(p1[0]-p3[0]))/x
|
||
|
|
if 0<=t1<=1 and 0<=t2<=1 : return [ [p1[0]*(1-t1)+p2[0]*t1, p1[1]*(1-t1)+p2[1]*t1] ]
|
||
|
|
else : return []
|
||
|
|
|
||
|
|
|
||
|
|
def point_to_point_d2(a,b):
|
||
|
|
return (a[0]-b[0])**2 + (a[1]-b[1])**2
|
||
|
|
|
||
|
|
|
||
|
|
def point_to_point_d(a,b):
|
||
|
|
return math.sqrt((a[0]-b[0])**2 + (a[1]-b[1])**2)
|
||
|
|
|
||
|
|
|
||
|
|
def point_to_line_segment_distance_2(p1, p2,p3) :
|
||
|
|
# p1 - point, p2,p3 - line segment
|
||
|
|
#draw_pointer(p1)
|
||
|
|
w0 = [p1[0]-p2[0], p1[1]-p2[1]]
|
||
|
|
v = [p3[0]-p2[0], p3[1]-p2[1]]
|
||
|
|
c1 = w0[0]*v[0] + w0[1]*v[1]
|
||
|
|
if c1 <= 0 :
|
||
|
|
return w0[0]*w0[0]+w0[1]*w0[1]
|
||
|
|
c2 = v[0]*v[0] + v[1]*v[1]
|
||
|
|
if c2 <= c1 :
|
||
|
|
return (p1[0]-p3[0])**2 + (p1[1]-p3[1])**2
|
||
|
|
return (p1[0]- p2[0]-v[0]*c1/c2)**2 + (p1[1]- p2[1]-v[1]*c1/c2)
|
||
|
|
|
||
|
|
|
||
|
|
def line_to_line_distance_2(p1,p2,p3,p4):
|
||
|
|
if line_line_intersect(p1,p2,p3,p4) : return 0
|
||
|
|
return min(
|
||
|
|
point_to_line_segment_distance_2(p1,p3,p4),
|
||
|
|
point_to_line_segment_distance_2(p2,p3,p4),
|
||
|
|
point_to_line_segment_distance_2(p3,p1,p2),
|
||
|
|
point_to_line_segment_distance_2(p4,p1,p2))
|
||
|
|
|
||
|
|
|
||
|
|
def csp_seg_bound_to_csp_seg_bound_max_min_distance(sp1,sp2,sp3,sp4) :
|
||
|
|
bez1 = csp_segment_to_bez(sp1,sp2)
|
||
|
|
bez2 = csp_segment_to_bez(sp3,sp4)
|
||
|
|
min_dist = 1e100
|
||
|
|
max_dist = 0.
|
||
|
|
for i in range(4) :
|
||
|
|
if csp_point_inside_bound(sp1, sp2, bez2[i]) or csp_point_inside_bound(sp3, sp4, bez1[i]) :
|
||
|
|
min_dist = 0.
|
||
|
|
break
|
||
|
|
for i in range(4) :
|
||
|
|
for j in range(4) :
|
||
|
|
d = line_to_line_distance_2(bez1[i-1],bez1[i],bez2[j-1],bez2[j])
|
||
|
|
if d < min_dist : min_dist = d
|
||
|
|
d = (bez2[j][0]-bez1[i][0])**2 + (bez2[j][1]-bez1[i][1])**2
|
||
|
|
if max_dist < d : max_dist = d
|
||
|
|
return min_dist, max_dist
|
||
|
|
|
||
|
|
|
||
|
|
def csp_reverse(csp) :
|
||
|
|
for i in range(len(csp)) :
|
||
|
|
n = []
|
||
|
|
for j in csp[i] :
|
||
|
|
n = [ [j[2][:],j[1][:],j[0][:]] ] + n
|
||
|
|
csp[i] = n[:]
|
||
|
|
return csp
|
||
|
|
|
||
|
|
|
||
|
|
def csp_normalized_slope(sp1,sp2,t) :
|
||
|
|
ax,ay,bx,by,cx,cy,dx,dy=bezmisc.bezierparameterize((sp1[1][:],sp1[2][:],sp2[0][:],sp2[1][:]))
|
||
|
|
if sp1[1]==sp2[1]==sp1[2]==sp2[0] : return [1.,0.]
|
||
|
|
f1x = 3*ax*t*t+2*bx*t+cx
|
||
|
|
f1y = 3*ay*t*t+2*by*t+cy
|
||
|
|
if abs(f1x*f1x+f1y*f1y) > 1e-20 :
|
||
|
|
l = math.sqrt(f1x*f1x+f1y*f1y)
|
||
|
|
return [f1x/l, f1y/l]
|
||
|
|
|
||
|
|
if t == 0 :
|
||
|
|
f1x = sp2[0][0]-sp1[1][0]
|
||
|
|
f1y = sp2[0][1]-sp1[1][1]
|
||
|
|
if abs(f1x*f1x+f1y*f1y) > 1e-20 :
|
||
|
|
l = math.sqrt(f1x*f1x+f1y*f1y)
|
||
|
|
return [f1x/l, f1y/l]
|
||
|
|
else :
|
||
|
|
f1x = sp2[1][0]-sp1[1][0]
|
||
|
|
f1y = sp2[1][1]-sp1[1][1]
|
||
|
|
if f1x*f1x+f1y*f1y != 0 :
|
||
|
|
l = math.sqrt(f1x*f1x+f1y*f1y)
|
||
|
|
return [f1x/l, f1y/l]
|
||
|
|
elif t == 1 :
|
||
|
|
f1x = sp2[1][0]-sp1[2][0]
|
||
|
|
f1y = sp2[1][1]-sp1[2][1]
|
||
|
|
if abs(f1x*f1x+f1y*f1y) > 1e-20 :
|
||
|
|
l = math.sqrt(f1x*f1x+f1y*f1y)
|
||
|
|
return [f1x/l, f1y/l]
|
||
|
|
else :
|
||
|
|
f1x = sp2[1][0]-sp1[1][0]
|
||
|
|
f1y = sp2[1][1]-sp1[1][1]
|
||
|
|
if f1x*f1x+f1y*f1y != 0 :
|
||
|
|
l = math.sqrt(f1x*f1x+f1y*f1y)
|
||
|
|
return [f1x/l, f1y/l]
|
||
|
|
else :
|
||
|
|
return [1.,0.]
|
||
|
|
|
||
|
|
|
||
|
|
def csp_normalized_normal(sp1,sp2,t) :
|
||
|
|
nx,ny = csp_normalized_slope(sp1,sp2,t)
|
||
|
|
return [-ny, nx]
|
||
|
|
|
||
|
|
|
||
|
|
def csp_parameterize(sp1,sp2):
|
||
|
|
return bezmisc.bezierparameterize(csp_segment_to_bez(sp1,sp2))
|
||
|
|
|
||
|
|
|
||
|
|
def csp_concat_subpaths(*s):
|
||
|
|
|
||
|
|
def concat(s1,s2) :
|
||
|
|
if s1 == [] : return s2
|
||
|
|
if s2 == [] : return s1
|
||
|
|
if (s1[-1][1][0]-s2[0][1][0])**2 + (s1[-1][1][1]-s2[0][1][1])**2 > 0.00001 :
|
||
|
|
return s1[:-1]+[ [s1[-1][0],s1[-1][1],s1[-1][1]], [s2[0][1],s2[0][1],s2[0][2]] ] + s2[1:]
|
||
|
|
else :
|
||
|
|
return s1[:-1]+[ [s1[-1][0],s2[0][1],s2[0][2]] ] + s2[1:]
|
||
|
|
|
||
|
|
if len(s) == 0 : return []
|
||
|
|
if len(s) ==1 : return s[0]
|
||
|
|
result = s[0]
|
||
|
|
for s1 in s[1:]:
|
||
|
|
result = concat(result,s1)
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def csp_draw(csp, color="#05f", group = None, style="fill:none;", width = .1, comment = "") :
|
||
|
|
if csp!=[] and csp!=[[]] :
|
||
|
|
if group == None : group = options.doc_root
|
||
|
|
style += "stroke:"+color+";"+ "stroke-width:%0.4fpx;"%width
|
||
|
|
args = {"d": cubicsuperpath.formatPath(csp), "style":style}
|
||
|
|
if comment!="" : args["comment"] = str(comment)
|
||
|
|
inkex.etree.SubElement( group, inkex.addNS('path','svg'), args )
|
||
|
|
|
||
|
|
|
||
|
|
def csp_subpaths_end_to_start_distance2(s1,s2):
|
||
|
|
return (s1[-1][1][0]-s2[0][1][0])**2 + (s1[-1][1][1]-s2[0][1][1])**2
|
||
|
|
|
||
|
|
|
||
|
|
def csp_clip_by_line(csp,l1,l2) :
|
||
|
|
result = []
|
||
|
|
for i in range(len(csp)):
|
||
|
|
s = csp[i]
|
||
|
|
intersections = []
|
||
|
|
for j in range(1,len(s)) :
|
||
|
|
intersections += [ [j,int_] for int_ in csp_line_intersection(l1,l2,s[j-1],s[j])]
|
||
|
|
splitted_s = csp_subpath_split_by_points(s, intersections)
|
||
|
|
for s in splitted_s[:] :
|
||
|
|
clip = False
|
||
|
|
for p in csp_true_bounds([s]) :
|
||
|
|
if (l1[1]-l2[1])*p[0] + (l2[0]-l1[0])*p[1] + (l1[0]*l2[1]-l2[0]*l1[1])<-0.01 :
|
||
|
|
clip = True
|
||
|
|
break
|
||
|
|
if clip :
|
||
|
|
splitted_s.remove(s)
|
||
|
|
result += splitted_s
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def csp_subpath_line_to(subpath, points) :
|
||
|
|
# Appends subpath with line or polyline.
|
||
|
|
if len(points)>0 :
|
||
|
|
if len(subpath)>0:
|
||
|
|
subpath[-1][2] = subpath[-1][1][:]
|
||
|
|
if type(points[0]) == type([1,1]) :
|
||
|
|
for p in points :
|
||
|
|
subpath += [ [p[:],p[:],p[:]] ]
|
||
|
|
else:
|
||
|
|
subpath += [ [points,points,points] ]
|
||
|
|
return subpath
|
||
|
|
|
||
|
|
|
||
|
|
def csp_join_subpaths(csp) :
|
||
|
|
result = csp[:]
|
||
|
|
done_smf = True
|
||
|
|
joined_result = []
|
||
|
|
while done_smf :
|
||
|
|
done_smf = False
|
||
|
|
while len(result)>0:
|
||
|
|
s1 = result[-1][:]
|
||
|
|
del(result[-1])
|
||
|
|
j = 0
|
||
|
|
joined_smf = False
|
||
|
|
while j<len(joined_result) :
|
||
|
|
if csp_subpaths_end_to_start_distance2(joined_result[j],s1) <0.000001 :
|
||
|
|
joined_result[j] = csp_concat_subpaths(joined_result[j],s1)
|
||
|
|
done_smf = True
|
||
|
|
joined_smf = True
|
||
|
|
break
|
||
|
|
if csp_subpaths_end_to_start_distance2(s1,joined_result[j]) <0.000001 :
|
||
|
|
joined_result[j] = csp_concat_subpaths(s1,joined_result[j])
|
||
|
|
done_smf = True
|
||
|
|
joined_smf = True
|
||
|
|
break
|
||
|
|
j += 1
|
||
|
|
if not joined_smf : joined_result += [s1[:]]
|
||
|
|
if done_smf :
|
||
|
|
result = joined_result[:]
|
||
|
|
joined_result = []
|
||
|
|
return joined_result
|
||
|
|
|
||
|
|
|
||
|
|
def triangle_cross(a,b,c):
|
||
|
|
return (a[0]-b[0])*(c[1]-b[1]) - (c[0]-b[0])*(a[1]-b[1])
|
||
|
|
|
||
|
|
|
||
|
|
def csp_segment_convex_hull(sp1,sp2):
|
||
|
|
a,b,c,d = sp1[1][:], sp1[2][:], sp2[0][:], sp2[1][:]
|
||
|
|
|
||
|
|
abc = triangle_cross(a,b,c)
|
||
|
|
abd = triangle_cross(a,b,d)
|
||
|
|
bcd = triangle_cross(b,c,d)
|
||
|
|
cad = triangle_cross(c,a,d)
|
||
|
|
if abc == 0 and abd == 0 : return [min(a,b,c,d), max(a,b,c,d)]
|
||
|
|
if abc == 0 : return [d, min(a,b,c), max(a,b,c)]
|
||
|
|
if abd == 0 : return [c, min(a,b,d), max(a,b,d)]
|
||
|
|
if bcd == 0 : return [a, min(b,c,d), max(b,c,d)]
|
||
|
|
if cad == 0 : return [b, min(c,a,d), max(c,a,d)]
|
||
|
|
|
||
|
|
m1, m2, m3 = abc*abd>0, abc*bcd>0, abc*cad>0
|
||
|
|
if m1 and m2 and m3 : return [a,b,c]
|
||
|
|
if m1 and m2 and not m3 : return [a,b,c,d]
|
||
|
|
if m1 and not m2 and m3 : return [a,b,d,c]
|
||
|
|
if not m1 and m2 and m3 : return [a,d,b,c]
|
||
|
|
if m1 and not (m2 and m3) : return [a,b,d]
|
||
|
|
if not (m1 and m2) and m3 : return [c,a,d]
|
||
|
|
if not (m1 and m3) and m2 : return [b,c,d]
|
||
|
|
|
||
|
|
raise ValueError, "csp_segment_convex_hull happend something that shouldnot happen!"
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Bezier additional functions
|
||
|
|
################################################################################
|
||
|
|
|
||
|
|
def bez_bounds_intersect(bez1, bez2) :
|
||
|
|
return bounds_intersect(bez_bound(bez2), bez_bound(bez1))
|
||
|
|
|
||
|
|
|
||
|
|
def bez_bound(bez) :
|
||
|
|
return [
|
||
|
|
min(bez[0][0], bez[1][0], bez[2][0], bez[3][0]),
|
||
|
|
min(bez[0][1], bez[1][1], bez[2][1], bez[3][1]),
|
||
|
|
max(bez[0][0], bez[1][0], bez[2][0], bez[3][0]),
|
||
|
|
max(bez[0][1], bez[1][1], bez[2][1], bez[3][1]),
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
def bounds_intersect(a, b) :
|
||
|
|
return not ( (a[0]>b[2]) or (b[0]>a[2]) or (a[1]>b[3]) or (b[1]>a[3]) )
|
||
|
|
|
||
|
|
|
||
|
|
def tpoint((x1,y1),(x2,y2),t):
|
||
|
|
return [x1+t*(x2-x1),y1+t*(y2-y1)]
|
||
|
|
|
||
|
|
|
||
|
|
def bez_to_csp_segment(bez) :
|
||
|
|
return [bez[0],bez[0],bez[1]], [bez[2],bez[3],bez[3]]
|
||
|
|
|
||
|
|
|
||
|
|
def bez_split(a,t=0.5) :
|
||
|
|
a1 = tpoint(a[0],a[1],t)
|
||
|
|
at = tpoint(a[1],a[2],t)
|
||
|
|
b2 = tpoint(a[2],a[3],t)
|
||
|
|
a2 = tpoint(a1,at,t)
|
||
|
|
b1 = tpoint(b2,at,t)
|
||
|
|
a3 = tpoint(a2,b1,t)
|
||
|
|
return [a[0],a1,a2,a3], [a3,b1,b2,a[3]]
|
||
|
|
|
||
|
|
|
||
|
|
def bez_at_t(bez,t) :
|
||
|
|
return csp_at_t([bez[0],bez[0],bez[1]],[bez[2],bez[3],bez[3]],t)
|
||
|
|
|
||
|
|
|
||
|
|
def bez_to_point_distance(bez,p,needed_dist=[0.,1e100]):
|
||
|
|
# returns [d^2,t]
|
||
|
|
return csp_seg_to_point_distance(bez_to_csp_segment(bez),p,needed_dist)
|
||
|
|
|
||
|
|
|
||
|
|
def bez_normalized_slope(bez,t):
|
||
|
|
return csp_normalized_slope([bez[0],bez[0],bez[1]], [bez[2],bez[3],bez[3]],t)
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Some vector functions
|
||
|
|
################################################################################
|
||
|
|
|
||
|
|
def normalize((x,y)) :
|
||
|
|
l = math.sqrt(x**2+y**2)
|
||
|
|
if l == 0 : return [0.,0.]
