Greetings all and thank you. I'm a Ph.D. candidate working on a 3D tessellation project and get stuck. I've simplified the system into a set of lines linked together which form a Line-Framework (points connectivity list). Now I want to get the tessellation of this Line-Framework in a set of minimal 'convex polyhedra' without changing the connectivity of the points.
Let me give an example for further description.
The Line-Framework is described in points pairs, e.g.{{P1,P2};{P2,P3};{P2,P9}...}, which can be drawn as follows. (Each $P_i$ has coordinate details for plotting.)
And I want to have the enclosed set {v1={P1,P2,P3,P4,P5,P6,P7,P8};v2={P9,P2,P3,P6,P7};v3={P10,P11,P1,P4,P5,P8}}; $V=v1+v2+v3$. For set $v2$: Face1 = $P2-9-6$, $F2$ = $P2-3-9$, $P3-7-9$, $P7-6-9$ and $P2-3-7-6$. This five faces form an enclosed polyhedron. Which I think may similar to find a circle in planer graph.
How can I work out the points set I need?
THANKS!