We present a C++ open-source implementation of an incremental algorithm for the computation of the Voronoi diagram of ellipses in the Euclidean plane. This is the first complete implementation, under the exact computation paradigm; it also computes the approximate diagram with any given precision. It is based on the cgal package for the Apollonius diagram. The ellipses are given in parametric r...

In 1639, the treatise Prodromi catoptricorum et dioptricorum sive Conicorum operis ad abdita radii reflexi refracti mysteria praevij facem praeferentis. Libri quatuor priores by Claude Mydorge was printed in Paris. This volume, which followed printing of his first two books 1631, has resonance especially writings those who, after him, addressed conics. fact raises question who and what knowledg...

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...

We present a methodology for creating a simulated foam microstructure for use in forward simulations of wave equations to quantitatively analyze the expected scattering phenomenon primarily responsible for the attenuation of interrogating signals in Sprayed-On Foam Insulation (SOFI). Our approach builds off of the popular use of Voronoi Tessalations for crystal growth modeling by using the Lagu...

the conception and creation of eternal samples is one of the most evident efforts made by man from the very beginning of human life when he observed death and mortality and found all the world's manifestations prone to collapse and destruction. one of the most significant images related to the concept of externality and immortality is circular symbols. in fact, man has represented the conc...