|
||
|
|
else : return [x/l, y/l]
|
||
|
|
|
||
|
|
|
||
|
|
def cross(a,b) :
|
||
|
|
return a[1] * b[0] - a[0] * b[1]
|
||
|
|
|
||
|
|
|
||
|
|
def dot(a,b) :
|
||
|
|
return a[0] * b[0] + a[1] * b[1]
|
||
|
|
|
||
|
|
|
||
|
|
def rotate_ccw(d) :
|
||
|
|
return [-d[1],d[0]]
|
||
|
|
|
||
|
|
|
||
|
|
def vectors_ccw(a,b):
|
||
|
|
return a[0]*b[1]-b[0]*a[1] < 0
|
||
|
|
|
||
|
|
|
||
|
|
def vector_from_to_length(a,b):
|
||
|
|
return math.sqrt((a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]))
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Common functions
|
||
|
|
################################################################################
|
||
|
|
|
||
|
|
def matrix_mul(a,b) :
|
||
|
|
return [ [ sum([a[i][k]*b[k][j] for k in range(len(a[0])) ]) for j in range(len(b[0]))] for i in range(len(a))]
|
||
|
|
try :
|
||
|
|
return [ [ sum([a[i][k]*b[k][j] for k in range(len(a[0])) ]) for j in range(len(b[0]))] for i in range(len(a))]
|
||
|
|
except :
|
||
|
|
return None
|
||
|
|
|
||
|
|
|
||
|
|
def transpose(a) :
|
||
|
|
try :
|
||
|
|
return [ [ a[i][j] for i in range(len(a)) ] for j in range(len(a[0])) ]
|
||
|
|
except :
|
||
|
|
return None
|
||
|
|
|
||
|
|
|
||
|
|
def det_3x3(a):
|
||
|
|
return float(
|
||
|
|
a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] + a[1][0]*a[2][1]*a[0][2]
|
||
|
|
- a[0][2]*a[1][1]*a[2][0] - a[0][0]*a[2][1]*a[1][2] - a[0][1]*a[2][2]*a[1][0]
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
def inv_3x3(a): # invert matrix 3x3
|
||
|
|
det = det_3x3(a)
|
||
|
|
if det==0: return None
|
||
|
|
return [
|
||
|
|
[ (a[1][1]*a[2][2] - a[2][1]*a[1][2])/det, -(a[0][1]*a[2][2] - a[2][1]*a[0][2])/det, (a[0][1]*a[1][2] - a[1][1]*a[0][2])/det ],
|
||
|
|
[ -(a[1][0]*a[2][2] - a[2][0]*a[1][2])/det, (a[0][0]*a[2][2] - a[2][0]*a[0][2])/det, -(a[0][0]*a[1][2] - a[1][0]*a[0][2])/det ],
|
||
|
|
[ (a[1][0]*a[2][1] - a[2][0]*a[1][1])/det, -(a[0][0]*a[2][1] - a[2][0]*a[0][1])/det, (a[0][0]*a[1][1] - a[1][0]*a[0][1])/det ]
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
def inv_2x2(a): # invert matrix 2x2
|
||
|
|
det = a[0][0]*a[1][1] - a[1][0]*a[0][1]
|
||
|
|
if det==0: return None
|
||
|
|
return [
|
||
|
|
[a[1][1]/det, -a[0][1]/det],
|
||
|
|
[-a[1][0]/det, a[0][0]/det]
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
def small(a) :
|
||
|
|
global small_tolerance
|
||
|
|
return abs(a)<small_tolerance
|
||
|
|
|
||
|
|
|
||
|
|
def atan2(*arg):
|
||
|
|
if len(arg)==1 and ( type(arg[0]) == type([0.,0.]) or type(arg[0])==type((0.,0.)) ) :
|
||
|
|
return (math.pi/2 - math.atan2(arg[0][0], arg[0][1]) ) % math.pi2
|
||
|
|
elif len(arg)==2 :
|
||
|
|
|
||
|
|
return (math.pi/2 - math.atan2(arg[0],arg[1]) ) % math.pi2
|
||
|
|
else :
|
||
|
|
raise ValueError, "Bad argumets for atan! (%s)" % arg
|
||
|
|
|
||
|
|
|
||
|
|
def draw_text(text,x,y,style = None, font_size = 20) :
|
||
|
|
if style == None :
|
||
|
|
style = "font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;fill:#000000;fill-opacity:1;stroke:none;"
|
||
|
|
style += "font-size:%fpx;"%font_size
|
||
|
|
t = inkex.etree.SubElement( options.doc_root, inkex.addNS('text','svg'), {
|
||
|
|
'x': str(x),
|
||
|
|
inkex.addNS("space","xml"):"preserve",
|
||
|
|
'y': str(y)
|
||
|
|
})
|
||
|
|
text = str(text).split("\n")
|
||
|
|
for s in text :
|
||
|
|
span = inkex.etree.SubElement( t, inkex.addNS('tspan','svg'),
|
||
|
|
{
|
||
|
|
'x': str(x),
|
||
|
|
'y': str(+y),
|
||
|
|
inkex.addNS("role","sodipodi"):"line",
|
||
|
|
})
|
||
|
|
y += font_size
|
||
|
|
span.text = s
|
||
|
|
|
||
|
|
|
||
|
|
def draw_pointer(x,color = "#f00", figure = "cross", comment = "", width = .1) :
|
||
|
|
if figure == "line" :
|
||
|
|
s = ""
|
||
|
|
for i in range(1,len(x)/2) :
|
||
|
|
s+= " %s, %s " %(x[i*2],x[i*2+1])
|
||
|
|
inkex.etree.SubElement( options.doc_root, inkex.addNS('path','svg'), {"d": "M %s,%s L %s"%(x[0],x[1],s), "style":"fill:none;stroke:%s;stroke-width:%f;"%(color,width),"comment":str(comment)} )
|
||
|
|
else :
|
||
|
|
inkex.etree.SubElement( options.doc_root, inkex.addNS('path','svg'), {"d": "m %s,%s l 10,10 -20,-20 10,10 -10,10, 20,-20"%(x[0],x[1]), "style":"fill:none;stroke:%s;stroke-width:%f;"%(color,width),"comment":str(comment)} )
|
||
|
|
|
||
|
|
|
||
|
|
def straight_segments_intersection(a,b, true_intersection = True) : # (True intersection means check ta and tb are in [0,1])
|
||
|
|
ax,bx,cx,dx, ay,by,cy,dy = a[0][0],a[1][0],b[0][0],b[1][0], a[0][1],a[1][1],b[0][1],b[1][1]
|
||
|
|
if (ax==bx and ay==by) or (cx==dx and cy==dy) : return False, 0, 0
|
||
|
|
if (bx-ax)*(dy-cy)-(by-ay)*(dx-cx)==0 : # Lines are parallel
|
||
|
|
ta = (ax-cx)/(dx-cx) if cx!=dx else (ay-cy)/(dy-cy)
|
||
|
|
tb = (bx-cx)/(dx-cx) if cx!=dx else (by-cy)/(dy-cy)
|
||
|
|
tc = (cx-ax)/(bx-ax) if ax!=bx else (cy-ay)/(by-ay)
|
||
|
|
td = (dx-ax)/(bx-ax) if ax!=bx else (dy-ay)/(by-ay)
|
||
|
|
return ("Overlap" if 0<=ta<=1 or 0<=tb<=1 or 0<=tc<=1 or 0<=td<=1 or not true_intersection else False), (ta,tb), (tc,td)
|
||
|
|
else :
|
||
|
|
ta = ( (ay-cy)*(dx-cx)-(ax-cx)*(dy-cy) ) / ( (bx-ax)*(dy-cy)-(by-ay)*(dx-cx) )
|
||
|
|
tb = ( ax-cx+ta*(bx-ax) ) / (dx-cx) if dx!=cx else ( ay-cy+ta*(by-ay) ) / (dy-cy)
|
||
|
|
return (0<=ta<=1 and 0<=tb<=1 or not true_intersection), ta, tb
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
def isnan(x): return type(x) is float and x != x
|
||
|
|
|
||
|
|
def isinf(x): inf = 1e5000; return x == inf or x == -inf
|
||
|
|
|
||
|
|
def between(c,x,y):
|
||
|
|
return x-straight_tolerance<=c<=y+straight_tolerance or y-straight_tolerance<=c<=x+straight_tolerance
|
||
|
|
|
||
|
|
|
||
|
|
def cubic_solver(a,b,c,d):
|
||
|
|
if a!=0:
|
||
|
|
# Monics formula see http://en.wikipedia.org/wiki/Cubic_function#Monic_formula_of_roots
|
||
|
|
a,b,c = (b/a, c/a, d/a)
|
||
|
|
m = 2*a**3 - 9*a*b + 27*c
|
||
|
|
k = a**2 - 3*b
|
||
|
|
n = m**2 - 4*k**3
|
||
|
|
w1 = -.5 + .5*cmath.sqrt(3)*1j
|
||
|
|
w2 = -.5 - .5*cmath.sqrt(3)*1j
|
||
|
|
if n>=0 :
|
||
|
|
t = m+math.sqrt(n)
|
||
|
|
m1 = pow(t/2,1./3) if t>=0 else -pow(-t/2,1./3)
|
||
|
|
t = m-math.sqrt(n)
|
||
|
|
n1 = pow(t/2,1./3) if t>=0 else -pow(-t/2,1./3)
|
||
|
|
else :
|
||
|
|
m1 = pow(complex((m+cmath.sqrt(n))/2),1./3)
|
||
|
|
n1 = pow(complex((m-cmath.sqrt(n))/2),1./3)
|
||
|
|
x1 = -1./3 * (a + m1 + n1)
|
||
|
|
x2 = -1./3 * (a + w1*m1 + w2*n1)
|
||
|
|
x3 = -1./3 * (a + w2*m1 + w1*n1)
|
||
|
|
return [x1,x2,x3]
|
||
|
|
elif b!=0:
|
||
|
|
det = c**2-4*b*d
|
||
|
|
if det>0 :
|
||
|
|
return [(-c+math.sqrt(det))/(2*b),(-c-math.sqrt(det))/(2*b)]
|
||
|
|
elif d == 0 :
|
||
|
|
return [-c/(b*b)]
|
||
|
|
else :
|
||
|
|
return [(-c+cmath.sqrt(det))/(2*b),(-c-cmath.sqrt(det))/(2*b)]
|
||
|
|
elif c!=0 :
|
||
|
|
return [-d/c]
|
||
|
|
else : return []
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### print_ prints any arguments into specified log file
|
||
|
|
################################################################################
|
||
|
|
|
||
|
|
def print_(*arg):
|
||
|
|
f = open(options.log_filename,"a")
|
||
|
|
for s in arg :
|
||
|
|
s = str(unicode(s).encode('unicode_escape'))+" "
|
||
|
|
f.write( s )
|
||
|
|
f.write("\n")
|
||
|
|
f.close()
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Point (x,y) operations
|
||
|
|
################################################################################
|
||
|
|
class P:
|
||
|
|
def __init__(self, x, y=None):
|
||
|
|
if not y==None:
|
||
|
|
self.x, self.y = float(x), float(y)
|
||
|
|
else:
|
||
|
|
self.x, self.y = float(x[0]), float(x[1])
|
||
|
|
def __add__(self, other): return P(self.x + other.x, self.y + other.y)
|
||
|
|
def __sub__(self, other): return P(self.x - other.x, self.y - other.y)
|
||
|
|
def __neg__(self): return P(-self.x, -self.y)
|
||
|
|
def __mul__(self, other):
|
||
|
|
if isinstance(other, P):
|
||
|
|
return self.x * other.x + self.y * other.y
|
||
|
|
return P(self.x * other, self.y * other)
|
||
|
|
__rmul__ = __mul__
|
||
|
|
def __div__(self, other): return P(self.x / other, self.y / other)
|
||
|
|
def mag(self): return math.hypot(self.x, self.y)
|
||
|
|
def unit(self):
|
||
|
|
h = self.mag()
|
||
|
|
if h: return self / h
|
||
|
|
else: return P(0,0)
|
||
|
|
def dot(self, other): return self.x * other.x + self.y * other.y
|
||
|
|
def rot(self, theta):
|
||
|
|
c = math.cos(theta)
|
||
|
|
s = math.sin(theta)
|
||
|
|
return P(self.x * c - self.y * s, self.x * s + self.y * c)
|
||
|
|
def angle(self): return math.atan2(self.y, self.x)
|
||
|
|
def __repr__(self): return '%f,%f' % (self.x, self.y)
|
||
|
|
def pr(self): return "%.2f,%.2f" % (self.x, self.y)
|
||
|
|
def to_list(self): return [self.x, self.y]
|
||
|
|
def ccw(self): return P(-self.y,self.x)
|
||
|
|
def l2(self): return self.x*self.x + self.y*self.y
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Offset function
|
||
|
|
###
|
||
|
|
### This function offsets given cubic super path.
|
||
|
|
### It's based on src/livarot/PathOutline.cpp from Inkscape's source code.
|
||
|
|
###
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def csp_offset(csp, r) :
|
||
|
|
offset_tolerance = 0.05
|
||
|
|
offset_subdivision_depth = 10
|
||
|
|
time_ = time.time()
|
||
|
|
time_start = time_
|
||
|
|
print_("Offset start at %s"% time_)
|
||
|
|
print_("Offset radius %s"% r)
|
||
|
|
|
||
|
|
|
||
|
|
def csp_offset_segment(sp1,sp2,r) :
|
||
|
|
result = []
|
||
|
|
t = csp_get_t_at_curvature(sp1,sp2,1/r)
|
||
|
|
if len(t) == 0 : t =[0.,1.]
|
||
|
|
t.sort()
|
||
|
|
if t[0]>.00000001 : t = [0.]+t
|
||
|
|
if t[-1]<.99999999 : t.append(1.)
|
||
|
|
for st,end in zip(t,t[1:]) :
|
||
|
|
c = csp_curvature_at_t(sp1,sp2,(st+end)/2)
|
||
|
|
sp = csp_split_by_two_points(sp1,sp2,st,end)
|
||
|
|
if sp[1]!=sp[2]:
|
||
|
|
if (c>1/r and r<0 or c<1/r and r>0) :
|
||
|
|
offset = offset_segment_recursion(sp[1],sp[2],r, offset_subdivision_depth, offset_tolerance)
|
||
|
|
else : # This part will be clipped for sure... TODO Optimize it...
|
||
|
|
offset = offset_segment_recursion(sp[1],sp[2],r, offset_subdivision_depth, offset_tolerance)
|
||
|
|
|
||
|
|
if result==[] :
|
||
|
|
result = offset[:]
|
||
|
|
else:
|
||
|
|
if csp_subpaths_end_to_start_distance2(result,offset)<0.0001 :
|
||
|
|
result = csp_concat_subpaths(result,offset)
|
||
|
|
else:
|
||
|
|
|
||
|
|
intersection = csp_get_subapths_last_first_intersection(result,offset)
|
||
|
|
if intersection != [] :
|
||
|
|
i,t1,j,t2 = intersection
|
||
|
|
sp1_,sp2_,sp3_ = csp_split(result[i-1],result[i],t1)
|
||
|
|
result = result[:i-1] + [ sp1_, sp2_ ]
|
||
|
|
sp1_,sp2_,sp3_ = csp_split(offset[j-1],offset[j],t2)
|
||
|
|
result = csp_concat_subpaths( result, [sp2_,sp3_] + offset[j+1:] )
|
||
|
|
else :
|
||
|
|
pass # ???
