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Primal-dual circle representation

Simultaneous circle-packing representations of a map M and its dual M are called primal-dual circle representation of M if it holds ... [Pg.11]

See Figure 1.2 for an illustration of this feature and an example of a primal-dual circle representation. [Pg.11]

Figure 1.2 Illustration of primal-dual circle representations... Figure 1.2 Illustration of primal-dual circle representations...
A map M is called reduced (see [Moh97, Section 3]) if its universal cover is 3-connected and is a cell-complex. It is shown in [Moh97, Corollary 5.4] that reduced maps admit unique primal-dual circle packing representations on a Riemann surface of the same genus moreover, a polynomial time algorithm allows one to find the coordinates of those points relatively easily. This means that the combinatorics of the map determines the structure of the Riemann surface. [Pg.11]

The edges, vertex circles and face circles of a primal-dual representation... [Pg.11]


See other pages where Primal-dual circle representation is mentioned: [Pg.143]    [Pg.143]   


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Circle

Primal

Primal-dual

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