Power Diagrams and Their Applications
نویسنده
چکیده
We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the final section we use Maslov dequantization to compute the medial axis.
منابع مشابه
A Comparative Study of Tooth Wear, Mechanical Power Losses and Efficiency in Normal and High Contact Ratio Asymmetric Spur Gears
The surface tooth wear which occurs at the gear contact region due to inadequate contact strength of the tooth is one of the predominant modes of gear failures. Currently, higher contact ratio spur gears are increasingly used in power transmission applications such as aircraft, wind turbine, automobiles and compact tracked vehicles due to their high load carrying capacity. In this work, the di...
متن کاملEuclidean proximity and power diagrams
Power diagrams [Aur87] are a useful generalization of Voronoi diagrams in which the sites defining the diagram are not points but balls. They derive their name from the fact that the distance used in their definition is not the standard Euclidean distance, but instead the classical notion of the power of a point with respect to a ball [Cox61]. The advantage of the power distance is that the ‘bi...
متن کاملX iv : m at h . M G / 0 50 80 37 v 2 2 A ug 2 00 5 POWER DIAGRAMS AND THEIR APPLICATIONS
We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the ...
متن کاملA ug 2 00 5 POWER DIAGRAMS AND THEIR APPLICATIONS
We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the ...
متن کاملA survey on RPL attacks and their countermeasures
RPL (Routing Protocol for Low Power and Lossy Networks) has been designed for low power networks with high packet loss. Generally, devices with low processing power and limited memory are used in this type of network. IoT (Internet of Things) is a typical example of low power lossy networks. In this technology, objects are interconnected through a network consisted of low-power circuits. Exampl...
متن کامل