|
||
|
|
#raise ValueError, "Offset curvature clipping error"
|
||
|
|
#csp_draw([result])
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def create_offset_segment(sp1,sp2,r) :
|
||
|
|
# See Gernot Hoffmann "Bezier Curves" p.34 -> 7.1 Bezier Offset Curves
|
||
|
|
p0,p1,p2,p3 = P(sp1[1]),P(sp1[2]),P(sp2[0]),P(sp2[1])
|
||
|
|
s0,s1,s3 = p1-p0,p2-p1,p3-p2
|
||
|
|
n0 = s0.ccw().unit() if s0.l2()!=0 else P(csp_normalized_normal(sp1,sp2,0))
|
||
|
|
n3 = s3.ccw().unit() if s3.l2()!=0 else P(csp_normalized_normal(sp1,sp2,1))
|
||
|
|
n1 = s1.ccw().unit() if s1.l2()!=0 else (n0.unit()+n3.unit()).unit()
|
||
|
|
|
||
|
|
q0,q3 = p0+r*n0, p3+r*n3
|
||
|
|
c = csp_curvature_at_t(sp1,sp2,0)
|
||
|
|
q1 = q0 + (p1-p0)*(1- (r*c if abs(c)<100 else 0) )
|
||
|
|
c = csp_curvature_at_t(sp1,sp2,1)
|
||
|
|
q2 = q3 + (p2-p3)*(1- (r*c if abs(c)<100 else 0) )
|
||
|
|
|
||
|
|
|
||
|
|
return [[q0.to_list(), q0.to_list(), q1.to_list()],[q2.to_list(), q3.to_list(), q3.to_list()]]
|
||
|
|
|
||
|
|
|
||
|
|
def csp_get_subapths_last_first_intersection(s1,s2):
|
||
|
|
_break = False
|
||
|
|
for i in range(1,len(s1)) :
|
||
|
|
sp11, sp12 = s1[-i-1], s1[-i]
|
||
|
|
for j in range(1,len(s2)) :
|
||
|
|
sp21,sp22 = s2[j-1], s2[j]
|
||
|
|
intersection = csp_segments_true_intersection(sp11,sp12,sp21,sp22)
|
||
|
|
if intersection != [] :
|
||
|
|
_break = True
|
||
|
|
break
|
||
|
|
if _break:break
|
||
|
|
if _break :
|
||
|
|
intersection = max(intersection)
|
||
|
|
return [len(s1)-i,intersection[0], j,intersection[1]]
|
||
|
|
else :
|
||
|
|
return []
|
||
|
|
|
||
|
|
|
||
|
|
def csp_join_offsets(prev,next,sp1,sp2,sp1_l,sp2_l,r):
|
||
|
|
if len(next)>1 :
|
||
|
|
if (P(prev[-1][1])-P(next[0][1])).l2()<0.001 :
|
||
|
|
return prev,[],next
|
||
|
|
intersection = csp_get_subapths_last_first_intersection(prev,next)
|
||
|
|
if intersection != [] :
|
||
|
|
i,t1,j,t2 = intersection
|
||
|
|
sp1_,sp2_,sp3_ = csp_split(prev[i-1],prev[i],t1)
|
||
|
|
sp3_,sp4_,sp5_ = csp_split(next[j-1], next[j],t2)
|
||
|
|
return prev[:i-1] + [ sp1_, sp2_ ], [], [sp4_,sp5_] + next[j+1:]
|
||
|
|
|
||
|
|
# Offsets do not intersect... will add an arc...
|
||
|
|
start = (P(csp_at_t(sp1_l,sp2_l,1.)) + r*P(csp_normalized_normal(sp1_l,sp2_l,1.))).to_list()
|
||
|
|
end = (P(csp_at_t(sp1,sp2,0.)) + r*P(csp_normalized_normal(sp1,sp2,0.))).to_list()
|
||
|
|
arc = csp_from_arc(start, end, sp1[1], r, csp_normalized_slope(sp1_l,sp2_l,1.) )
|
||
|
|
if arc == [] :
|
||
|
|
return prev,[],next
|
||
|
|
else:
|
||
|
|
# Clip prev by arc
|
||
|
|
if csp_subpaths_end_to_start_distance2(prev,arc)>0.00001 :
|
||
|
|
intersection = csp_get_subapths_last_first_intersection(prev,arc)
|
||
|
|
if intersection != [] :
|
||
|
|
i,t1,j,t2 = intersection
|
||
|
|
sp1_,sp2_,sp3_ = csp_split(prev[i-1],prev[i],t1)
|
||
|
|
sp3_,sp4_,sp5_ = csp_split(arc[j-1],arc[j],t2)
|
||
|
|
prev = prev[:i-1] + [ sp1_, sp2_ ]
|
||
|
|
arc = [sp4_,sp5_] + arc[j+1:]
|
||
|
|
#else : raise ValueError, "Offset curvature clipping error"
|
||
|
|
# Clip next by arc
|
||
|
|
if next == [] :
|
||
|
|
return prev,[],arc
|
||
|
|
if csp_subpaths_end_to_start_distance2(arc,next)>0.00001 :
|
||
|
|
intersection = csp_get_subapths_last_first_intersection(arc,next)
|
||
|
|
if intersection != [] :
|
||
|
|
i,t1,j,t2 = intersection
|
||
|
|
sp1_,sp2_,sp3_ = csp_split(arc[i-1],arc[i],t1)
|
||
|
|
sp3_,sp4_,sp5_ = csp_split(next[j-1],next[j],t2)
|
||
|
|
arc = arc[:i-1] + [ sp1_, sp2_ ]
|
||
|
|
next = [sp4_,sp5_] + next[j+1:]
|
||
|
|
#else : raise ValueError, "Offset curvature clipping error"
|
||
|
|
|
||
|
|
return prev,arc,next
|
||
|
|
|
||
|
|
|
||
|
|
def offset_segment_recursion(sp1,sp2,r, depth, tolerance) :
|
||
|
|
sp1_r,sp2_r = create_offset_segment(sp1,sp2,r)
|
||
|
|
err = max(
|
||
|
|
csp_seg_to_point_distance(sp1_r,sp2_r, (P(csp_at_t(sp1,sp2,.25)) + P(csp_normalized_normal(sp1,sp2,.25))*r).to_list())[0],
|
||
|
|
csp_seg_to_point_distance(sp1_r,sp2_r, (P(csp_at_t(sp1,sp2,.50)) + P(csp_normalized_normal(sp1,sp2,.50))*r).to_list())[0],
|
||
|
|
csp_seg_to_point_distance(sp1_r,sp2_r, (P(csp_at_t(sp1,sp2,.75)) + P(csp_normalized_normal(sp1,sp2,.75))*r).to_list())[0],
|
||
|
|
)
|
||
|
|
|
||
|
|
if err>tolerance**2 and depth>0:
|
||
|
|
#print_(csp_seg_to_point_distance(sp1_r,sp2_r, (P(csp_at_t(sp1,sp2,.25)) + P(csp_normalized_normal(sp1,sp2,.25))*r).to_list())[0], tolerance)
|
||
|
|
if depth > offset_subdivision_depth-2 :
|
||
|
|
t = csp_max_curvature(sp1,sp2)
|
||
|
|
t = max(.1,min(.9 ,t))
|
||
|
|
else :
|
||
|
|
t = .5
|
||
|
|
sp3,sp4,sp5 = csp_split(sp1,sp2,t)
|
||
|
|
r1 = offset_segment_recursion(sp3,sp4,r, depth-1, tolerance)
|
||
|
|
r2 = offset_segment_recursion(sp4,sp5,r, depth-1, tolerance)
|
||
|
|
return r1[:-1]+ [[r1[-1][0],r1[-1][1],r2[0][2]]] + r2[1:]
|
||
|
|
else :
|
||
|
|
#csp_draw([[sp1_r,sp2_r]])
|
||
|
|
#draw_pointer(sp1[1]+sp1_r[1], "#057", "line")
|
||
|
|
#draw_pointer(sp2[1]+sp2_r[1], "#705", "line")
|
||
|
|
return [sp1_r,sp2_r]
|
||
|
|
|
||
|
|
|
||
|
|
############################################################################
|
||
|
|
# Some small definitions
|
||
|
|
############################################################################
|
||
|
|
csp_len = len(csp)
|
||
|
|
|
||
|
|
############################################################################
|
||
|
|
# Prepare the path
|
||
|
|
############################################################################
|
||
|
|
# Remove all small segments (segment length < 0.001)
|
||
|
|
|
||
|
|
for i in xrange(len(csp)) :
|
||
|
|
for j in xrange(len(csp[i])) :
|
||
|
|
sp = csp[i][j]
|
||
|
|
if (P(sp[1])-P(sp[0])).mag() < 0.001 :
|
||
|
|
csp[i][j][0] = sp[1]
|
||
|
|
if (P(sp[2])-P(sp[0])).mag() < 0.001 :
|
||
|
|
csp[i][j][2] = sp[1]
|
||
|
|
for i in xrange(len(csp)) :
|
||
|
|
for j in xrange(1,len(csp[i])) :
|
||
|
|
if cspseglength(csp[i][j-1], csp[i][j])<0.001 :
|
||
|
|
csp[i] = csp[i][:j] + csp[i][j+1:]
|
||
|
|
if cspseglength(csp[i][-1],csp[i][0])>0.001 :
|
||
|
|
csp[i][-1][2] = csp[i][-1][1]
|
||
|
|
csp[i]+= [ [csp[i][0][1],csp[i][0][1],csp[i][0][1]] ]
|
||
|
|
|
||
|
|
# TODO Get rid of self intersections.
|
||
|
|
|
||
|
|
original_csp = csp[:]
|
||
|
|
# Clip segments which has curvature>1/r. Because their offset will be selfintersecting and very nasty.
|
||
|
|
|
||
|
|
print_("Offset prepared the path in %s"%(time.time()-time_))
|
||
|
|
print_("Path length = %s"% sum([len(i)for i in csp] ) )
|
||
|
|
time_ = time.time()
|
||
|
|
|
||
|
|
############################################################################
|
||
|
|
# Offset
|
||
|
|
############################################################################
|
||
|
|
# Create offsets for all segments in the path. And join them together inside each subpath.
|
||
|
|
unclipped_offset = [[] for i in xrange(csp_len)]
|
||
|
|
offsets_original = [[] for i in xrange(csp_len)]
|
||
|
|
join_points = [[] for i in xrange(csp_len)]
|
||
|
|
intersection = [[] for i in xrange(csp_len)]
|
||
|
|
for i in xrange(csp_len) :
|
||
|
|
subpath = csp[i]
|
||
|
|
subpath_offset = []
|
||
|
|
last_offset_len = 0
|
||
|
|
for sp1,sp2 in zip(subpath, subpath[1:]) :
|
||
|
|
segment_offset = csp_offset_segment(sp1,sp2,r)
|
||
|
|
if subpath_offset == [] :
|
||
|
|
subpath_offset = segment_offset
|
||
|
|
|
||
|
|
prev_l = len(subpath_offset)
|
||
|
|
else :
|
||
|
|
prev, arc, next = csp_join_offsets(subpath_offset[-prev_l:],segment_offset,sp1,sp2,sp1_l,sp2_l,r)
|
||
|
|
#csp_draw([prev],"Blue")
|
||
|
|
#csp_draw([arc],"Magenta")
|
||
|
|
subpath_offset = csp_concat_subpaths(subpath_offset[:-prev_l+1],prev,arc,next)
|
||
|
|
prev_l = len(next)
|
||
|
|
sp1_l, sp2_l = sp1[:], sp2[:]
|
||
|
|
|
||
|
|
# Join last and first offsets togother to close the curve
|
||
|
|
|
||
|
|
prev, arc, next = csp_join_offsets(subpath_offset[-prev_l:], subpath_offset[:2], subpath[0], subpath[1], sp1_l,sp2_l, r)
|
||
|
|
subpath_offset[:2] = next[:]
|
||
|
|
subpath_offset = csp_concat_subpaths(subpath_offset[:-prev_l+1],prev,arc)
|
||
|
|
#csp_draw([prev],"Blue")
|
||
|
|
#csp_draw([arc],"Red")
|
||
|
|
#csp_draw([next],"Red")
|
||
|
|
|
||
|
|
# Collect subpath's offset and save it to unclipped offset list.
|
||
|
|
unclipped_offset[i] = subpath_offset[:]
|
||
|
|
|
||
|
|
#for k,t in intersection[i]:
|
||
|
|
# draw_pointer(csp_at_t(subpath_offset[k-1], subpath_offset[k], t))
|
||
|
|
|
||
|
|
#inkex.etree.SubElement( options.doc_root, inkex.addNS('path','svg'), {"d": cubicsuperpath.formatPath(unclipped_offset), "style":"fill:none;stroke:#0f0;"} )
|
||
|
|
print_("Offsetted path in %s"%(time.time()-time_))
|
||
|
|
time_ = time.time()
|
||
|
|
|
||
|
|
#for i in range(len(unclipped_offset)):
|
||
|
|
# csp_draw([unclipped_offset[i]], color = ["Green","Red","Blue"][i%3], width = .1)
|
||
|
|
#return []
|
||
|
|
############################################################################
|
||
|
|
# Now to the clipping.
|
||
|
|
############################################################################
|
||
|
|
# First of all find all intersection's between all segments of all offseted subpaths, including self intersections.
|
||
|
|
|
||
|
|
#TODO define offset tolerance here
|
||
|
|
global small_tolerance
|
||
|
|
small_tolerance = 0.01
|
||
|
|
summ = 0
|
||
|
|
summ1 = 0
|
||
|
|
for subpath_i in xrange(csp_len) :
|
||
|
|
for subpath_j in xrange(subpath_i,csp_len) :
|
||
|
|
subpath = unclipped_offset[subpath_i]
|
||
|
|
subpath1 = unclipped_offset[subpath_j]
|
||
|
|
for i in xrange(1,len(subpath)) :
|
||
|
|
# If subpath_i==subpath_j we are looking for self intersections, so
|
||
|
|
# we'll need search intersections only for xrange(i,len(subpath1))
|
||
|
|
for j in ( xrange(i,len(subpath1)) if subpath_i==subpath_j else xrange(len(subpath1))) :
|
||
|
|
if subpath_i==subpath_j and j==i :
|
||
|
|
# Find self intersections of a segment
|
||
|
|
sp1,sp2,sp3 = csp_split(subpath[i-1],subpath[i],.5)
|
||
|
|
intersections = csp_segments_intersection(sp1,sp2,sp2,sp3)
|
||
|
|
summ +=1
|
||
|
|
for t in intersections :
|
||
|
|
summ1 += 1
|
||
|
|
if not ( small(t[0]-1) and small(t[1]) ) and 0<=t[0]<=1 and 0<=t[1]<=1 :
|
||
|
|
intersection[subpath_i] += [ [i,t[0]/2],[j,t[1]/2+.5] ]
|
||
|
|
else :
|
||
|
|
intersections = csp_segments_intersection(subpath[i-1],subpath[i],subpath1[j-1],subpath1[j])
|
||
|
|
summ +=1
|
||
|
|
for t in intersections :
|
||
|
|
summ1 += 1
|
||
|
|
#TODO tolerance dependence to cpsp_length(t)
|
||
|
|
if len(t) == 2 and 0<=t[0]<=1 and 0<=t[1]<=1 and not (
|
||
|
|
subpath_i==subpath_j and (
|
||
|
|
(j-i-1) % (len(subpath)-1) == 0 and small(t[0]-1) and small(t[1]) or
|
||
|
|
(i-j-1) % (len(subpath)-1) == 0 and small(t[1]-1) and small(t[0]) ) ) :
|
||
|
|
intersection[subpath_i] += [ [i,t[0]] ]
|
||
|
|
intersection[subpath_j] += [ [j,t[1]] ]
|
||
|
|
#draw_pointer(csp_at_t(subpath[i-1],subpath[i],t[0]),"#f00")
|
||
|
|
#print_(t)
|
||
|
|
#print_(i,j)
|
||
|
|
elif len(t)==5 and t[4]=="Overlap":
|
||
|
|
intersection[subpath_i] += [ [i,t[0]], [i,t[1]] ]
|
||
|
|
intersection[subpath_j] += [ [j,t[1]], [j,t[3]] ]
|
||
|
|
|
||
|
|
print_("Intersections found in %s"%(time.time()-time_))
|
||
|
|
print_("Examined %s segments"%(summ))
|
||
|
|
print_("found %s intersections"%(summ1))
|
||
|
|
time_ = time.time()
|
||
|
|
|
||
|
|
########################################################################
|
||
|
|
# Split unclipped offset by intersection points into splitted_offset
|
||
|
|
########################################################################
|
||
|
|
splitted_offset = []
|
||
|
|
for i in xrange(csp_len) :
|
||
|
|
subpath = unclipped_offset[i]
|
||
|
|
if len(intersection[i]) > 0 :
|
||
|
|
parts = csp_subpath_split_by_points(subpath, intersection[i])
|
||
|
|
# Close parts list to close path (The first and the last parts are joined together)
|
||
|
|
if [1,0.] not in intersection[i] :
|
||
|
|
parts[0][0][0] = parts[-1][-1][0]
|
||
|
|
parts[0] = csp_concat_subpaths(parts[-1], parts[0])
|
||
|
|
splitted_offset += parts[:-1]
|
||
|
|
else:
|
||
|
|
splitted_offset += parts[:]
|
||
|
|
else :
|
||
|
|
splitted_offset += [subpath[:]]
|
||
|
|
|
||
|
|
#for i in range(len(splitted_offset)):
|
||
|
|
# csp_draw([splitted_offset[i]], color = ["Green","Red","Blue"][i%3])
|
||
|
|
print_("Splitted in %s"%(time.time()-time_))
|
||
|
|
time_ = time.time()
|
||
|
|
|
||
|
|
|
||
|
|
########################################################################
|
||
|
|
# Clipping
|
||
|
|
########################################################################
|
||
|
|
result = []
|
||
|
|
for subpath_i in range(len(splitted_offset)):
|
||
|
|
clip = False
|
||
|
|
s1 = splitted_offset[subpath_i]
|
||
|
|
for subpath_j in range(len(splitted_offset)):
|
||
|
|
s2 = splitted_offset[subpath_j]
|
||
|
|
if (P(s1[0][1])-P(s2[-1][1])).l2()<0.0001 and ( (subpath_i+1) % len(splitted_offset) != subpath_j ):
|
||
|
|
if dot(csp_normalized_normal(s2[-2],s2[-1],1.),csp_normalized_slope(s1[0],s1[1],0.))*r<-0.0001 :
|
||
|
|
clip = True
|
||
|
|
break
|
||
|
|
if (P(s2[0][1])-P(s1[-1][1])).l2()<0.0001 and ( (subpath_j+1) % len(splitted_offset) != subpath_i ):
|
||
|
|
if dot(csp_normalized_normal(s2[0],s2[1],0.),csp_normalized_slope(s1[-2],s1[-1],1.))*r>0.0001 :
|
||
|
|
clip = True
|
||
|
|
break
|
||
|
|
|
||
|
|
if not clip :
|
||
|
|
result += [s1[:]]
|
||
|
|
elif options.offset_draw_clippend_path :
|
||
|
|
csp_draw([s1],color="Red",width=.1)
|
||
|
|
draw_pointer( csp_at_t(s2[-2],s2[-1],1.)+
|
||
|
|
(P(csp_at_t(s2[-2],s2[-1],1.))+ P(csp_normalized_normal(s2[-2],s2[-1],1.))*10).to_list(),"Green", "line" )
|
||
|
|
draw_pointer( csp_at_t(s1[0],s1[1],0.)+
|
||
|
|
(P(csp_at_t(s1[0],s1[1],0.))+ P(csp_normalized_slope(s1[0],s1[1],0.))*10).to_list(),"Red", "line" )
|
||
|
|
|
||
|
|
# Now join all together and check closure and orientation of result
|
||
|
|
joined_result = csp_join_subpaths(result)
|
||
|
|
# Check if each subpath from joined_result is closed
|
||
|
|
#csp_draw(joined_result,color="Green",width=1)
|
||
|
|
|
||
|
|
|
||
|
|
for s in joined_result[:] :
|
||
|
|
if csp_subpaths_end_to_start_distance2(s,s) > 0.001 :
|
||
|
|
# Remove open parts
|
||
|
|
if options.offset_draw_clippend_path:
|
||
|
|
csp_draw([s],color="Orange",width=1)
|
||
|
|
draw_pointer(s[0][1], comment= csp_subpaths_end_to_start_distance2(s,s))
|
||
|
|
draw_pointer(s[-1][1], comment = csp_subpaths_end_to_start_distance2(s,s))
|
||
|
|
joined_result.remove(s)
|
||
|
|
else :
|
||
|
|
# Remove small parts
|
||
|
|
minx,miny,maxx,maxy = csp_true_bounds([s])
|
||
|
|
if (minx[0]-maxx[0])**2 + (miny[1]-maxy[1])**2 < 0.1 :
|
||
|
|
joined_result.remove(s)
|
||
|
|
print_("Clipped and joined path in %s"%(time.time()-time_))
|
||
|
|
time_ = time.time()
