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mrbeam.py
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mrbeam.py
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#!/usr/bin/env python
"""
based on Copyright (C) 2009 Nick Drobchenko, nick@cnc-club.ru
based on gcode.py (C) 2007 hugomatic...
based on addnodes.py (C) 2005,2007 Aaron Spike, aaron@ekips.org
based on dots.py (C) 2005 Aaron Spike, aaron@ekips.org
based on interp.py (C) 2005 Aaron Spike, aaron@ekips.org
based on bezmisc.py (C) 2005 Aaron Spike, aaron@ekips.org
based on cubicsuperpath.py (C) 2005 Aaron Spike, aaron@ekips.org
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
"""
###
### Laserengraver v 0.01
###
Laserengraver_current_version = "0.01"
import inkex
import simplestyle
import simplepath
import cubicsuperpath
import simpletransform
import bezmisc
import color2intensity
import infill_generator
import machine_settings
from img2gcode import ImageProcessor
import optparse
import os
import math
import bezmisc
import re
import copy
import sys
import time
import cmath
import numpy
import random
import gettext
_ = gettext.gettext
### Check if inkex has errormsg (0.46 version doesnot have one.) Could be removed later.
if "errormsg" not in dir(inkex):
inkex.errormsg = lambda msg: sys.stderr.write((unicode(msg) + "\n").encode("UTF-8"))
def bezierslopeatt(((bx0,by0),(bx1,by1),(bx2,by2),(bx3,by3)),t):
ax,ay,bx,by,cx,cy,x0,y0=bezmisc.bezierparameterize(((bx0,by0),(bx1,by1),(bx2,by2),(bx3,by3)))
dx=3*ax*(t**2)+2*bx*t+cx
dy=3*ay*(t**2)+2*by*t+cy
if dx==dy==0 :
dx = 6*ax*t+2*bx
dy = 6*ay*t+2*by
if dx==dy==0 :
dx = 6*ax
dy = 6*ay
if dx==dy==0 :
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))
print_(((bx0,by0),(bx1,by1),(bx2,by2),(bx3,by3)))
dx, dy = 1, 1
return dx,dy
bezmisc.bezierslopeatt = bezierslopeatt
def ireplace(self,old,new,count=0):
pattern = re.compile(re.escape(old),re.I)
return re.sub(pattern,new,self,count)
################################################################################
###
### Styles and additional parameters
###
################################################################################
math.pi2 = math.pi*2
straight_tolerance = 0.0001
straight_distance_tolerance = 0.0001
engraving_tolerance = 0.0001
loft_lengths_tolerance = 0.0000001
options = {}
intersection_recursion_depth = 10
intersection_tolerance = 0.00001
styles = {
"loft_style" : {
'main curve': simplestyle.formatStyle({ 'stroke': '#88f', 'fill': 'none', 'stroke-width':'1', 'marker-end':'url(#Arrow2Mend)' }),
},
"biarc_style" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#88f', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#8f8', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'line': simplestyle.formatStyle({ 'stroke': '#f88', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'area': simplestyle.formatStyle({ 'stroke': '#777', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
},
"biarc_style_dark" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#33a', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#3a3', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'line': simplestyle.formatStyle({ 'stroke': '#a33', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'area': simplestyle.formatStyle({ 'stroke': '#222', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"biarc_style_dark_area" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#33a', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#3a3', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
'line': simplestyle.formatStyle({ 'stroke': '#a33', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.1' }),
'area': simplestyle.formatStyle({ 'stroke': '#222', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"biarc_style_i" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#880', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#808', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'line': simplestyle.formatStyle({ 'stroke': '#088', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'area': simplestyle.formatStyle({ 'stroke': '#999', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"biarc_style_dark_i" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#dd5', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#d5d', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'line': simplestyle.formatStyle({ 'stroke': '#5dd', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'1' }),
