This paper presents new sufficient conditions for packing circles into square and triangular containers, using only the sum of the circles’ areas, which can be used as a constant-factor approximation algorithm when looking for the smallest container in which a given set of circles can be packed.Expand

This paper presents a new sufficient condition for packing circles into any right or obtuse triangle using only the circles’ combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle’s incircle.Expand

The critical packing density δ∗ is the largest value A/C for which any set of area A can be packed into a container of area C, and this work describes algorithms that establish the critical density.Expand

An efficient algorithm that computes the Minkowski sum of two polygons, which may have holes, based on the convolution approach that can always fill up all the holes of at least onepolygon, transforming it into a simple polygon, and still obtain exactly the same Minkowsky sum.Expand

In the classic circle packing problem, one asks whether a given set of circles can be packed into the unit square. This problem is known to be NP-hard. In this thesis, we present a new sufficient… Expand

This work illustrates and animate the classic problem of deciding whether a given graph has an Eulerian path, and presents a set of pictorial instructions that have proven to be both entertaining for experts and enlightened for novices.Expand

There is a class of programming languages that are not actually designed to be used for programming. These so-called “esoteric” programming languages have other purposes: To entertain, to be… Expand