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#!/usr/bin/env python
"""
cubicsuperpath.py
Copyright (C) 2005 Aaron Spike, aaron@ekips.org
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
"""
import simplepath
from math import *
def matprod(mlist):
prod=mlist[0]
for m in mlist[1:]:
a00=prod[0][0]*m[0][0]+prod[0][1]*m[1][0]
a01=prod[0][0]*m[0][1]+prod[0][1]*m[1][1]
a10=prod[1][0]*m[0][0]+prod[1][1]*m[1][0]
a11=prod[1][0]*m[0][1]+prod[1][1]*m[1][1]
prod=[[a00,a01],[a10,a11]]
return prod
def rotmat(teta):
return [[cos(teta),-sin(teta)],[sin(teta),cos(teta)]]
def applymat(mat, pt):
x=mat[0][0]*pt[0]+mat[0][1]*pt[1]
y=mat[1][0]*pt[0]+mat[1][1]*pt[1]
pt[0]=x
pt[1]=y
def norm(pt):
return sqrt(pt[0]*pt[0]+pt[1]*pt[1])
def ArcToPath(p1,params):
A=p1[:]
rx,ry,teta,longflag,sweepflag,x2,y2=params[:]
teta = teta*pi/180.0
B=[x2,y2]
if rx==0 or ry==0 or A==B:
return([[A[:],A[:],A[:]],[B[:],B[:],B[:]]])
mat=matprod((rotmat(teta),[[1/rx,0],[0,1/ry]],rotmat(-teta)))
applymat(mat, A)
applymat(mat, B)
k=[-(B[1]-A[1]),B[0]-A[0]]
d=k[0]*k[0]+k[1]*k[1]
k[0]/=sqrt(d)
k[1]/=sqrt(d)
d=sqrt(max(0,1-d/4))
if longflag==sweepflag:
d*=-1
O=[(B[0]+A[0])/2+d*k[0],(B[1]+A[1])/2+d*k[1]]
OA=[A[0]-O[0],A[1]-O[1]]
OB=[B[0]-O[0],B[1]-O[1]]
start=acos(OA[0]/norm(OA))
if OA[1]<0:
start*=-1
end=acos(OB[0]/norm(OB))
if OB[1]<0:
end*=-1
if sweepflag and start>end:
end +=2*pi
if (not sweepflag) and start<end:
end -=2*pi
NbSectors=int(abs(start-end)*2/pi)+1
dTeta=(end-start)/NbSectors
#v=dTeta*2/pi*0.552
#v=dTeta*2/pi*4*(sqrt(2)-1)/3
v = 4*tan(dTeta/4)/3
#if not sweepflag:
# v*=-1
p=[]
for i in range(0,NbSectors+1,1):
angle=start+i*dTeta
v1=[O[0]+cos(angle)-(-v)*sin(angle),O[1]+sin(angle)+(-v)*cos(angle)]
pt=[O[0]+cos(angle) ,O[1]+sin(angle) ]
v2=[O[0]+cos(angle)- v *sin(angle),O[1]+sin(angle)+ v *cos(angle)]
p.append([v1,pt,v2])
mat=matprod((rotmat(teta),[[rx,0],[0,ry]],rotmat(-teta)))
for pts in p:
applymat(mat, pts[0])
applymat(mat, pts[1])
applymat(mat, pts[2])
# Use exact coordinates for the endpoints. This prevents small drifts when relative coordinates are used and guarantees that a path ending with a z command closes perfectly.
p[0][0] = p1[:]
p[0][1] = p1[:]
p[-1][1] = [x2, y2]
p[-1][2] = [x2, y2]
return p
def CubicSuperPath(simplepath):
csp = []
subpath = -1
subpathstart = []
last = []
lastctrl = []
for s in simplepath:
cmd, params = s
if cmd == 'M':
if last:
csp[subpath].append([lastctrl[:],last[:],last[:]])
subpath += 1
csp.append([])
subpathstart = params[:]
last = params[:]
lastctrl = params[:]
elif cmd == 'L':
csp[subpath].append([lastctrl[:],last[:],last[:]])
last = params[:]
lastctrl = params[:]
elif cmd == 'C':
csp[subpath].append([lastctrl[:],last[:],params[:2]])
last = params[-2:]
lastctrl = params[2:4]
elif cmd == 'Q':
q0=last[:]
q1=params[0:2]
q2=params[2:4]
x0= q0[0]
x1=1./3*q0[0]+2./3*q1[0]
x2= 2./3*q1[0]+1./3*q2[0]
x3= q2[0]
y0= q0[1]
y1=1./3*q0[1]+2./3*q1[1]
y2= 2./3*q1[1]+1./3*q2[1]
y3= q2[1]
csp[subpath].append([lastctrl[:],[x0,y0],[x1,y1]])
last = [x3,y3]
lastctrl = [x2,y2]
elif cmd == 'A':
arcp=ArcToPath(last[:],params[:])
arcp[ 0][0]=lastctrl[:]
last=arcp[-1][1]
lastctrl = arcp[-1][0]
csp[subpath]+=arcp[:-1]
elif cmd == 'Z':
csp[subpath].append([lastctrl[:],last[:],last[:]])
last = subpathstart[:]
lastctrl = subpathstart[:]
#append final superpoint
csp[subpath].append([lastctrl[:],last[:],last[:]])
return csp
def unCubicSuperPath(csp):
a = []
for subpath in csp:
if subpath:
a.append(['M',subpath[0][1][:]])
for i in range(1,len(subpath)):
a.append(['C',subpath[i-1][2][:] + subpath[i][0][:] + subpath[i][1][:]])
return a
def parsePath(d):
return CubicSuperPath(simplepath.parsePath(d))
def formatPath(p):
return simplepath.formatPath(unCubicSuperPath(p))
# vim: expandtab shiftwidth=4 tabstop=8 softtabstop=4 fileencoding=utf-8 textwidth=99
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