|
||
|
|
|
||
|
|
########################################################################
|
||
|
|
# Now to the Dummy cliping: remove parts from splitted offset if their
|
||
|
|
# centers are closer to the original path than offset radius.
|
||
|
|
########################################################################
|
||
|
|
|
||
|
|
r1,r2 = ( (0.99*r)**2, (1.01*r)**2 ) if abs(r*.01)<1 else ((abs(r)-1)**2, (abs(r)+1)**2)
|
||
|
|
for s in joined_result[:]:
|
||
|
|
dist = csp_to_point_distance(original_csp, s[int(len(s)/2)][1], dist_bounds = [r1,r2], tolerance = .000001)
|
||
|
|
if not r1 < dist[0] < r2 :
|
||
|
|
joined_result.remove(s)
|
||
|
|
if options.offset_draw_clippend_path:
|
||
|
|
csp_draw([s], comment = math.sqrt(dist[0]))
|
||
|
|
draw_pointer(csp_at_t(csp[dist[1]][dist[2]-1],csp[dist[1]][dist[2]],dist[3])+s[int(len(s)/2)][1],"blue", "line", comment = [math.sqrt(dist[0]),i,j,sp] )
|
||
|
|
|
||
|
|
print_("-----------------------------")
|
||
|
|
print_("Total offset time %s"%(time.time()-time_start))
|
||
|
|
print_()
|
||
|
|
return joined_result
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Biarc function
|
||
|
|
###
|
||
|
|
### Calculates biarc approximation of cubic super path segment
|
||
|
|
### splits segment if needed or approximates it with straight line
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def biarc(sp1, sp2, z1, z2, depth=0):
|
||
|
|
def biarc_split(sp1,sp2, z1, z2, depth):
|
||
|
|
if depth<options.biarc_max_split_depth:
|
||
|
|
sp1,sp2,sp3 = csp_split(sp1,sp2)
|
||
|
|
l1, l2 = cspseglength(sp1,sp2), cspseglength(sp2,sp3)
|
||
|
|
if l1+l2 == 0 : zm = z1
|
||
|
|
else : zm = z1+(z2-z1)*l1/(l1+l2)
|
||
|
|
return biarc(sp1,sp2,z1,zm,depth+1)+biarc(sp2,sp3,zm,z2,depth+1)
|
||
|
|
else: return [ [sp1[1],'line', 0, 0, sp2[1], [z1,z2]] ]
|
||
|
|
|
||
|
|
P0, P4 = P(sp1[1]), P(sp2[1])
|
||
|
|
TS, TE, v = (P(sp1[2])-P0), -(P(sp2[0])-P4), P0 - P4
|
||
|
|
tsa, tea, va = TS.angle(), TE.angle(), v.angle()
|
||
|
|
if TE.mag()<straight_distance_tolerance and TS.mag()<straight_distance_tolerance:
|
||
|
|
# Both tangents are zerro - line straight
|
||
|
|
return [ [sp1[1],'line', 0, 0, sp2[1], [z1,z2]] ]
|
||
|
|
if TE.mag() < straight_distance_tolerance:
|
||
|
|
TE = -(TS+v).unit()
|
||
|
|
r = TS.mag()/v.mag()*2
|
||
|
|
elif TS.mag() < straight_distance_tolerance:
|
||
|
|
TS = -(TE+v).unit()
|
||
|
|
r = 1/( TE.mag()/v.mag()*2 )
|
||
|
|
else:
|
||
|
|
r=TS.mag()/TE.mag()
|
||
|
|
TS, TE = TS.unit(), TE.unit()
|
||
|
|
tang_are_parallel = ((tsa-tea)%math.pi<straight_tolerance or math.pi-(tsa-tea)%math.pi<straight_tolerance )
|
||
|
|
if ( tang_are_parallel and
|
||
|
|
((v.mag()<straight_distance_tolerance or TE.mag()<straight_distance_tolerance or TS.mag()<straight_distance_tolerance) or
|
||
|
|
1-abs(TS*v/(TS.mag()*v.mag()))<straight_tolerance) ):
|
||
|
|
# Both tangents are parallel and start and end are the same - line straight
|
||
|
|
# or one of tangents still smaller then tollerance
|
||
|
|
|
||
|
|
# Both tangents and v are parallel - line straight
|
||
|
|
return [ [sp1[1],'line', 0, 0, sp2[1], [z1,z2]] ]
|
||
|
|
|
||
|
|
c,b,a = v*v, 2*v*(r*TS+TE), 2*r*(TS*TE-1)
|
||
|
|
if v.mag()==0:
|
||
|
|
return biarc_split(sp1, sp2, z1, z2, depth)
|
||
|
|
asmall, bsmall, csmall = abs(a)<10**-10,abs(b)<10**-10,abs(c)<10**-10
|
||
|
|
if asmall and b!=0: beta = -c/b
|
||
|
|
elif csmall and a!=0: beta = -b/a
|
||
|
|
elif not asmall:
|
||
|
|
discr = b*b-4*a*c
|
||
|
|
if discr < 0: raise ValueError, (a,b,c,discr)
|
||
|
|
disq = discr**.5
|
||
|
|
beta1 = (-b - disq) / 2 / a
|
||
|
|
beta2 = (-b + disq) / 2 / a
|
||
|
|
if beta1*beta2 > 0 : raise ValueError, (a,b,c,disq,beta1,beta2)
|
||
|
|
beta = max(beta1, beta2)
|
||
|
|
elif asmall and bsmall:
|
||
|
|
return biarc_split(sp1, sp2, z1, z2, depth)
|
||
|
|
alpha = beta * r
|
||
|
|
ab = alpha + beta
|
||
|
|
P1 = P0 + alpha * TS
|
||
|
|
P3 = P4 - beta * TE
|
||
|
|
P2 = (beta / ab) * P1 + (alpha / ab) * P3
|
||
|
|
|
||
|
|
|
||
|
|
def calculate_arc_params(P0,P1,P2):
|
||
|
|
D = (P0+P2)/2
|
||
|
|
if (D-P1).mag()==0: return None, None
|
||
|
|
R = D - ( (D-P0).mag()**2/(D-P1).mag() )*(P1-D).unit()
|
||
|
|
p0a, p1a, p2a = (P0-R).angle()%(2*math.pi), (P1-R).angle()%(2*math.pi), (P2-R).angle()%(2*math.pi)
|
||
|
|
alpha = (p2a - p0a) % (2*math.pi)
|
||
|
|
if (p0a<p2a and (p1a<p0a or p2a<p1a)) or (p2a<p1a<p0a) :
|
||
|
|
alpha = -2*math.pi+alpha
|
||
|
|
if abs(R.x)>1000000 or abs(R.y)>1000000 or (R-P0).mag<.1 :
|
||
|
|
return None, None
|
||
|
|
else :
|
||
|
|
return R, alpha
|
||
|
|
R1,a1 = calculate_arc_params(P0,P1,P2)
|
||
|
|
R2,a2 = calculate_arc_params(P2,P3,P4)
|
||
|
|
if R1==None or R2==None or (R1-P0).mag()<straight_tolerance or (R2-P2).mag()<straight_tolerance : return [ [sp1[1],'line', 0, 0, sp2[1], [z1,z2]] ]
|
||
|
|
|
||
|
|
d = csp_to_arc_distance(sp1,sp2, [P0,P2,R1,a1],[P2,P4,R2,a2])
|
||
|
|
if d > 1 and depth<options.biarc_max_split_depth : return biarc_split(sp1, sp2, z1, z2, depth)
|
||
|
|
else:
|
||
|
|
if R2.mag()*a2 == 0 : zm = z2
|
||
|
|
else : zm = z1 + (z2-z1)*(abs(R1.mag()*a1))/(abs(R2.mag()*a2)+abs(R1.mag()*a1))
|
||
|
|
return [ [ sp1[1], 'arc', [R1.x,R1.y], a1, [P2.x,P2.y], [z1,zm] ], [ [P2.x,P2.y], 'arc', [R2.x,R2.y], a2, [P4.x,P4.y], [zm,z2] ] ]
|
||
|
|
|
||
|
|
|
||
|
|
def biarc_curve_segment_length(seg):
|
||
|
|
if seg[1] == "arc" :
|
||
|
|
return math.sqrt((seg[0][0]-seg[2][0])**2+(seg[0][1]-seg[2][1])**2)*seg[3]
|
||
|
|
elif seg[1] == "line" :
|
||
|
|
return math.sqrt((seg[0][0]-seg[4][0])**2+(seg[0][1]-seg[4][1])**2)
|
||
|
|
else:
|
||
|
|
return 0
|
||
|
|
|
||
|
|
|
||
|
|
def biarc_curve_clip_at_l(curve, l, clip_type = "strict") :
|
||
|
|
# get first subcurve and ceck it's length
|
||
|
|
subcurve, subcurve_l, moved = [], 0, False
|
||
|
|
for seg in curve:
|
||
|
|
if seg[1] == "move" and moved or seg[1] == "end" :
|
||
|
|
break
|
||
|
|
if seg[1] == "move" : moved = True
|
||
|
|
subcurve_l += biarc_curve_segment_length(seg)
|
||
|
|
if seg[1] == "arc" or seg[1] == "line" :
|
||
|
|
subcurve += [seg]
|
||
|
|
|
||
|
|
if subcurve_l < l and clip_type == "strict" : return []
|
||
|
|
lc = 0
|
||
|
|
if (subcurve[-1][4][0]-subcurve[0][0][0])**2 + (subcurve[-1][4][1]-subcurve[0][0][1])**2 < 10**-7 : subcurve_closed = True
|
||
|
|
i = 0
|
||
|
|
reverse = False
|
||
|
|
while lc<l :
|
||
|
|
seg = subcurve[i]
|
||
|
|
if reverse :
|
||
|
|
if seg[1] == "line" :
|
||
|
|
seg = [seg[4], "line", 0 , 0, seg[0], seg[5]] # Hmmm... Do we have to swap seg[5][0] and seg[5][1] (zstart and zend) or not?
|
||
|
|
elif seg[1] == "arc" :
|
||
|
|
seg = [seg[4], "arc", seg[2] , -seg[3], seg[0], seg[5]] # Hmmm... Do we have to swap seg[5][0] and seg[5][1] (zstart and zend) or not?
|
||
|
|
ls = biarc_curve_segment_length(seg)
|
||
|
|
if ls != 0 :
|
||
|
|
if l-lc>ls :
|
||
|
|
res += [seg]
|
||
|
|
else :
|
||
|
|
if seg[1] == "arc" :
|
||
|
|
r = math.sqrt((seg[0][0]-seg[2][0])**2+(seg[0][1]-seg[2][1])**2)
|
||
|
|
x,y = seg[0][0]-seg[2][0], seg[0][1]-seg[2][1]
|
||
|
|
a = seg[3]/ls*(l-lc)
|
||
|
|
x,y = x*math.cos(a) - y*math.sin(a), x*math.sin(a) + y*math.cos(a)
|
||
|
|
x,y = x+seg[2][0], y+seg[2][1]
|
||
|
|
res += [[ seg[0], "arc", seg[2], a, [x,y], [seg[5][0],seg[5][1]/ls*(l-lc)] ]]
|
||
|
|
if seg[1] == "line" :
|
||
|
|
res += [[ seg[0], "line", 0, 0, [(seg[4][0]-seg[0][0])/ls*(l-lc),(seg[4][1]-seg[0][1])/ls*(l-lc)], [seg[5][0],seg[5][1]/ls*(l-lc)] ]]
|
||
|
|
i += 1
|
||
|
|
if i >= len(subcurve) and not subcurve_closed:
|
||
|
|
reverse = not reverse
|
||
|
|
i = i%len(subcurve)
|
||
|
|
return res
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Polygon class
|
||
|
|
################################################################################
|
||
|
|
class Polygon:
|
||
|
|
def __init__(self, polygon=None):
|
||
|
|
self.polygon = [] if polygon==None else polygon[:]
|
||
|
|
|
||
|
|
|
||
|
|
def move(self, x, y) :
|
||
|
|
for i in range(len(self.polygon)) :
|
||
|
|
for j in range(len(self.polygon[i])) :
|
||
|
|
self.polygon[i][j][0] += x
|
||
|
|
self.polygon[i][j][1] += y
|
||
|
|
|
||
|
|
|
||
|
|
def bounds(self) :
|
||
|
|
minx,miny,maxx,maxy = 1e400, 1e400, -1e400, -1e400
|
||
|
|
for poly in self.polygon :
|
||
|
|
for p in poly :
|
||
|
|
if minx > p[0] : minx = p[0]
|
||
|
|
if miny > p[1] : miny = p[1]
|
||
|
|
if maxx < p[0] : maxx = p[0]
|
||
|
|
if maxy < p[1] : maxy = p[1]
|
||
|
|
return minx*1,miny*1,maxx*1,maxy*1
|
||
|
|
|
||
|
|
|
||
|
|
def width(self):
|
||
|
|
b = self.bounds()
|
||
|
|
return b[2]-b[0]
|
||
|
|
|
||
|
|
|
||
|
|
def rotate_(self,sin,cos) :
|
||
|
|
for i in range(len(self.polygon)) :
|
||
|
|
for j in range(len(self.polygon[i])) :
|
||
|
|
x,y = self.polygon[i][j][0], self.polygon[i][j][1]
|
||
|
|
self.polygon[i][j][0] = x*cos - y*sin
|
||
|
|
self.polygon[i][j][1] = x*sin + y*cos
|
||
|
|
|
||
|
|
|
||
|
|
def rotate(self, a):
|
||
|
|
cos, sin = math.cos(a), math.sin(a)
|
||
|
|
self.rotate_(sin,cos)
|
||
|
|
|
||
|
|
|
||
|
|
def drop_into_direction(self, direction, surface) :
|
||
|
|
# Polygon is a list of simple polygons
|
||
|
|
# Surface is a polygon + line y = 0
|
||
|
|
# Direction is [dx,dy]
|
||
|
|
if len(self.polygon) == 0 or len(self.polygon[0])==0 : return
|
||
|
|
if direction[0]**2 + direction[1]**2 <1e-10 : return
|
||
|
|
direction = normalize(direction)
|
||
|
|
sin,cos = direction[0], -direction[1]
|
||
|
|
self.rotate_(-sin,cos)
|
||
|
|
surface.rotate_(-sin,cos)
|
||
|
|
self.drop_down(surface, zerro_plane = False)
|
||
|
|
self.rotate_(sin,cos)
|
||
|
|
surface.rotate_(sin,cos)
|
||
|
|
|
||
|
|
|
||
|
|
def centroid(self):
|
||
|
|
centroids = []
|
||
|
|
sa = 0
|
||
|
|
for poly in self.polygon:
|
||
|
|
cx,cy,a = 0,0,0
|
||
|
|
for i in range(len(poly)):
|
||
|
|
[x1,y1],[x2,y2] = poly[i-1],poly[i]
|
||
|
|
cx += (x1+x2)*(x1*y2-x2*y1)
|
||
|
|
cy += (y1+y2)*(x1*y2-x2*y1)
|
||
|
|
a += (x1*y2-x2*y1)
|
||
|
|
a *= 3.
|
||
|
|
if abs(a)>0 :
|
||
|
|
cx /= a
|
||
|
|
cy /= a
|
||
|
|
sa += abs(a)
|
||
|
|
centroids += [ [cx,cy,a] ]
|
||
|
|
if sa == 0 : return [0.,0.]
|
||
|
|
cx,cy = 0.,0.
