Optimal Morphs of Planar Orthogonal Drawings

We describe an algorithm that morphs between two planar orthogonal drawings Gamma_I and Gamma_O of a connected graph G, while preserving planarity and orthogonality. Necessarily Gamma_I and Gamma_O share the same combinatorial embedding. Our morph uses a linear number of linear morphs (linear interpolations between two drawings) and preserves linear complexity throughout the process, thereby answering an open question from Biedl et al. [Biedl et al., 2013]. Our algorithm first unifies the two drawings to ensure an equal number of (virtual) bends on each edge. We then interpret bends as vertices which form obstacles for so-called wires: horizontal and vertical lines separating the vertices of Gamma_O. We can find corresponding wires in Gamma_I that share topological properties with the wires in Gamma_O. The structural difference between the two drawings can be captured by the spirality of the wires in Gamma_I, which guides our morph from Gamma_I to Gamma_O

Harmonious Simplification of Isolines

Current techniques for simplification focus on reducing complexity while maintaining the geometric similarity to the input. For isolines that jointly describe a scalar field, however, we postulate that geometric similarity of each isoline separately is not sufficient. Rather, we need to maintain the harmony between these isolines to make them visually relate and describe the structures of the underlying terrain. Based on principles of manual cartography, we propose an algorithm for simplifying isolines while considering harmony explicitly. Our preliminary visual and quantitative results suggest that our algorithm is effective

Фізіологічна активність оздоровлювального напою "Трускавецька кришталева, збагачена алоє". Повідомлення 2: Холеретично-абсорбційний, екскреторно-депураційний та адаптогенний ефекти

Показано, что влияние напитка “Трускавецька кришталева, збагачена алоє“ на холерез, салурез, обмен уратов и состояние адаптации имеет место, но уступает таковому эталона - биоактивной воды "Нафтуся".In rats experiments by comparativ investigations it is shown that tonic drink "Трускавецька кришталева, збагачена алоє" causes effects on cholerese, salurese, exchange of urates and adaptation less than thouse of bioactiv water Naftussya

Состояние и перспективы развития рынка лакокрасочных материалов Украины

Целью статьи является рассмотрение состояние рынка лакокрасочных материалов Украины и мира на сегодняшний день, анализ объемов поставок и производства ЛКМ,а также разработка предложений по улучшению этой отрасли

Competitive Searching for a Line on a Line Arrangement

We discuss the problem of searching for an unknown line on a known or unknown line arrangement by a searcher S, and show that a search strategy exists that finds the line competitively, that is, with detour factor at most a constant when compared to the situation where S has all knowledge. In the case where S knows all lines but not which one is sought, the strategy is 79-competitive. We also show that it may be necessary to travel on Omega(n) lines to realize a constant competitive ratio. In the case where initially, S does not know any line, but learns about the ones it encounters during the search, we give a 414.2-competitive search strategy

Optimal morphs of planar orthogonal drawings

We describe an algorithm that morphs between two planar orthogonal drawings ΓI and ΓO of a graph G, while preserving planarity and orthogonality. Necessarily drawings ΓI and ΓO must be equivalent, that is, there exists a homeomorphism of the plane that transforms ΓI into ΓO . Our morph uses a linear number of linear morphs (linear interpolations between two drawings) and preserves linear complexity throughout the process, thereby answering an open question from Biedl et al. (ACM Transactions on Algorithms, 2013). Our algorithm first unifies the two drawings to ensure an equal number of (virtual) bends on each edge. We then interpret bends as vertices which form obstacles for so-called wires: horizontal and vertical lines separating the vertices of ΓO . We can find corresponding wires in ΓI that share topological properties with the wires in ΓO . The structural difference between the two drawings can be captured by the spirality s of the wires in ΓI, which guides our morph from ΓI to ΓO . We prove that s = O(n) and that s + 1 linear morphs are always sufficient to morph between two planar orthogonal drawings, even for disconnected graphs

Connecting Global and Local Agent Navigation via Topology

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