1 #!/usr/bin/env python
2 """
3 cubicsuperpath.py
5 Copyright (C) 2005 Aaron Spike, aaron@ekips.org
7 This program is free software; you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation; either version 2 of the License, or
10 (at your option) any later version.
12 This program is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with this program; if not, write to the Free Software
19 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21 """
22 import simplepath
23 from math import *
25 def matprod(mlist):
26 prod=mlist[0]
27 for m in mlist[1:]:
28 a00=prod[0][0]*m[0][0]+prod[0][1]*m[1][0]
29 a01=prod[0][0]*m[0][1]+prod[0][1]*m[1][1]
30 a10=prod[1][0]*m[0][0]+prod[1][1]*m[1][0]
31 a11=prod[1][0]*m[0][1]+prod[1][1]*m[1][1]
32 prod=[[a00,a01],[a10,a11]]
33 return prod
34 def rotmat(teta):
35 return [[cos(teta),-sin(teta)],[sin(teta),cos(teta)]]
36 def applymat(mat, pt):
37 x=mat[0][0]*pt[0]+mat[0][1]*pt[1]
38 y=mat[1][0]*pt[0]+mat[1][1]*pt[1]
39 pt[0]=x
40 pt[1]=y
41 def norm(pt):
42 return sqrt(pt[0]*pt[0]+pt[1]*pt[1])
44 def ArcToPath(p1,params):
45 A=p1[:]
46 rx,ry,teta,longflag,sweepflag,x2,y2=params[:]
47 teta = teta*pi/180.0
48 B=[x2,y2]
49 if rx==0 or ry==0:
50 return([[A,A,A],[B,B,B]])
51 mat=matprod((rotmat(teta),[[1/rx,0],[0,1/ry]],rotmat(-teta)))
52 applymat(mat, A)
53 applymat(mat, B)
54 k=[-(B[1]-A[1]),B[0]-A[0]]
55 d=k[0]*k[0]+k[1]*k[1]
56 k[0]/=sqrt(d)
57 k[1]/=sqrt(d)
58 d=sqrt(max(0,1-d/4))
59 if longflag==sweepflag:
60 d*=-1
61 O=[(B[0]+A[0])/2+d*k[0],(B[1]+A[1])/2+d*k[1]]
62 OA=[A[0]-O[0],A[1]-O[1]]
63 OB=[B[0]-O[0],B[1]-O[1]]
64 start=acos(OA[0]/norm(OA))
65 if OA[1]<0:
66 start*=-1
67 end=acos(OB[0]/norm(OB))
68 if OB[1]<0:
69 end*=-1
71 if sweepflag and start>end:
72 end +=2*pi
73 if (not sweepflag) and start<end:
74 end -=2*pi
76 NbSectors=int(abs(start-end)*2/pi)+1
77 dTeta=(end-start)/NbSectors
78 #v=dTeta*2/pi*0.552
79 #v=dTeta*2/pi*4*(sqrt(2)-1)/3
80 v = 4*tan(dTeta/4)/3
81 #if not sweepflag:
82 # v*=-1
83 p=[]
84 for i in range(0,NbSectors+1,1):
85 angle=start+i*dTeta
86 v1=[O[0]+cos(angle)-(-v)*sin(angle),O[1]+sin(angle)+(-v)*cos(angle)]
87 pt=[O[0]+cos(angle) ,O[1]+sin(angle) ]
88 v2=[O[0]+cos(angle)- v *sin(angle),O[1]+sin(angle)+ v *cos(angle)]
89 p.append([v1,pt,v2])
90 p[ 0][0]=p[ 0][1][:]
91 p[-1][2]=p[-1][1][:]
93 mat=matprod((rotmat(teta),[[rx,0],[0,ry]],rotmat(-teta)))
94 for pts in p:
95 applymat(mat, pts[0])
96 applymat(mat, pts[1])
97 applymat(mat, pts[2])
98 return(p)
100 def CubicSuperPath(simplepath):
101 csp = []
102 subpath = -1
103 subpathstart = []
104 last = []
105 lastctrl = []
106 for s in simplepath:
107 cmd, params = s
108 if cmd == 'M':
109 if last:
110 csp[subpath].append([lastctrl[:],last[:],last[:]])
111 subpath += 1
112 csp.append([])
113 subpathstart = params[:]
114 last = params[:]
115 lastctrl = params[:]
116 elif cmd == 'L':
117 csp[subpath].append([lastctrl[:],last[:],last[:]])
118 last = params[:]
119 lastctrl = params[:]
120 elif cmd == 'C':
121 csp[subpath].append([lastctrl[:],last[:],params[:2]])
122 last = params[-2:]
123 lastctrl = params[2:4]
124 elif cmd == 'Q':
125 q0=last[:]
126 q1=params[0:2]
127 q2=params[2:4]
128 x0= q0[0]
129 x1=1./3*q0[0]+2./3*q1[0]
130 x2= 2./3*q1[0]+1./3*q2[0]
131 x3= q2[0]
132 y0= q0[1]
133 y1=1./3*q0[1]+2./3*q1[1]
134 y2= 2./3*q1[1]+1./3*q2[1]
135 y3= q2[1]
136 csp[subpath].append([lastctrl[:],[x0,y0],[x1,y1]])
137 last = [x3,y3]
138 lastctrl = [x2,y2]
139 elif cmd == 'A':
140 arcp=ArcToPath(last[:],params[:])
141 arcp[ 0][0]=lastctrl[:]
142 last=arcp[-1][1]
143 lastctrl = arcp[-1][0]
144 csp[subpath]+=arcp[:-1]
145 elif cmd == 'Z':
146 csp[subpath].append([lastctrl[:],last[:],last[:]])
147 last = subpathstart[:]
148 lastctrl = subpathstart[:]
149 #append final superpoint
150 csp[subpath].append([lastctrl[:],last[:],last[:]])
151 return csp
153 def unCubicSuperPath(csp):
154 a = []
155 for subpath in csp:
156 if subpath:
157 a.append(['M',subpath[0][1][:]])
158 for i in range(1,len(subpath)):
159 a.append(['C',subpath[i-1][2][:] + subpath[i][0][:] + subpath[i][1][:]])
160 return a
162 def parsePath(d):
163 return CubicSuperPath(simplepath.parsePath(d))
165 def formatPath(p):
166 return simplepath.formatPath(unCubicSuperPath(p))
169 # vim: expandtab shiftwidth=4 tabstop=8 softtabstop=4 encoding=utf-8 textwidth=99