The Argonautica of Apollonius Rhodius

Spellbinding Performance: Poet as Witch in Theocritus' Second Idyll and Apollonius' Argonautica

Apollonius Solutions in Rd

Voronoi and related diagrams have technological applications, for example, in motion planning and surface reconstruction, and also find significant use in materials science, molecular biology, and crystallography. Apollonius diagrams arguably provide the most natural division of space for many materials and technology problems, but compared to Voronoi and power diagrams, their use has been limi...

The predicates of the Apollonius diagram: Algorithmic analysis and implementation

We study the predicates involved in an efficient dynamic algorithm for computing the Apollonius diagram in the plane, also known as the additively weighted Voronoi diagram. We present a complete algorithmic analysis of these predicates, some of which are reduced to simpler and more easily computed primitives. This gives rise to an exact and efficient implementation of the algorithm, that handle...

Algebraic study of the Apollonius circle of three ellipses

We study the external tritangent Apollonius (or Voronoi) circle to three ellipses. This problem arises when one wishes to compute the Apollonius (or Voronoi) diagram of a set of ellipses, but is also of independent interest in enumerative geometry. This paper is restricted to non-intersecting ellipses, but the extension to arbitrary ellipses is possible. We propose an efficient representation o...

the effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...