'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"biarc_style_lathe_feed" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#07f', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#0f7', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'line': simplestyle.formatStyle({ 'stroke': '#f44', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"biarc_style_lathe_passing feed" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#07f', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#0f7', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'line': simplestyle.formatStyle({ 'stroke': '#f44', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"biarc_style_lathe_fine feed" : {
'biarc0': simplestyle.formatStyle({ 'stroke': '#7f0', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'biarc1': simplestyle.formatStyle({ 'stroke': '#f70', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'line': simplestyle.formatStyle({ 'stroke': '#744', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'.4' }),
'area': simplestyle.formatStyle({ 'stroke': '#aaa', 'fill': 'none', "marker-end":"url(#DrawCurveMarker)", 'stroke-width':'0.3' }),
},
"area artefact": simplestyle.formatStyle({ 'stroke': '#ff0000', 'fill': '#ffff00', 'stroke-width':'1' }),
"area artefact arrow": simplestyle.formatStyle({ 'stroke': '#ff0000', 'fill': '#ffff00', 'stroke-width':'1' }),
"dxf_points": simplestyle.formatStyle({ "stroke": "#ff0000", "fill": "#ff0000"}),
}
################################################################################
### Cubic Super Path additional functions
################################################################################
def csp_simple_bound(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 minx,miny,maxx,maxy
def csp_segment_to_bez(sp1,sp2) :
return sp1[1:]+sp2[:2]
def bound_to_bound_distance(sp1,sp2,sp3,sp4) :
min_dist = 1e100
max_dist = 0
points1 = csp_segment_to_bez(sp1,sp2)
points2 = csp_segment_to_bez(sp3,sp4)
for i in range(4) :
for j in range(4) :
min_, max_ = line_to_line_min_max_distance_2(points1[i-1], points1[i], points2[j-1], points2[j])
min_dist = min(min_dist,min_)
max_dist = max(max_dist,max_)
print_("bound_to_bound", min_dist, max_dist)
return min_dist, max_dist
def csp_to_point_distance(csp, p, dist_bounds = [0,1e100], tolerance=.01) :
min_dist = [1e100,0,0,0]
for j in range(len(csp)) :
for i in range(1,len(csp[j])) :
d = csp_seg_to_point_distance(csp[j][i-1],csp[j][i],p,sample_points = 5, tolerance = .01)
if d[0] < dist_bounds[0] :
# draw_pointer( list(csp_at_t(subpath[dist[2]-1],subpath[dist[2]],dist[3]))
# +list(csp_at_t(csp[dist[4]][dist[5]-1],csp[dist[4]][dist[5]],dist[6])),"red","line", comment = math.sqrt(dist[0]))
return [d[0],j,i,d[1]]
else :
if d[0] < min_dist[0] : min_dist = [d[0],j,i,d[1]]
return min_dist
def csp_seg_to_point_distance(sp1,sp2,p,sample_points = 5, tolerance = .01) :
ax,ay,bx,by,cx,cy,dx,dy = csp_parameterize(sp1,sp2)
dx, dy = dx-p[0], dy-p[1]
if sample_points < 2 : sample_points = 2
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.] )
for k in range(sample_points) :
t = float(k)/(sample_points-1)
i = 0
while i==0 or abs(f)>0.000001 and i<20 :
t2,t3 = t**2,t**3
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)
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
if df!=0 :
t = t - f/df
else :
break
i += 1
if 0<=t<=1 :
p1 = csp_at_t(sp1,sp2,t)
d1 = (p1[0]-p[0])**2 + (p1[1]-p[1])**2
if d1 < d[0] :
d = [d1,t]
return d
def csp_seg_to_csp_seg_distance(sp1,sp2,sp3,sp4, dist_bounds = [0,1e100], sample_points = 5, tolerance=.01) :
# check the ending points first
dist = csp_seg_to_point_distance(sp1,sp2,sp3[1],sample_points, tolerance)
dist += [0.]
if dist[0] <= dist_bounds[0] : return dist
d = csp_seg_to_point_distance(sp1,sp2,sp4[1],sample_points, tolerance)
if d[0]<dist[0] :
dist = d+[1.]
if dist[0] <= dist_bounds[0] : return dist
d = csp_seg_to_point_distance(sp3,sp4,sp1[1],sample_points, tolerance)
if d[0]<dist[0] :
dist = [d[0],0.,d[1]]
if dist[0] <= dist_bounds[0] : return dist
d = csp_seg_to_point_distance(sp3,sp4,sp2[1],sample_points, tolerance)
if d[0]<dist[0] :
dist = [d[0],1.,d[1]]
if dist[0] <= dist_bounds[0] : return dist
sample_points -= 2
if sample_points < 1 : sample_points = 1
ax1,ay1,bx1,by1,cx1,cy1,dx1,dy1 = csp_parameterize(sp1,sp2)
ax2,ay2,bx2,by2,cx2,cy2,dx2,dy2 = csp_parameterize(sp3,sp4)
# try to find closes points using Newtons method
for k in range(sample_points) :
for j in range(sample_points) :
t1,t2 = float(k+1)/(sample_points+1), float(j)/(sample_points+1)
t12, t13, t22, t23 = t1*t1, t1*t1*t1, t2*t2, t2*t2*t2
i = 0
F1, F2, F = [0,0], [[0,0],[0,0]], 1e100
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)
while i<2 or abs(F-Flast)>tolerance and i<30 :
#draw_pointer(csp_at_t(sp1,sp2,t1))
f1x = 3*ax1*t12+2*bx1*t1+cx1
f1y = 3*ay1*t12+2*by1*t1+cy1
f2x = 3*ax2*t22+2*bx2*t2+cx2
f2y = 3*ay2*t22+2*by2*t2+cy2
F1[0] = 2*f1x*x + 2*f1y*y
F1[1] = -2*f2x*x - 2*f2y*y
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) :