We present a general framework for computing two-dimensional Voronoi diagrams of different site classes under various distance functions. The computation of the diagrams employs the cgal software for constructing envelopes of surfaces in 3-space, which implements a divide-and-conquer algorithm. A straightforward application of the divide-and-conquer approach for Voronoi diagrams yields highly i...

conventional methods for fungal identification in the clinical laboratory rely on morphological andphysiological tests. these tests often need several days or weeks to complete and are frequentlyunspecific. molecular identification mostly implies sequencing, which is relatively expensive andtime-consuming, as well as impractical for large numbers of isolates. the rolling circleamplification app...

Simple and fast methods for transforming color photographs into non-photorealistic images such as stained-glass and color-sketch images. We propose two types of methods decomposing images into homogeneous color regions. One type is an edge-based method and the other is a region-based approach. In the edge-based methods, an input image is tessellated into Apollonius cells by using the distance t...

In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse c based on the given axes of c, which make use of the Apollonius definition of c via its focal points or via two perspective affinities (de la Hire’s construction). Even there is no parallel relation neither in a hyperbolic plane nor in an elliptic plane it is still possible to modify many of the...

There is no need to try to ease into the discussion because the issue being discussed here is too involved to waste words that way. It is important to get right to the point. The starting premise is that we seek to understand the world in which we live. This leads immediately to a whole set of related premises that define the problem as being the answer to the question “how we can obtain that w...