|
||
|
|
for c in centroids :
|
||
|
|
cx += c[0]*c[2]
|
||
|
|
cy += c[1]*c[2]
|
||
|
|
cx /= sa
|
||
|
|
cy /= sa
|
||
|
|
return [cx,cy]
|
||
|
|
|
||
|
|
|
||
|
|
def drop_down(self, surface, zerro_plane = True) :
|
||
|
|
# Polygon is a list of simple polygons
|
||
|
|
# Surface is a polygon + line y = 0
|
||
|
|
# Down means min y (0,-1)
|
||
|
|
if len(self.polygon) == 0 or len(self.polygon[0])==0 : return
|
||
|
|
# Get surface top point
|
||
|
|
top = surface.bounds()[3]
|
||
|
|
if zerro_plane : top = max(0, top)
|
||
|
|
# Get polygon bottom point
|
||
|
|
bottom = self.bounds()[1]
|
||
|
|
self.move(0, top - bottom + 10)
|
||
|
|
# Now get shortest distance from surface to polygon in positive x=0 direction
|
||
|
|
# Such distance = min(distance(vertex, edge)...) where edge from surface and
|
||
|
|
# vertex from polygon and vice versa...
|
||
|
|
dist = 1e300
|
||
|
|
for poly in surface.polygon :
|
||
|
|
for i in range(len(poly)) :
|
||
|
|
for poly1 in self.polygon :
|
||
|
|
for i1 in range(len(poly1)) :
|
||
|
|
st,end = poly[i-1], poly[i]
|
||
|
|
vertex = poly1[i1]
|
||
|
|
if st[0]<=vertex[0]<= end[0] or end[0]<=vertex[0]<=st[0] :
|
||
|
|
if st[0]==end[0] : d = min(vertex[1]-st[1],vertex[1]-end[1])
|
||
|
|
else : d = vertex[1] - st[1] - (end[1]-st[1])*(vertex[0]-st[0])/(end[0]-st[0])
|
||
|
|
if dist > d : dist = d
|
||
|
|
# and vice versa just change the sign because vertex now under the edge
|
||
|
|
st,end = poly1[i1-1], poly1[i1]
|
||
|
|
vertex = poly[i]
|
||
|
|
if st[0]<=vertex[0]<=end[0] or end[0]<=vertex[0]<=st[0] :
|
||
|
|
if st[0]==end[0] : d = min(- vertex[1]+st[1],-vertex[1]+end[1])
|
||
|
|
else : d = - vertex[1] + st[1] + (end[1]-st[1])*(vertex[0]-st[0])/(end[0]-st[0])
|
||
|
|
if dist > d : dist = d
|
||
|
|
|
||
|
|
if zerro_plane and dist > 10 + top : dist = 10 + top
|
||
|
|
#print_(dist, top, bottom)
|
||
|
|
#self.draw()
|
||
|
|
self.move(0, -dist)
|
||
|
|
|
||
|
|
|
||
|
|
def draw(self,color="#075",width=.1) :
|
||
|
|
for poly in self.polygon :
|
||
|
|
csp_draw( [csp_subpath_line_to([],poly+[poly[0]])], color=color,width=width )
|
||
|
|
|
||
|
|
|
||
|
|
def add(self, add) :
|
||
|
|
if type(add) == type([]) :
|
||
|
|
self.polygon += add[:]
|
||
|
|
else :
|
||
|
|
self.polygon += add.polygon[:]
|
||
|
|
|
||
|
|
|
||
|
|
def point_inside(self,p) :
|
||
|
|
inside = False
|
||
|
|
for poly in self.polygon :
|
||
|
|
for i in range(len(poly)):
|
||
|
|
st,end = poly[i-1], poly[i]
|
||
|
|
if p==st or p==end : return True # point is a vertex = point is on the edge
|
||
|
|
if st[0]>end[0] : st, end = end, st # This will be needed to check that edge if open only at rigth end
|
||
|
|
c = (p[1]-st[1])*(end[0]-st[0])-(end[1]-st[1])*(p[0]-st[0])
|
||
|
|
#print_(c)
|
||
|
|
if st[0]<=p[0]<end[0] :
|
||
|
|
if c<0 :
|
||
|
|
inside = not inside
|
||
|
|
elif c == 0 : return True # point is on the edge
|
||
|
|
elif st[0]==end[0]==p[0] and (st[1]<=p[1]<=end[1] or end[1]<=p[1]<=st[1]) : # point is on the edge
|
||
|
|
return True
|
||
|
|
return inside
|
||
|
|
|
||
|
|
|
||
|
|
def hull(self) :
|
||
|
|
# Add vertices at all self intersection points.
|
||
|
|
hull = []
|
||
|
|
for i1 in range(len(self.polygon)):
|
||
|
|
poly1 = self.polygon[i1]
|
||
|
|
poly_ = []
|
||
|
|
for j1 in range(len(poly1)):
|
||
|
|
s, e = poly1[j1-1],poly1[j1]
|
||
|
|
poly_ += [s]
|
||
|
|
|
||
|
|
# Check self intersections
|
||
|
|
for j2 in range(j1+1,len(poly1)):
|
||
|
|
s1, e1 = poly1[j2-1],poly1[j2]
|
||
|
|
int_ = line_line_intersection_points(s,e,s1,e1)
|
||
|
|
for p in int_ :
|
||
|
|
if point_to_point_d2(p,s)>0.000001 and point_to_point_d2(p,e)>0.000001 :
|
||
|
|
poly_ += [p]
|
||
|
|
# Check self intersections with other polys
|
||
|
|
for i2 in range(len(self.polygon)):
|
||
|
|
if i1==i2 : continue
|
||
|
|
poly2 = self.polygon[i2]
|
||
|
|
for j2 in range(len(poly2)):
|
||
|
|
s1, e1 = poly2[j2-1],poly2[j2]
|
||
|
|
int_ = line_line_intersection_points(s,e,s1,e1)
|
||
|
|
for p in int_ :
|
||
|
|
if point_to_point_d2(p,s)>0.000001 and point_to_point_d2(p,e)>0.000001 :
|
||
|
|
poly_ += [p]
|
||
|
|
hull += [poly_]
|
||
|
|
# Create the dictionary containing all edges in both directions
|
||
|
|
edges = {}
|
||
|
|
for poly in self.polygon :
|
||
|
|
for i in range(len(poly)):
|
||
|
|
s,e = tuple(poly[i-1]), tuple(poly[i])
|
||
|
|
if (point_to_point_d2(e,s)<0.000001) : continue
|
||
|
|
break_s, break_e = False, False
|
||
|
|
for p in edges :
|
||
|
|
if point_to_point_d2(p,s)<0.000001 :
|
||
|
|
break_s = True
|
||
|
|
s = p
|
||
|
|
if point_to_point_d2(p,e)<0.000001 :
|
||
|
|
break_e = True
|
||
|
|
e = p
|
||
|
|
if break_s and break_e : break
|
||
|
|
l = point_to_point_d(s,e)
|
||
|
|
if not break_s and not break_e :
|
||
|
|
edges[s] = [ [s,e,l] ]
|
||
|
|
edges[e] = [ [e,s,l] ]
|
||
|
|
#draw_pointer(s+e,"red","line")
|
||
|
|
#draw_pointer(s+e,"red","line")
|
||
|
|
else :
|
||
|
|
if e in edges :
|
||
|
|
for edge in edges[e] :
|
||
|
|
if point_to_point_d2(edge[1],s)<0.000001 :
|
||
|
|
break
|
||
|
|
if point_to_point_d2(edge[1],s)>0.000001 :
|
||
|
|
edges[e] += [ [e,s,l] ]
|
||
|
|
#draw_pointer(s+e,"red","line")
|
||
|
|
|
||
|
|
else :
|
||
|
|
edges[e] = [ [e,s,l] ]
|
||
|
|
#draw_pointer(s+e,"green","line")
|
||
|
|
if s in edges :
|
||
|
|
for edge in edges[s] :
|
||
|
|
if point_to_point_d2(edge[1],e)<0.000001 :
|
||
|
|
break
|
||
|
|
if point_to_point_d2(edge[1],e)>0.000001 :
|
||
|
|
edges[s] += [ [s,e, l] ]
|
||
|
|
#draw_pointer(s+e,"red","line")
|
||
|
|
else :
|
||
|
|
edges[s] = [ [s,e,l] ]
|
||
|
|
#draw_pointer(s+e,"green","line")
|
||
|
|
|
||
|
|
|
||
|
|
def angle_quadrant(sin,cos):
|
||
|
|
# quadrants are (0,pi/2], (pi/2,pi], (pi,3*pi/2], (3*pi/2, 2*pi], i.e. 0 is in the 4-th quadrant
|
||
|
|
if sin>0 and cos>=0 : return 1
|
||
|
|
if sin>=0 and cos<0 : return 2
|
||
|
|
if sin<0 and cos<=0 : return 3
|
||
|
|
if sin<=0 and cos>0 : return 4
|
||
|
|
|
||
|
|
|
||
|
|
def angle_is_less(sin,cos,sin1,cos1):
|
||
|
|
# 0 = 2*pi is the largest angle
|
||
|
|
if [sin1, cos1] == [0,1] : return True
|
||
|
|
if [sin, cos] == [0,1] : return False
|
||
|
|
if angle_quadrant(sin,cos)>angle_quadrant(sin1,cos1) :
|
||
|
|
return False
|
||
|
|
if angle_quadrant(sin,cos)<angle_quadrant(sin1,cos1) :
|
||
|
|
return True
|
||
|
|
if sin>=0 and cos>0 : return sin<sin1
|
||
|
|
if sin>0 and cos<=0 : return sin>sin1
|
||
|
|
if sin<=0 and cos<0 : return sin>sin1
|
||
|
|
if sin<0 and cos>=0 : return sin<sin1
|
||
|
|
|
||
|
|
|
||
|
|
def get_closes_edge_by_angle(edges, last):
|
||
|
|
# Last edge is normalized vector of the last edge.
|
||
|
|
min_angle = [0,1]
|
||
|
|
next = last
|
||
|
|
last_edge = [(last[0][0]-last[1][0])/last[2], (last[0][1]-last[1][1])/last[2]]
|
||
|
|
for p in edges:
|
||
|
|
#draw_pointer(list(p[0])+[p[0][0]+last_edge[0]*40,p[0][1]+last_edge[1]*40], "Red", "line", width=1)
|
||
|
|
#print_("len(edges)=",len(edges))
|
||
|
|
cur = [(p[1][0]-p[0][0])/p[2],(p[1][1]-p[0][1])/p[2]]
|
||
|
|
cos, sin = dot(cur,last_edge), cross(cur,last_edge)
|
||
|
|
#draw_pointer(list(p[0])+[p[0][0]+cur[0]*40,p[0][1]+cur[1]*40], "Orange", "line", width=1, comment = [sin,cos])
|
||
|
|
#print_("cos, sin=",cos,sin)
|
||
|
|
#print_("min_angle_before=",min_angle)
|
||
|
|
|
||
|
|
if angle_is_less(sin,cos,min_angle[0],min_angle[1]) :
|
||
|
|
min_angle = [sin,cos]
|
||
|
|
next = p
|
||
|
|
#print_("min_angle=",min_angle)
|
||
|
|
|
||
|
|
return next
|
||
|
|
|
||
|
|
# Join edges together into new polygon cutting the vertexes inside new polygon
|
||
|
|
self.polygon = []
|
||
|
|
len_edges = sum([len(edges[p]) for p in edges])
|
||
|
|
loops = 0
|
||
|
|
|
||
|
|
while len(edges)>0 :
|
||
|
|
poly = []
|
||
|
|
if loops > len_edges : raise ValueError, "Hull error"
|
||
|
|
loops+=1
|
||
|
|
# Find left most vertex.
|
||
|
|
start = (1e100,1)
|
||
|
|
for edge in edges :
|
||
|
|
start = min(start, min(edges[edge]))
|
||
|
|
last = [(start[0][0]-1,start[0][1]),start[0],1]
|
||
|
|
first_run = True
|
||
|
|
loops1 = 0
|
||
|
|
while (last[1]!=start[0] or first_run) :
|
||
|
|
first_run = False
|
||
|
|
if loops1 > len_edges : raise ValueError, "Hull error"
|
||
|
|
loops1 += 1
|
||
|
|
next = get_closes_edge_by_angle(edges[last[1]],last)
|
||
|
|
#draw_pointer(next[0]+next[1],"Green","line", comment=i, width= 1)
|
||
|
|
#print_(next[0],"-",next[1])
|
||
|
|
|
||
|
|
last = next
|
||
|
|
poly += [ list(last[0]) ]
|
||
|
|
self.polygon += [ poly ]
|
||
|
|
# Remove all edges that are intersects new poly (any vertex inside new poly)
|
||
|
|
poly_ = Polygon([poly])
|
||
|
|
for p in edges.keys()[:] :
|
||
|
|
if poly_.point_inside(list(p)) : del edges[p]
|
||
|
|
self.draw(color="Green", width=1)
|
||
|
|
|
||
|
|
|
||
|
|
class Arangement_Genetic:
|
||
|
|
# gene = [fittness, order, rotation, xposition]
|
||
|
|
# spieces = [gene]*shapes count
|
||
|
|
# population = [spieces]
|
||
|
|
def __init__(self, polygons, material_width):
|
||
|
|
self.population = []
|
||
|
|
self.genes_count = len(polygons)
|
||
|
|
self.polygons = polygons
|
||
|
|
self.width = material_width
|
||
|
|
self.mutation_factor = 0.1
|
||
|
|
self.order_mutate_factor = 1.
|
||
|
|
self.move_mutate_factor = 1.
|
||
|
|
|
||
|
|
|
||
|
|
def add_random_species(self,count):
|
||
|
|
for i in range(count):
|
||
|
|
specimen = []
|
||
|
|
order = range(self.genes_count)
|
||
|
|
random.shuffle(order)
|
||
|
|
for j in order:
|
||
|
|
specimen += [ [j, random.random(), random.random()] ]
|
||
|
|
self.population += [ [None,specimen] ]
|
||
|
|
|
||
|
|
|
||
|
|
def species_distance2(self,sp1,sp2) :
|
||
|
|
# retun distance, each component is normalized
|
||
|
|
s = 0
|
||
|
|
for j in range(self.genes_count) :
|
||
|
|
s += ((sp1[j][0]-sp2[j][0])/self.genes_count)**2 + (( sp1[j][1]-sp2[j][1]))**2 + ((sp1[j][2]-sp2[j][2]))**2
|
||
|
|
return s
|
||
|
|
|
||
|
|
|
||
|
|
def similarity(self,sp1,top) :
|
||
|
|
# Define similarity as a simple distance between two points in len(gene)*len(spiece) -th dimentions
|
||
|
|
# for sp2 in top_spieces sum(|sp1-sp2|)/top_count
|
||
|
|
sim = 0
|
||
|
|
for sp2 in top :
|
||
|
|
sim += math.sqrt(species_distance2(sp1,sp2[1]))
|
||
|
|
return sim/len(top)
|
||
|
|
|
||
|
|
|
||
|
|
def leave_top_species(self,count):
|
||
|
|
self.population.sort()
|
||
|
|
res = [ copy.deepcopy(self.population[0]) ]
|
||
|
|
del self.population[0]
|
||
|
|
for i in range(count-1) :
|
||
|
|
t = []
|
||
|
|
for j in range(20) :
|
||
|
|
i1 = random.randint(0,len(self.population)-1)
|
||
|
|
t += [ [self.population[i1][0],i1] ]
|
||
|
|
t.sort()
|
||
|
|
res += [ copy.deepcopy(self.population[t[0][1]]) ]
|
||
|
|
del self.population[t[0][1]]
|
||
|
|
self.population = res
|
||
|
|
#del self.population[0]
|
||
|
|
#for c in range(count-1) :
|
||
|
|
# rank = []
|
||
|
|
# for i in range(len(self.population)) :
|
||
|
|
# sim = self.similarity(self.population[i][1],res)
|
||
|
|
# rank += [ [self.population[i][0] / sim if sim>0 else 1e100,i] ]
|
||
|
|
# rank.sort()
|
||
|
|
# res += [ copy.deepcopy(self.population[rank[0][1]]) ]
|
||
|
|
# print_(rank[0],self.population[rank[0][1]][0])
|
||
|
|
# print_(res[-1])
|
||
|
|
# del self.population[rank[0][1]]
|
||
|
|
|
||
|
|
self.population = res
|
||
|
|
|
||
|
|
|
||
|
|
def populate_species(self,count, parent_count):
|
||
|
|
self.population.sort()
|
||
|
|
self.inc = 0
|
||
|
|
for c in range(count):
|
||
|
|
parent1 = random.randint(0,parent_count-1)
|
||
|
|
parent2 = random.randint(0,parent_count-1)
|
||
|
|
if parent1==parent2 : parent2 = (parent2+1) % parent_count
|
||
|
|
parent1, parent2 = self.population[parent1][1], self.population[parent2][1]
|
||
|
|
i1,i2 = 0, 0
|
||
|
|
genes_order = []
|
||
|
|
specimen = [ [0,0.,0.] for i in range(self.genes_count) ]
|
||
|
|
|
||
|
|
self.incest_mutation_multiplyer = 1.
|
||
|
|
self.incest_mutation_count_multiplyer = 1.
