Cyclooctane.world
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1 
3 [CONSTANTS]
4 
5 % We define a reference frame attache to each C atom with the
6 % X axis along one of the C-C bonds and with the X-Y plane in
7 % the planed defined by the two bonds coincident in the C.
8 
9 % All distances are in Amstrongs and all angles are in radiants
10 
11 % H-C bond length
12 HCb:=1.09
13 
14 % H-C distance for C the neighbouring C of the C to which H
15 % is connected
16 HCb2:=2.151077
17 
18 % C-C bond length
19 CCb:=1.526
20 
21 % Bond bending angle
22 BBa:=1.9111
23 
24 % The firts CC bond is aligned with the X axis and has lenght CCb
25 % The second is in the XY plane at position:
26 CC2x:=CCb*cos(BBa)
27 CC2y:=CCb*sin(BBa)
28 
29 % x-y-z position of one of the H w.r.t. a frame attached to the C
30 % The second H is symmetrically placed (w.r.t. the X-Y plane).
31 % This H is at (Hx,Hy,Hz) that is at the intersection of three circunferences
32 % Hx^2+Hy^2+Hz^2=HCb^2
33 % (Hx-CCb)^2+Hy^2+Hz^2=HCb2^2
34 % (Hx-CC2x)^2+(Hy-CC2y)^2+Hz^2=HCb2^2
35 %
36 Hx:=(HCb^2-HCb2^2+CCb^2)/(2*CCb)
37 Hy:=((Hx-CC2x)^2-(Hx-CCb)^2+CC2y^2)/(2*CC2y)
38 Hz:=sqrt(Hx^2+Hy^2)
39 
40 % Radious of the spheres representing atoms (25% Van der Waals radii)
41 rC:=1.7*0.5
42 
43 % super simplest (RRT*)
44 % rH:=1.2*0.50
45 
46 % simplest C8 (singularity samples)
47 % rH:=1.2*0.60
48 
49 % simple C8 (WAFR,IJRR)
50 % rH:=1.2*0.7125 % 0.72 ?
51 
52 % Hard C8 (ISRR,TRO samples)
53 rH:=1.2*0.7226 % with a factor of 0.73 it seems to be impossible to avoid collisions
54 % rH:=1.2*0.7227 % this is too hard (apparently)
55 
56 % Radious of the cylinders representing bonds
57 rCC:=0.15
58 rCH:=0.15
59 
60 % Colors for the atoms
61 Cr:=0.2
62 Cg:=0.6
63 Cb:=0.6
64 
65 Hr:=1
66 Hg:=1
67 Hb:=1
68 
69 [LINKS]
70 
71 C1 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
72  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
73  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
74  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
75  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
76  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
77  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
78  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
79  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
80 
81 C2 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
82  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
83  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
84  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
85  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
86  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
87  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
88  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
89  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
90 
91 C3 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
92  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
93  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
94  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
95  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
96  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
97  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
98  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
99  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
100 
101 C4 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
102  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
103  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
104  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
105  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
106  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
107  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
108  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
109  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
110 
111 C5 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
112  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
113  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
114  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
115  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
116  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
117  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
118  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
119  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
120 
121 C6 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
122  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
123  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
124  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
125  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
126  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
127  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
128  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
129  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
130 
131 C7 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
132  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
133  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
134  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
135  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
136  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
137  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
138  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
139  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
140 
141 C8 : sphere rC (0,0,0) color (Cr,Cg,Cb) decoration
142  cylinder rCC (0,0,0) (CCb/2,0,0) color (Cr,Cg,Cb) decoration
143  cylinder rCC (0,0,0) (CC2x/2,CC2y/2,0) color (Cr,Cg,Cb) decoration
144  cylinder rCH (0,0,0) (Hx/2,Hy/2,Hz/2) color (Cr,Cg,Cb) decoration
145  cylinder rCH (Hx/2,Hy/2,Hz/2) (Hx,Hy,Hz) color (Hr,Hg,Hb) decoration
146  sphere rH (Hx,Hy,Hz) color (Hr,Hg,Hb)
147  cylinder rCH (0,0,0) (Hx/2,Hy/2,-Hz/2) color (Cr,Cg,Cb) decoration
148  cylinder rCH (Hx/2,Hy/2,-Hz/2) (Hx,Hy,-Hz) color (Hr,Hg,Hb) decoration
149  sphere rH (Hx,Hy,-Hz) color (Hr,Hg,Hb)
150 
151 [JOINTS]
152 
153 % We define the revolute joints trying to use as much zeros as possible
154 % in the two first points of the two axes in local coordinates. This produces
155 % simpler equation sets.
156 revolute: C1 (CCb,0,0) (0,0,0)
157  C2 (0,0,0) (CC2x,CC2y,0)
158 
159 revolute: C2 (CCb,0,0) (0,0,0)
160  C3 (0,0,0) (CC2x,CC2y,0)
161 
162 revolute: C3 (CCb,0,0) (0,0,0)
163  C4 (0,0,0) (CC2x,CC2y,0)
164 
165 revolute: C4 (CCb,0,0) (0,0,0)
166  C5 (0,0,0) (CC2x,CC2y,0)
167 
168 revolute: C5 (CCb,0,0) (0,0,0)
169  C6 (0,0,0) (CC2x,CC2y,0)
170 
171 revolute: C6 (CCb,0,0) (0,0,0)
172  C7 (0,0,0) (CC2x,CC2y,0)
173 
174 revolute: C7 (CCb,0,0) (0,0,0)
175  C8 (0,0,0) (CC2x,CC2y,0)
176 
177 revolute: C8 (CCb,0,0) (0,0,0)
178  C1 (0,0,0) (CC2x,CC2y,0)
179 
180 
181 [COLLISIONS]
182 
183 do not check: all
184 
185 check : C1,C4
186 check : C1,C5
187 check : C1,C6
188 
189 check : C2,C5
190 check : C2,C6
191 check : C2,C7
192 
193 check : C3,C6
194 check : C3,C7
195 check : C3,C8
196 
197 check : C4,C7
198 check : C4,C8
199 
200 check : C5,C8
201