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After detecting every planar patch, the geometry architecture of object is obtained.
It is clear that every planar domain V ⊂ C is a domain of holomorphy, because in this case one may take f w ( z ) : = ( w − z ) − 1 where w ∈ b V has been fixed.
In [29] it was shown that every planar graph is 3-clique colourable and in [26] it was proposed a polynomial algorithm to decide if a planar graph is 2-clique colourable.
It is easy to verify that compatible split systems are circular (actually, every planar drawing of an X-tree provides such a circular ordering), and that circular split systems are weakly compatible – i.e., A1 ∩ A2 ∩ A3, A1 ∩ A ¯ 2 ∩ A ¯ 3, A ¯ 1 ∩ A2 ∩ A ¯ 3 or A ¯ 1 ∩ A ¯ 2 ∩ A3 is empty for any three splits A1| A ¯ 1, A2| A ¯ 2, A3| A ¯ 3 in a circular split system, cf. [ 13].
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We prove that every IC-planar graph admits a straight-line RAC drawing, which may require however exponential area.
If we do not require right angle crossings, we can draw every IC-planar graph with straight-line edges in linear time and quadratic area.
Since is a maximal planar graph, every face boundary in is a 3-cycle.
The Arps hyperbolic decline model (Robertson 1988) is used to calculate EUR of every well, and a planar EUR distribution (Fig. 9) is established through interpolation.
In practice, CoM2 method maximizes the contrast function (3) iteratively by applying a planar Givens rotation to every whitened signal pair until convergence as in Jacobi sweeping algorithm for matrix diagonalization.
To assist modeling of a 9-fold symmetric ring, a planar wheel with spokes every 40° was generated, and a Cα model of the crCC-dimer structure was positioned with its 2-fold axis aligned with one spoke.
For every sampling zone the assumption of a planar grating holds [10] if the grating vector is slowly varying.
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