|
||
|
|
|
||
|
|
if self.species_distance2(parent1, parent2) <= .01/self.genes_count :
|
||
|
|
# OMG it's a incest :O!!!
|
||
|
|
# Damn you bastards!
|
||
|
|
self.inc +=1
|
||
|
|
self.incest_mutation_multiplyer = 2.
|
||
|
|
self.incest_mutation_count_multiplyer = 2.
|
||
|
|
else :
|
||
|
|
if random.random()<.01 : print_(self.species_distance2(parent1, parent2))
|
||
|
|
start_gene = random.randint(0,self.genes_count)
|
||
|
|
end_gene = (max(1,random.randint(0,self.genes_count),int(self.genes_count/4))+start_gene) % self.genes_count
|
||
|
|
if end_gene<start_gene :
|
||
|
|
end_gene, start_gene = start_gene, end_gene
|
||
|
|
parent1, parent2 = parent2, parent1
|
||
|
|
for i in range(start_gene,end_gene) :
|
||
|
|
#rotation_mutate_param = random.random()/100
|
||
|
|
#xposition_mutate_param = random.random()/100
|
||
|
|
tr = 1. #- rotation_mutate_param
|
||
|
|
tp = 1. #- xposition_mutate_param
|
||
|
|
specimen[i] = [parent1[i][0], parent1[i][1]*tr+parent2[i][1]*(1-tr),parent1[i][2]*tp+parent2[i][2]*(1-tp)]
|
||
|
|
genes_order += [ parent1[i][0] ]
|
||
|
|
|
||
|
|
for i in range(0,start_gene)+range(end_gene,self.genes_count) :
|
||
|
|
tr = 0. #rotation_mutate_param
|
||
|
|
tp = 0. #xposition_mutate_param
|
||
|
|
j = i
|
||
|
|
while parent2[j][0] in genes_order :
|
||
|
|
j = (j+1)%self.genes_count
|
||
|
|
specimen[i] = [parent2[j][0], parent1[i][1]*tr+parent2[i][1]*(1-tr),parent1[i][2]*tp+parent2[i][2]*(1-tp)]
|
||
|
|
genes_order += [ parent2[j][0] ]
|
||
|
|
|
||
|
|
|
||
|
|
for i in range(random.randint(self.mutation_genes_count[0],self.mutation_genes_count[0]*self.incest_mutation_count_multiplyer )) :
|
||
|
|
if random.random() < self.order_mutate_factor * self.incest_mutation_multiplyer :
|
||
|
|
i1,i2 = random.randint(0,self.genes_count-1),random.randint(0,self.genes_count-1)
|
||
|
|
specimen[i1][0], specimen[i2][0] = specimen[i2][0], specimen[i1][0]
|
||
|
|
if random.random() < self.move_mutation_factor * self.incest_mutation_multiplyer:
|
||
|
|
i1 = random.randint(0,self.genes_count-1)
|
||
|
|
specimen[i1][1] = (specimen[i1][1]+random.random()*math.pi2*self.move_mutation_multiplier)%1.
|
||
|
|
specimen[i1][2] = (specimen[i1][2]+random.random()*self.move_mutation_multiplier)%1.
|
||
|
|
self.population += [ [None,specimen] ]
|
||
|
|
|
||
|
|
|
||
|
|
def test_spiece_drop_down(self,spiece) :
|
||
|
|
surface = Polygon()
|
||
|
|
for p in spiece :
|
||
|
|
time_ = time.time()
|
||
|
|
poly = Polygon(copy.deepcopy(self.polygons[p[0]].polygon))
|
||
|
|
poly.rotate(p[1]*math.pi2)
|
||
|
|
w = poly.width()
|
||
|
|
left = poly.bounds()[0]
|
||
|
|
poly.move( -left + (self.width-w)*p[2],0)
|
||
|
|
poly.drop_down(surface)
|
||
|
|
surface.add(poly)
|
||
|
|
return surface
|
||
|
|
|
||
|
|
|
||
|
|
def test(self,test_function):
|
||
|
|
for i in range(len(self.population)) :
|
||
|
|
if self.population[i][0] == None :
|
||
|
|
surface = test_function(self.population[i][1])
|
||
|
|
b = surface.bounds()
|
||
|
|
self.population[i][0] = (b[3]-b[1])*(b[2]-b[0])
|
||
|
|
self.population.sort()
|
||
|
|
|
||
|
|
|
||
|
|
def test_spiece_centroid(self,spiece) :
|
||
|
|
poly = Polygon(copy.deepcopy(self.polygons[spiece[0][0]].polygon))
|
||
|
|
poly.rotate(spiece[0][2]*math.pi2)
|
||
|
|
surface = Polygon(poly.polygon)
|
||
|
|
i = 0
|
||
|
|
for p in spiece[1:] :
|
||
|
|
i += 1
|
||
|
|
poly = Polygon(copy.deepcopy(self.polygons[p[0]].polygon))
|
||
|
|
poly.rotate(p[2]*math.pi2)
|
||
|
|
c = surface.centroid()
|
||
|
|
c1 = poly.centroid()
|
||
|
|
direction = [math.cos(p[1]*math.pi2), -math.sin(p[1]*math.pi2)]
|
||
|
|
poly.move(c[0]-c1[0]-direction[0]*100,c[1]-c1[1]-direction[1]*100)
|
||
|
|
poly.drop_into_direction(direction,surface)
|
||
|
|
surface.add(poly)
|
||
|
|
return surface
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
#surface.draw()
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Gcodetools class
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
|
||
|
|
class laser_gcode(inkex.Effect):
|
||
|
|
|
||
|
|
def export_gcode(self,gcode):
|
||
|
|
gcode_pass = gcode
|
||
|
|
for x in range(1,self.options.passes):
|
||
|
|
gcode += "G91\nG1 Z-" + self.options.pass_depth + "\nG90\n" + gcode_pass
|
||
|
|
f = open(self.options.directory+self.options.file, "w")
|
||
|
|
f.write(self.options.laser_off_command + " S0" + "\n" + self.header + "G1 F" + self.options.travel_speed + "\n" + gcode + self.footer)
|
||
|
|
f.close()
|
||
|
|
|
||
|
|
def __init__(self):
|
||
|
|
inkex.Effect.__init__(self)
|
||
|
|
self.OptionParser.add_option("-d", "--directory", action="store", type="string", dest="directory", default="", help="Output directory")
|
||
|
|
self.OptionParser.add_option("-f", "--filename", action="store", type="string", dest="file", default="output.gcode", help="File name")
|
||
|
|
self.OptionParser.add_option("", "--add-numeric-suffix-to-filename", action="store", type="inkbool", dest="add_numeric_suffix_to_filename", default=False, help="Add numeric suffix to file name")
|
||
|
|
self.OptionParser.add_option("", "--laser-command", action="store", type="string", dest="laser_command", default="M03", help="Laser gcode command")
|
||
|
|
self.OptionParser.add_option("", "--laser-off-command", action="store", type="string", dest="laser_off_command", default="M05", help="Laser gcode end command")
|
||
|
|
self.OptionParser.add_option("", "--laser-speed", action="store", type="int", dest="laser_speed", default="750", help="Laser speed (mm/min)")
|
||
|
|
self.OptionParser.add_option("", "--travel-speed", action="store", type="string", dest="travel_speed", default="3000", help="Travel speed (mm/min)")
|
||
|
|
self.OptionParser.add_option("", "--laser-power", action="store", type="int", dest="laser_power", default="255", help="S# is 256 or 10000 for full power")
|
||
|
|
self.OptionParser.add_option("", "--passes", action="store", type="int", dest="passes", default="1", help="Quantity of passes")
|
||
|
|
self.OptionParser.add_option("", "--pass-depth", action="store", type="string", dest="pass_depth", default="1", help="Depth of laser cut")
|
||
|
|
self.OptionParser.add_option("", "--power-delay", action="store", type="string", dest="power_delay", default="0", help="Laser power-on delay (ms)")
|
||
|
|
self.OptionParser.add_option("", "--suppress-all-messages", action="store", type="inkbool", dest="suppress_all_messages", default=True, help="Hide messages during g-code generation")
|
||
|
|
self.OptionParser.add_option("", "--create-log", action="store", type="inkbool", dest="log_create_log", default=False, help="Create log files")
|
||
|
|
self.OptionParser.add_option("", "--log-filename", action="store", type="string", dest="log_filename", default='', help="Create log files")
|
||
|
|
self.OptionParser.add_option("", "--engraving-draw-calculation-paths",action="store", type="inkbool", dest="engraving_draw_calculation_paths", default=False, help="Draw additional graphics to debug engraving path")
|
||
|
|
self.OptionParser.add_option("", "--unit", action="store", type="string", dest="unit", default="G21 (All units in mm)", help="Units either mm or inches")
|
||
|
|
self.OptionParser.add_option("", "--active-tab", action="store", type="string", dest="active_tab", default="", help="Defines which tab is active")
|
||
|
|
self.OptionParser.add_option("", "--biarc-max-split-depth", action="store", type="int", dest="biarc_max_split_depth", default="4", help="Defines maximum depth of splitting while approximating using biarcs.")
|
||
|
|
|
||
|
|
def parse_curve(self, p, layer, w = None, f = None):
|
||
|
|
c = []
|
||
|
|
if len(p)==0 :
|
||
|
|
return []
|
||
|
|
p = self.transform_csp(p, layer)
|
||
|
|
|
||
|
|
|
||
|
|
### Sort to reduce Rapid distance
|
||
|
|
k = range(1,len(p))
|
||
|
|
keys = [0]
|
||
|
|
while len(k)>0:
|
||
|
|
end = p[keys[-1]][-1][1]
|
||
|
|
dist = None
|
||
|
|
for i in range(len(k)):
|
||
|
|
start = p[k[i]][0][1]
|
||
|
|
dist = max( ( -( ( end[0]-start[0])**2+(end[1]-start[1])**2 ) ,i) , dist )
|
||
|
|
keys += [k[dist[1]]]
|
||
|
|
del k[dist[1]]
|
||
|
|
for k in keys:
|
||
|
|
subpath = p[k]
|
||
|
|
c += [ [ [subpath[0][1][0],subpath[0][1][1]] , 'move', 0, 0] ]
|
||
|
|
for i in range(1,len(subpath)):
|
||
|
|
sp1 = [ [subpath[i-1][j][0], subpath[i-1][j][1]] for j in range(3)]
|
||
|
|
sp2 = [ [subpath[i ][j][0], subpath[i ][j][1]] for j in range(3)]
|
||
|
|
c += biarc(sp1,sp2,0,0) if w==None else biarc(sp1,sp2,-f(w[k][i-1]),-f(w[k][i]))
|
||
|
|
# l1 = biarc(sp1,sp2,0,0) if w==None else biarc(sp1,sp2,-f(w[k][i-1]),-f(w[k][i]))
|
||
|
|
# print_((-f(w[k][i-1]),-f(w[k][i]), [i1[5] for i1 in l1]) )
|
||
|
|
c += [ [ [subpath[-1][1][0],subpath[-1][1][1]] ,'end',0,0] ]
|
||
|
|
print_("Curve: " + str(c))
|
||
|
|
return c
|
||
|
|
|
||
|
|
|
||
|
|
def draw_curve(self, curve, layer, group=None, style=styles["biarc_style"]):
|
||
|
|
|
||
|
|
self.get_defs()
|
||
|
|
# Add marker to defs if it doesnot exists
|
||
|
|
if "DrawCurveMarker" not in self.defs :
|
||
|
|
defs = inkex.etree.SubElement( self.document.getroot(), inkex.addNS("defs","svg"))
|
||
|
|
marker = inkex.etree.SubElement( defs, inkex.addNS("marker","svg"), {"id":"DrawCurveMarker","orient":"auto","refX":"-8","refY":"-2.41063","style":"overflow:visible"})
|
||
|
|
inkex.etree.SubElement( marker, inkex.addNS("path","svg"),
|
||
|
|
{ "d":"m -6.55552,-2.41063 0,0 L -13.11104,0 c 1.0473,-1.42323 1.04126,-3.37047 0,-4.82126",
|
||
|
|
"style": "fill:#000044; fill-rule:evenodd;stroke-width:0.62500000;stroke-linejoin:round;" }
|
||
|
|
)
|
||
|
|
if "DrawCurveMarker_r" not in self.defs :
|
||
|
|
defs = inkex.etree.SubElement( self.document.getroot(), inkex.addNS("defs","svg"))
|
||
|
|
marker = inkex.etree.SubElement( defs, inkex.addNS("marker","svg"), {"id":"DrawCurveMarker_r","orient":"auto","refX":"8","refY":"-2.41063","style":"overflow:visible"})
|
||
|
|
inkex.etree.SubElement( marker, inkex.addNS("path","svg"),
|
||
|
|
{ "d":"m 6.55552,-2.41063 0,0 L 13.11104,0 c -1.0473,-1.42323 -1.04126,-3.37047 0,-4.82126",
|
||
|
|
"style": "fill:#000044; fill-rule:evenodd;stroke-width:0.62500000;stroke-linejoin:round;" }
|
||
|
|
)
|
||
|
|
for i in [0,1]:
|
||
|
|
style['biarc%s_r'%i] = simplestyle.parseStyle(style['biarc%s'%i])
|
||
|
|
style['biarc%s_r'%i]["marker-start"] = "url(#DrawCurveMarker_r)"
|
||
|
|
del(style['biarc%s_r'%i]["marker-end"])
|
||
|
|
style['biarc%s_r'%i] = simplestyle.formatStyle(style['biarc%s_r'%i])
|
||
|
|
|
||
|
|
if group==None:
|
||
|
|
group = inkex.etree.SubElement( self.layers[min(1,len(self.layers)-1)], inkex.addNS('g','svg'), {"gcodetools": "Preview group"} )
|
||
|
|
s, arcn = '', 0
|
||
|
|
|
||
|
|
|
||
|
|
a,b,c = [0.,0.], [1.,0.], [0.,1.]
|
||
|
|
k = (b[0]-a[0])*(c[1]-a[1])-(c[0]-a[0])*(b[1]-a[1])
|
||
|
|
a,b,c = self.transform(a, layer, True), self.transform(b, layer, True), self.transform(c, layer, True)
|
||
|
|
if ((b[0]-a[0])*(c[1]-a[1])-(c[0]-a[0])*(b[1]-a[1]))*k > 0 : reverse_angle = 1
|
||
|
|
else : reverse_angle = -1
|
||
|
|
for sk in curve:
|
||
|
|
si = sk[:]
|
||
|
|
si[0], si[2] = self.transform(si[0], layer, True), (self.transform(si[2], layer, True) if type(si[2])==type([]) and len(si[2])==2 else si[2])
|
||
|
|
|
||
|
|
if s!='':
|
||
|
|
if s[1] == 'line':
|
||
|
|
inkex.etree.SubElement( group, inkex.addNS('path','svg'),
|
||
|
|
{
|
||
|
|
'style': style['line'],
|
||
|
|
'd':'M %s,%s L %s,%s' % (s[0][0], s[0][1], si[0][0], si[0][1]),
|
||
|
|
"gcodetools": "Preview",
|
||
|
|
}
|
||
|
|
)
|
||
|
|
elif s[1] == 'arc':
|
||
|
|
arcn += 1
|
||
|
|
sp = s[0]
|
||
|
|
c = s[2]
|
||
|
|
s[3] = s[3]*reverse_angle
|
||
|
|
|
||
|
|
a = ( (P(si[0])-P(c)).angle() - (P(s[0])-P(c)).angle() )%math.pi2 #s[3]
|
||
|
|
if s[3]*a<0:
|
||
|
|
if a>0: a = a-math.pi2
|
||
|
|
else: a = math.pi2+a
|
||
|
|
r = math.sqrt( (sp[0]-c[0])**2 + (sp[1]-c[1])**2 )
|
||
|
|
a_st = ( math.atan2(sp[0]-c[0],- (sp[1]-c[1])) - math.pi/2 ) % (math.pi*2)
|
||
|
|
st = style['biarc%s' % (arcn%2)][:]
|
||
|
|
if a>0:
|
||
|
|
a_end = a_st+a
|
||
|
|
st = style['biarc%s'%(arcn%2)]
|
||
|
|
else:
|
||
|
|
a_end = a_st*1
|
||
|
|
a_st = a_st+a
|
||
|
|
st = style['biarc%s_r'%(arcn%2)]
|
||
|
|
inkex.etree.SubElement( group, inkex.addNS('path','svg'),
|
||
|
|
{
|
||
|
|
'style': st,
|
||
|
|
inkex.addNS('cx','sodipodi'): str(c[0]),
|
||
|
|
inkex.addNS('cy','sodipodi'): str(c[1]),
|
||
|
|
inkex.addNS('rx','sodipodi'): str(r),
|
||
|
|
inkex.addNS('ry','sodipodi'): str(r),
|
||
|
|
inkex.addNS('start','sodipodi'): str(a_st),
|
||
|
|
inkex.addNS('end','sodipodi'): str(a_end),
|
||
|
|
inkex.addNS('open','sodipodi'): 'true',
|
||
|
|
inkex.addNS('type','sodipodi'): 'arc',
|
||
|
|
"gcodetools": "Preview",
|
||
|
|
})
|
||
|
|
s = si
|
||
|
|
|
||
|
|
|
||
|
|
def check_dir(self):
|
||
|
|
if self.options.directory[-1] not in ["/","\\"]:
|
||
|
|
if "\\" in self.options.directory :
|
||
|
|
self.options.directory += "\\"
|
||
|
|
else :
|
||
|
|
self.options.directory += "/"
|
||
|
|
print_("Checking direcrory: '%s'"%self.options.directory)
|
||
|
|
if (os.path.isdir(self.options.directory)):
|
||
|
|
if (os.path.isfile(self.options.directory+'header')):
|
||
|
|
f = open(self.options.directory+'header', 'r')
|
||
|
|
self.header = f.read()
|
||
|
|
f.close()
|
||
|
|
else:
|
||
|
|
self.header = defaults['header']
|
||
|
|
if (os.path.isfile(self.options.directory+'footer')):
|
||
|
|
f = open(self.options.directory+'footer','r')
|
||
|
|
self.footer = f.read()
|
||
|
|
f.close()
|
||
|
|
else:
|
||
|
|
self.footer = defaults['footer']
|
||
|
|
|
||
|
|
if self.options.unit == "G21 (All units in mm)" :
|
||
|
|
self.header += "G21\n"
|
||
|
|
elif self.options.unit == "G20 (All units in inches)" :
|
||
|
|
self.header += "G20\n"
|
||
|
|
else:
|
||
|
|
self.error(_("Directory does not exist! Please specify existing directory at options tab!"),"error")
|
||
|
|
return False
|
||
|
|
|
||
|
|
if self.options.add_numeric_suffix_to_filename :
|
||
|
|
dir_list = os.listdir(self.options.directory)
|
||
|
|
if "." in self.options.file :
|
||
|
|
r = re.match(r"^(.*)(\..*)$",self.options.file)
|
||
|
|
ext = r.group(2)
|
||
|
|
name = r.group(1)
|
||
|
|
else:
|
||
|
|
ext = ""
|
||
|
|
name = self.options.file
|
||
|
|
max_n = 0
|
||
|
|
for s in dir_list :
|
||
|
|
r = re.match(r"^%s_0*(\d+)%s$"%(re.escape(name),re.escape(ext) ), s)
|
||
|
|
if r :
|
||
|
|
max_n = max(max_n,int(r.group(1)))
|
||
|
|
filename = name + "_" + ( "0"*(4-len(str(max_n+1))) + str(max_n+1) ) + ext
|
||
|
|
self.options.file = filename
|
||
|
|
|
||
|
|
print_("Testing writing rights on '%s'"%(self.options.directory+self.options.file))
|
||
|
|
try:
|
||
|
|
f = open(self.options.directory+self.options.file, "w")
|
||
|
|
f.close()
|
||
|
|
except:
|
||
|
|
self.error(_("Can not write to specified file!\n%s"%(self.options.directory+self.options.file)),"error")
|
||
|
|
return False
|
||
|
|
return True
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Generate Gcode
|
||
|
|
### Generates Gcode on given curve.
|
||
|
|
###
|
||
|
|
### Crve defenitnion [start point, type = {'arc','line','move','end'}, arc center, arc angle, end point, [zstart, zend]]
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def generate_gcode(self, curve, layer, depth):
|
||
|
|
tool = self.tools
|
||
|
|
print_("Tool in g-code generator: " + str(tool))
|
||
|
|
def c(c):
|
||
|
|
c = [c[i] if i<len(c) else None for i in range(6)]
|
||
|
|
if c[5] == 0 : c[5]=None
|
||
|
|
s = [" X", " Y", " Z", " I", " J", " K"]
|
||
|
|
r = ''
|
||
|
|
for i in range(6):
|
||
|
|
if c[i]!=None:
|
||
|
|
r += s[i] + ("%f" % (round(c[i],4))).rstrip('0')
|
||
|
|
return r
|
||
|
|
|
||
|
|
def calculate_angle(a, current_a):
|
||
|
|
return min(
|
||
|
|
[abs(a-current_a%math.pi2+math.pi2), a+current_a-current_a%math.pi2+math.pi2],
|
||
|
|
[abs(a-current_a%math.pi2-math.pi2), a+current_a-current_a%math.pi2-math.pi2],
|
||
|
|
[abs(a-current_a%math.pi2), a+current_a-current_a%math.pi2])[1]
|
||
|
|
if len(curve)==0 : return ""
|
||
|
|
|
||
|
|
try :
|
||
|
|
self.last_used_tool == None
|
||
|
|
except :
|
||
|
|
self.last_used_tool = None
|
||
|
|
print_("working on curve")
|
||
|
|
print_("Curve: " + str(curve))
|
||
|
|
g = ""
|
||
|
|
|
||
|
|
lg, f = 'G00', "F%f"%tool['penetration feed']
|
||
|
|
penetration_feed = "F%s"%tool['penetration feed']
|
||
|
|
current_a = 0
|
||
|
|
for i in range(1,len(curve)):
|
||
|
|
# Creating Gcode for curve between s=curve[i-1] and si=curve[i] start at s[0] end at s[4]=si[0]
|
||
|
|
s, si = curve[i-1], curve[i]
|
||
|
|
feed = f if lg not in ['G01','G02','G03'] else ''
|
||
|
|
if s[1] == 'move':
|
||
|
|
g += "G1 " + c(si[0]) + "\n" + tool['gcode before path'] + "\n"
|
||
|
|
lg = 'G00'
|
||
|
|
elif s[1] == 'end':
|
||
|
|
g += tool['gcode after path'] + "\n"
|
||
|
|
lg = 'G00'
|
||
|
|
elif s[1] == 'line':
|
||
|
|
if lg=="G00": g += "G1 " + feed + "\n"
|
||
|
|
g += "G1 " + c(si[0]) + "\n"
|
||
|
|
lg = 'G01'
|
||
|
|
elif s[1] == 'arc':
|
||
|
|
r = [(s[2][0]-s[0][0]), (s[2][1]-s[0][1])]
|
||
|
|
if lg=="G00": g += "G1 " + feed + "\n"
|
||
|
|
if (r[0]**2 + r[1]**2)>.1:
|
||
|
|
r1, r2 = (P(s[0])-P(s[2])), (P(si[0])-P(s[2]))
|
||
|
|
if abs(r1.mag()-r2.mag()) < 0.001 :
|
||
|
|
g += ("G2" if s[3]<0 else "G3") + c(si[0]+[ None, (s[2][0]-s[0][0]),(s[2][1]-s[0][1]) ]) + "\n"
|
||
|
|
else:
|
||
|
|
r = (r1.mag()+r2.mag())/2
|
||
|
|
g += ("G2" if s[3]<0 else "G3") + c(si[0]) + " R%f" % (r) + "\n"
|
||
|
|
lg = 'G02'
|
||
|
|
else:
|
||
|
|
g += "G1 " + c(si[0]) + " " + feed + "\n"
|
||
|
|
lg = 'G01'
|
||
|
|
if si[1] == 'end':
|
||
|
|
g += tool['gcode after path'] + "\n"
|
||
|
|
return g
|
||
|
|
|
||
|
|
|
||
|
|
def get_transforms(self,g):
|
||
|
|
root = self.document.getroot()
|
||
|
|
trans = []
|
||
|
|
while (g!=root):
|
||
|
|
if 'transform' in g.keys():
|
||
|
|
t = g.get('transform')
|
||
|
|
t = simpletransform.parseTransform(t)
|
||
|
|
trans = simpletransform.composeTransform(t,trans) if trans != [] else t
|
||
|
|
print_(trans)
|
||
|
|
g=g.getparent()
|
||
|
|
return trans
|
||
|
|
|
||
|
|
|
||
|
|
def apply_transforms(self,g,csp):
|
||
|
|
trans = self.get_transforms(g)
|
||
|
|
if trans != []:
|
||
|
|
simpletransform.applyTransformToPath(trans, csp)
|
||
|
|
return csp
|
||
|
|
|
||
|
|
|
||
|
|
def transform(self, source_point, layer, reverse=False):
|
||
|
|
if layer == None :
|
||
|
|
layer = self.current_layer if self.current_layer is not None else self.document.getroot()
|
||
|
|
if layer not in self.transform_matrix:
|
||
|
|
for i in range(self.layers.index(layer),-1,-1):
|
||
|
|
if self.layers[i] in self.orientation_points :
|
||
|
|
break
|
||
|
|
|
||
|
|
print_(str(self.layers))
|
||
|
|
print_(str("I: " + str(i)))
|
||
|
|
print_("Transform: " + str(self.layers[i]))
|
||
|
|
if self.layers[i] not in self.orientation_points :
|
||
|
|
self.error(_("Orientation points for '%s' layer have not been found! Please add orientation points using Orientation tab!") % layer.get(inkex.addNS('label','inkscape')),"no_orientation_points")
|
||
|
|
elif self.layers[i] in self.transform_matrix :
|
||
|
|
self.transform_matrix[layer] = self.transform_matrix[self.layers[i]]
|
||
|
|
else :
|
||
|
|
orientation_layer = self.layers[i]
|
||
|
|
if len(self.orientation_points[orientation_layer])>1 :
|
||
|
|
self.error(_("There are more than one orientation point groups in '%s' layer") % orientation_layer.get(inkex.addNS('label','inkscape')),"more_than_one_orientation_point_groups")
|
||
|
|
points = self.orientation_points[orientation_layer][0]
|
||
|
|
if len(points)==2:
|
||
|
|
points += [ [ [(points[1][0][1]-points[0][0][1])+points[0][0][0], -(points[1][0][0]-points[0][0][0])+points[0][0][1]], [-(points[1][1][1]-points[0][1][1])+points[0][1][0], points[1][1][0]-points[0][1][0]+points[0][1][1]] ] ]
|
||
|
|
if len(points)==3:
|
||
|
|
print_("Layer '%s' Orientation points: " % orientation_layer.get(inkex.addNS('label','inkscape')))
|
||
|
|
for point in points:
|
||
|
|
print_(point)
|
||
|
|
# Zcoordinates definition taken from Orientatnion point 1 and 2
|
||
|
|
self.Zcoordinates[layer] = [max(points[0][1][2],points[1][1][2]), min(points[0][1][2],points[1][1][2])]
|
||
|
|
matrix = numpy.array([
|
||
|
|
[points[0][0][0], points[0][0][1], 1, 0, 0, 0, 0, 0, 0],
|
||
|
|
[0, 0, 0, points[0][0][0], points[0][0][1], 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, points[0][0][0], points[0][0][1], 1],
|
||
|
|
[points[1][0][0], points[1][0][1], 1, 0, 0, 0, 0, 0, 0],
|
||
|
|
[0, 0, 0, points[1][0][0], points[1][0][1], 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, points[1][0][0], points[1][0][1], 1],
|
||
|
|
[points[2][0][0], points[2][0][1], 1, 0, 0, 0, 0, 0, 0],
|
||
|
|
[0, 0, 0, points[2][0][0], points[2][0][1], 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, points[2][0][0], points[2][0][1], 1]
|
||
|
|
])
|
||
|
|
|
||
|
|
if numpy.linalg.det(matrix)!=0 :
|
||
|
|
m = numpy.linalg.solve(matrix,
|
||
|
|
numpy.array(
|
||
|
|
[[points[0][1][0]], [points[0][1][1]], [1], [points[1][1][0]], [points[1][1][1]], [1], [points[2][1][0]], [points[2][1][1]], [1]]
|
||
|
|
)
|
||
|
|
).tolist()
|
||
|
|
self.transform_matrix[layer] = [[m[j*3+i][0] for i in range(3)] for j in range(3)]
|
||
|
|
|
||
|
|
else :
|
||
|
|
self.error(_("Orientation points are wrong! (if there are two orientation points they sould not be the same. If there are three orientation points they should not be in a straight line.)"),"wrong_orientation_points")
|
||
|
|
else :
|
||
|
|
self.error(_("Orientation points are wrong! (if there are two orientation points they sould not be the same. If there are three orientation points they should not be in a straight line.)"),"wrong_orientation_points")
|
||
|
|
|
||
|
|
self.transform_matrix_reverse[layer] = numpy.linalg.inv(self.transform_matrix[layer]).tolist()
|
||
|
|
print_("\n Layer '%s' transformation matrixes:" % layer.get(inkex.addNS('label','inkscape')) )
|
||
|
|
print_(self.transform_matrix)
|
||
|
|
print_(self.transform_matrix_reverse)
|
||
|
|
|
||
|
|
###self.Zauto_scale[layer] = math.sqrt( (self.transform_matrix[layer][0][0]**2 + self.transform_matrix[layer][1][1]**2)/2 )
|
||
|
|
### Zautoscale is absolete
|
||
|
|
self.Zauto_scale[layer] = 1
|
||
|
|
print_("Z automatic scale = %s (computed according orientation points)" % self.Zauto_scale[layer])
|
||
|
|
|
||
|
|
x,y = source_point[0], source_point[1]
|
||
|
|
if not reverse :
|
||
|
|
t = self.transform_matrix[layer]
|
||
|
|
else :
|
||
|
|
t = self.transform_matrix_reverse[layer]
|
||
|
|
return [t[0][0]*x+t[0][1]*y+t[0][2], t[1][0]*x+t[1][1]*y+t[1][2]]
|
||
|
|
|
||
|
|
|
||
|
|
def transform_csp(self, csp_, layer, reverse = False):
|
||
|
|
csp = [ [ [csp_[i][j][0][:],csp_[i][j][1][:],csp_[i][j][2][:]] for j in range(len(csp_[i])) ] for i in range(len(csp_)) ]
|
||
|
|
for i in xrange(len(csp)):
|
||
|
|
for j in xrange(len(csp[i])):
|
||
|
|
for k in xrange(len(csp[i][j])):
|
||
|
|
csp[i][j][k] = self.transform(csp[i][j][k],layer, reverse)
|
||
|
|
return csp
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Errors handling function, notes are just printed into Logfile,
|
||
|
|
### warnings are printed into log file and warning message is displayed but
|
||
|
|
### extension continues working, errors causes log and execution is halted
|
||
|
|
### Notes, warnings adn errors could be assigned to space or comma or dot
|
||
|
|
### sepparated strings (case is ignoreg).
|
||
|
|
################################################################################
|
||
|
|
def error(self, s, type_= "Warning"):
|
||
|
|
notes = "Note "
|
||
|
|
warnings = """
|
||
|
|
Warning tools_warning
|
||
|
|
bad_orientation_points_in_some_layers
|
||
|
|
more_than_one_orientation_point_groups
|
||
|
|
more_than_one_tool
|
||
|
|
orientation_have_not_been_defined
|
||
|
|
tool_have_not_been_defined
|
||
|
|
selection_does_not_contain_paths
|
||
|
|
selection_does_not_contain_paths_will_take_all
|
||
|
|
selection_is_empty_will_comupe_drawing
|
||
|
|
selection_contains_objects_that_are_not_paths
|
||
|
|
"""
|
||
|
|
errors = """
|
||
|
|
Error
|
||
|
|
wrong_orientation_points
|
||
|
|
area_tools_diameter_error
|
||
|
|
no_tool_error
|
||
|
|
active_layer_already_has_tool
|
||
|
|
active_layer_already_has_orientation_points
|
||
|
|
"""
|
||
|
|
if type_.lower() in re.split("[\s\n,\.]+", errors.lower()) :
|
||
|
|
print_(s)
|
||
|
|
inkex.errormsg(s+"\n")
|
||
|
|
sys.exit()
|
||
|
|
elif type_.lower() in re.split("[\s\n,\.]+", warnings.lower()) :
|
||
|
|
print_(s)
|
||
|
|
if not self.options.suppress_all_messages :
|
||
|
|
inkex.errormsg(s+"\n")
|
||
|
|
elif type_.lower() in re.split("[\s\n,\.]+", notes.lower()) :
|
||
|
|
print_(s)
|
||
|
|
else :
|
||
|
|
print_(s)
|
||
|
|
inkex.errormsg(s)
|
||
|
|
sys.exit()
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
### Get defs from svg
|
||
|
|
################################################################################
|
||
|
|
def get_defs(self) :
|
||
|
|
self.defs = {}
|
||
|
|
def recursive(g) :
|
||
|
|
for i in g:
|
||
|
|
if i.tag == inkex.addNS("defs","svg") :
|
||
|
|
for j in i:
|
||
|
|
self.defs[j.get("id")] = i
|
||
|
|
if i.tag ==inkex.addNS("g",'svg') :
|
||
|
|
recursive(i)
|
||
|
|
recursive(self.document.getroot())
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Get Gcodetools info from the svg
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def get_info(self):
|
||
|
|
self.selected_paths = {}
|
||
|
|
self.paths = {}
|
||
|
|
self.orientation_points = {}
|
||
|
|
self.layers = [self.document.getroot()]
|
||
|
|
self.Zcoordinates = {}
|
||
|
|
self.transform_matrix = {}
|
||
|
|
self.transform_matrix_reverse = {}
|
||
|
|
self.Zauto_scale = {}
|
||
|
|
|
||
|
|
def recursive_search(g, layer, selected=False):
|
||
|
|
items = g.getchildren()
|
||
|
|
items.reverse()
|
||
|
|
for i in items:
|
||
|
|
if selected:
|
||
|
|
self.selected[i.get("id")] = i
|
||
|
|
if i.tag == inkex.addNS("g",'svg') and i.get(inkex.addNS('groupmode','inkscape')) == 'layer':
|
||
|
|
self.layers += [i]
|
||
|
|
recursive_search(i,i)
|
||
|
|
elif i.get('gcodetools') == "Gcodetools orientation group" :
|
||
|
|
points = self.get_orientation_points(i)
|
||
|
|
if points != None :
|
||
|
|
self.orientation_points[layer] = self.orientation_points[layer]+[points[:]] if layer in self.orientation_points else [points[:]]
|
||
|
|
print_("Found orientation points in '%s' layer: %s" % (layer.get(inkex.addNS('label','inkscape')), points))
|
||
|
|
else :
|
||
|
|
self.error(_("Warning! Found bad orientation points in '%s' layer. Resulting Gcode could be corrupt!") % layer.get(inkex.addNS('label','inkscape')), "bad_orientation_points_in_some_layers")
|
||
|
|
elif i.tag == inkex.addNS('path','svg'):
|
||
|
|
if "gcodetools" not in i.keys() :
|
||
|
|
self.paths[layer] = self.paths[layer] + [i] if layer in self.paths else [i]
|
||
|
|
if i.get("id") in self.selected :
|
||
|
|
self.selected_paths[layer] = self.selected_paths[layer] + [i] if layer in self.selected_paths else [i]
|
||
|
|
elif i.tag == inkex.addNS("g",'svg'):
|
||
|
|
recursive_search(i,layer, (i.get("id") in self.selected) )
|
||
|
|
elif i.get("id") in self.selected :
|
||
|
|
self.error(_("This extension works with Paths and Dynamic Offsets and groups of them only! All other objects will be ignored!\nSolution 1: press Path->Object to path or Shift+Ctrl+C.\nSolution 2: Path->Dynamic offset or Ctrl+J.\nSolution 3: export all contours to PostScript level 2 (File->Save As->.ps) and File->Import this file."),"selection_contains_objects_that_are_not_paths")
|
||
|
|
|
||
|
|
|
||
|
|
recursive_search(self.document.getroot(),self.document.getroot())
|
||
|
|
|
||
|
|
|
||
|
|
def get_orientation_points(self,g):
|
||
|
|
items = g.getchildren()
|
||
|
|
items.reverse()
|
||
|
|
p2, p3 = [], []
|
||
|
|
p = None
|
||
|
|
for i in items:
|
||
|
|
if i.tag == inkex.addNS("g",'svg') and i.get("gcodetools") == "Gcodetools orientation point (2 points)":
|
||
|
|
p2 += [i]
|
||
|
|
if i.tag == inkex.addNS("g",'svg') and i.get("gcodetools") == "Gcodetools orientation point (3 points)":
|
||
|
|
p3 += [i]
|
||
|
|
if len(p2)==2 : p=p2
|
||
|
|
elif len(p3)==3 : p=p3
|
||
|
|
if p==None : return None
|
||
|
|
points = []
|
||
|
|
for i in p :
|
||
|
|
point = [[],[]]
|
||
|
|
for node in i :
|
||
|
|
if node.get('gcodetools') == "Gcodetools orientation point arrow":
|
||
|
|
point[0] = self.apply_transforms(node,cubicsuperpath.parsePath(node.get("d")))[0][0][1]
|
||
|
|
if node.get('gcodetools') == "Gcodetools orientation point text":
|
||
|
|
r = re.match(r'(?i)\s*\(\s*(-?\s*\d*(?:,|\.)*\d*)\s*;\s*(-?\s*\d*(?:,|\.)*\d*)\s*;\s*(-?\s*\d*(?:,|\.)*\d*)\s*\)\s*',node.text)
|
||
|
|
point[1] = [float(r.group(1)),float(r.group(2)),float(r.group(3))]
|
||
|
|
if point[0]!=[] and point[1]!=[]: points += [point]
|
||
|
|
if len(points)==len(p2)==2 or len(points)==len(p3)==3 : return points
|
||
|
|
else : return None
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### dxfpoints
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def dxfpoints(self):
|
||
|
|
if self.selected_paths == {}:
|
||
|
|
self.error(_("Noting is selected. Please select something to convert to drill point (dxfpoint) or clear point sign."),"warning")
|
||
|
|
for layer in self.layers :
|
||
|
|
if layer in self.selected_paths :
|
||
|
|
for path in self.selected_paths[layer]:
|
||
|
|
if self.options.dxfpoints_action == 'replace':
|
||
|
|
path.set("dxfpoint","1")
|
||
|
|
r = re.match("^\s*.\s*(\S+)",path.get("d"))
|
||
|
|
if r!=None:
|
||
|
|
print_(("got path=",r.group(1)))
|
||
|
|
path.set("d","m %s 2.9375,-6.343750000001 0.8125,1.90625 6.843748640396,-6.84374864039 0,0 0.6875,0.6875 -6.84375,6.84375 1.90625,0.812500000001 z" % r.group(1))
|
||
|
|
path.set("style",styles["dxf_points"])
|
||
|
|
|
||
|
|
if self.options.dxfpoints_action == 'save':
|
||
|
|
path.set("dxfpoint","1")
|
||
|
|
|
||
|
|
if self.options.dxfpoints_action == 'clear' and path.get("dxfpoint") == "1":
|
||
|
|
path.set("dxfpoint","0")
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Laser
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def laser(self) :
|
||
|
|
|
||
|
|
def get_boundaries(points):
|
||
|
|
minx,miny,maxx,maxy=None,None,None,None
|
||
|
|
out=[[],[],[],[]]
|
||
|
|
for p in points:
|
||
|
|
if minx==p[0]:
|
||
|
|
out[0]+=[p]
|
||
|
|
if minx==None or p[0]<minx:
|
||
|
|
minx=p[0]
|
||
|
|
out[0]=[p]
|
||
|
|
|
||
|
|
if miny==p[1]:
|
||
|
|
out[1]+=[p]
|
||
|
|
if miny==None or p[1]<miny:
|
||
|
|
miny=p[1]
|
||
|
|
out[1]=[p]
|
||
|
|
|
||
|
|
if maxx==p[0]:
|
||
|
|
out[2]+=[p]
|
||
|
|
if maxx==None or p[0]>maxx:
|
||
|
|
maxx=p[0]
|
||
|
|
out[2]=[p]
|
||
|
|
|
||
|
|
if maxy==p[1]:
|
||
|
|
out[3]+=[p]
|
||
|
|
if maxy==None or p[1]>maxy:
|
||
|
|
maxy=p[1]
|
||
|
|
out[3]=[p]
|
||
|
|
return out
|
||
|
|
|
||
|
|
|
||
|
|
def remove_duplicates(points):
|
||
|
|
i=0
|
||
|
|
out=[]
|
||
|
|
for p in points:
|
||
|
|
for j in xrange(i,len(points)):
|
||
|
|
if p==points[j]: points[j]=[None,None]
|
||
|
|
if p!=[None,None]: out+=[p]
|
||
|
|
i+=1
|
||
|
|
return(out)
|
||
|
|
|
||
|
|
|
||
|
|
def get_way_len(points):
|
||
|
|
l=0
|
||
|
|
for i in xrange(1,len(points)):
|
||
|
|
l+=math.sqrt((points[i][0]-points[i-1][0])**2 + (points[i][1]-points[i-1][1])**2)
|
||
|
|
return l
|
||
|
|
|
||
|
|
|
||
|
|
def sort_dxfpoints(points):
|
||
|
|
points=remove_duplicates(points)
|
||
|
|
|
||
|
|
ways=[
|
||
|
|
# l=0, d=1, r=2, u=3
|
||
|
|
[3,0], # ul
|
||
|
|
[3,2], # ur
|
||
|
|
[1,0], # dl
|
||
|
|
[1,2], # dr
|
||
|
|
[0,3], # lu
|
||
|
|
[0,1], # ld
|
||
|
|
[2,3], # ru
|
||
|
|
[2,1], # rd
|
||
|
|
]
|
||
|
|
|
||
|
|
minimal_way=[]
|
||
|
|
minimal_len=None
|
||
|
|
minimal_way_type=None
|
||
|
|
for w in ways:
|
||
|
|
tpoints=points[:]
|
||
|
|
cw=[]
|
||
|
|
for j in xrange(0,len(points)):
|
||
|
|
p=get_boundaries(get_boundaries(tpoints)[w[0]])[w[1]]
|
||
|
|
tpoints.remove(p[0])
|
||
|
|
cw+=p
|
||
|
|
curlen = get_way_len(cw)
|
||
|
|
if minimal_len==None or curlen < minimal_len:
|
||
|
|
minimal_len=curlen
|
||
|
|
minimal_way=cw
|
||
|
|
minimal_way_type=w
|
||
|
|
|
||
|
|
return minimal_way
|
||
|
|
|
||
|
|
if self.selected_paths == {} :
|
||
|
|
paths=self.paths
|
||
|
|
self.error(_("No paths are selected! Trying to work on all available paths."),"warning")
|
||
|
|
else :
|
||
|
|
paths = self.selected_paths
|
||
|
|
|
||
|
|
self.check_dir()
|
||
|
|
gcode = ""
|
||
|
|
|
||
|
|
biarc_group = inkex.etree.SubElement( self.selected_paths.keys()[0] if len(self.selected_paths.keys())>0 else self.layers[0], inkex.addNS('g','svg') )
|
||
|
|
print_(("self.layers=",self.layers))
|
||
|
|
print_(("paths=",paths))
|
||
|
|
for layer in self.layers :
|
||
|
|
if layer in paths :
|
||
|
|
print_(("layer",layer))
|
||
|
|
p = []
|
||
|
|
dxfpoints = []
|
||
|
|
for path in paths[layer] :
|
||
|
|
print_(str(layer))
|
||
|
|
if "d" not in path.keys() :
|
||
|
|
self.error(_("Warning: One or more paths dont have 'd' parameter, try to Ungroup (Ctrl+Shift+G) and Object to Path (Ctrl+Shift+C)!"),"selection_contains_objects_that_are_not_paths")
|
||
|
|
continue
|
||
|
|
csp = cubicsuperpath.parsePath(path.get("d"))
|
||
|
|
csp = self.apply_transforms(path, csp)
|
||
|
|
if path.get("dxfpoint") == "1":
|
||
|
|
tmp_curve=self.transform_csp(csp, layer)
|
||
|
|
x=tmp_curve[0][0][0][0]
|
||
|
|
y=tmp_curve[0][0][0][1]
|
||
|
|
print_("got dxfpoint (scaled) at (%f,%f)" % (x,y))
|
||
|
|
dxfpoints += [[x,y]]
|
||
|
|
else:
|
||
|
|
p += csp
|
||
|
|
dxfpoints=sort_dxfpoints(dxfpoints)
|
||
|
|
curve = self.parse_curve(p, layer)
|
||
|
|
self.draw_curve(curve, layer, biarc_group)
|
||
|
|
gcode += self.generate_gcode(curve, layer, 0)
|
||
|
|
|
||
|
|
self.export_gcode(gcode)
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Orientation
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def orientation(self, layer=None) :
|
||
|
|
print_("entering orientations")
|
||
|
|
if layer == None :
|
||
|
|
layer = self.current_layer if self.current_layer is not None else self.document.getroot()
|
||
|
|
if layer in self.orientation_points:
|
||
|
|
self.error(_("Active layer already has orientation points! Remove them or select another layer!"),"active_layer_already_has_orientation_points")
|
||
|
|
|
||
|
|
orientation_group = inkex.etree.SubElement(layer, inkex.addNS('g','svg'), {"gcodetools":"Gcodetools orientation group"})
|
||
|
|
|
||
|
|
# translate == ['0', '-917.7043']
|
||
|
|
if layer.get("transform") != None :
|
||
|
|
translate = layer.get("transform").replace("translate(", "").replace(")", "").split(",")
|
||
|
|
else :
|
||
|
|
translate = [0,0]
|
||
|
|
|
||
|
|
# doc height in pixels (38 mm == 143.62204724px)
|
||
|
|
doc_height = self.unittouu(self.document.getroot().xpath('@height', namespaces=inkex.NSS)[0])
|
||
|
|
|
||
|
|
if self.document.getroot().get('height') == "100%" :
|
||
|
|
doc_height = 1052.3622047
|
||
|
|
print_("Overruding height from 100 percents to %s" % doc_height)
|
||
|
|
|
||
|
|
print_("Document height: " + str(doc_height));
|
||
|
|
|
||
|
|
if self.options.unit == "G21 (All units in mm)" :
|
||
|
|
points = [[0.,0.,0.],[100.,0.,0.],[0.,100.,0.]]
|
||
|
|
orientation_scale = 1
|
||
|
|
print_("orientation_scale < 0 ===> switching to mm units=%0.10f"%orientation_scale )
|
||
|
|
elif self.options.unit == "G20 (All units in inches)" :
|
||
|
|
points = [[0.,0.,0.],[5.,0.,0.],[0.,5.,0.]]
|
||
|
|
orientation_scale = 90
|
||
|
|
print_("orientation_scale < 0 ===> switching to inches units=%0.10f"%orientation_scale )
|
||
|
|
|
||
|
|
points = points[:2]
|
||
|
|
|
||
|
|
print_(("using orientation scale",orientation_scale,"i=",points))
|
||
|
|
for i in points :
|
||
|
|
# X == Correct!
|
||
|
|
# si == x,y coordinate in px
|
||
|
|
# si have correct coordinates
|
||
|
|
# if layer have any tranform it will be in translate so lets add that
|
||
|
|
si = [i[0]*orientation_scale, (i[1]*orientation_scale)+float(translate[1])]
|
||
|
|
g = inkex.etree.SubElement(orientation_group, inkex.addNS('g','svg'), {'gcodetools': "Gcodetools orientation point (2 points)"})
|
||
|
|
inkex.etree.SubElement( g, inkex.addNS('path','svg'),
|
||
|
|
{
|
||
|
|
'style': "stroke:none;fill:#000000;",
|
||
|
|
'd':'m %s,%s 2.9375,-6.343750000001 0.8125,1.90625 6.843748640396,-6.84374864039 0,0 0.6875,0.6875 -6.84375,6.84375 1.90625,0.812500000001 z z' % (si[0], -si[1]+doc_height),
|
||
|
|
'gcodetools': "Gcodetools orientation point arrow"
|
||
|
|
})
|
||
|
|
t = inkex.etree.SubElement( g, inkex.addNS('text','svg'),
|
||
|
|
{
|
||
|
|
'style': "font-size:10px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;fill:#000000;fill-opacity:1;stroke:none;",
|
||
|
|
inkex.addNS("space","xml"):"preserve",
|
||
|
|
'x': str(si[0]+10),
|
||
|
|
'y': str(-si[1]-10+doc_height),
|
||
|
|
'gcodetools': "Gcodetools orientation point text"
|
||
|
|
})
|
||
|
|
t.text = "(%s; %s; %s)" % (i[0],i[1],i[2])
|
||
|
|
|
||
|
|
|
||
|
|
################################################################################
|
||
|
|
###
|
||
|
|
### Effect
|
||
|
|
###
|
||
|
|
### Main function of Gcodetools class
|
||
|
|
###
|
||
|
|
################################################################################
|
||
|
|
def effect(self) :
|
||
|
|
global options
|
||
|
|
options = self.options
|
||
|
|
options.self = self
|
||
|
|
options.doc_root = self.document.getroot()
|
||
|
|
# define print_ function
|
||
|
|
global print_
|
||
|
|
if self.options.log_create_log :
|
||
|
|
try :
|
||
|
|
if os.path.isfile(self.options.log_filename) : os.remove(self.options.log_filename)
|
||
|
|
f = open(self.options.log_filename,"a")
|
||
|
|
f.write("Gcodetools log file.\nStarted at %s.\n%s\n" % (time.strftime("%d.%m.%Y %H:%M:%S"),options.log_filename))
|
||
|
|
f.write("%s tab is active.\n" % self.options.active_tab)
|
||
|
|
f.close()
|
||
|
|
except :
|
||
|
|
print_ = lambda *x : None
|
||
|
|
else : print_ = lambda *x : None
|
||
|
|
self.get_info()
|
||
|
|
if self.orientation_points == {} :
|
||
|
|
self.error(_("Orientation points have not been defined! A default set of orientation points has been automatically added."),"warning")
|
||
|
|
self.orientation( self.layers[min(0,len(self.layers)-1)] )
|
||
|
|
self.get_info()
|
||
|
|
|
||
|
|
self.tools = {
|
||
|
|
"name": "Laser Engraver",
|
||
|
|
"id": "Laser Engraver",
|
||
|
|
"penetration feed": self.options.laser_speed,
|
||
|
|
"feed": self.options.laser_speed,
|
||
|
|
"gcode before path": ("G4 P0 \n" + self.options.laser_command + " S" + str(int(self.options.laser_power)) + "\nG4 P" + self.options.power_delay),
|
||
|
|
"gcode after path": ("G4 P0 \n" + self.options.laser_off_command + " S0" + "\n" + "G1 F" + self.options.travel_speed),
|
||
|
|
}
|
||
|
|
|
||
|
|
self.get_info()
|
||
|
|
self.laser()
|
||
|
|
|
||
|
|
e = laser_gcode()
|
||
|
|
e.affect()
|