circlesin

Circlesin is a term used in computational geometry and graphics to denote a family of algorithms and data structures focused on the construction, analysis, and packing of circles within geometric shapes. The central idea is to determine circles that fit inside a given container while obeying tangency and density constraints, as well as to derive sequences of mutually tangent circles (Apollonian-type packings).

Core operations include computing the largest inscribed circle (inradius) of a polygon, placing a circle tangent to multiple boundary elements, and generating circle packs by iterative tangency selection. Algorithms may be greedy, gradient-based, or based on constraint satisfaction. In practice, circlesin implementations aim for numerical stability with floating-point geometry.

Applications span graphic layout, two-dimensional circle packing problems, texture tiling, architectural design patterns, and educational tools that illustrate principles of circle packing and tangency. The concept also informs problems in visual computing where precise inscribed or tangent circles influence aesthetics or functional constraints.

Software and implementations often label projects under circlesin or circles-in and may provide modules for polygonal inradius computation, tangent circle placement, and iterative packing routines. Typical toolchains include languages such as Python, C++, and JavaScript, with emphasis on robust geometric predicates, numerical tolerance handling, and visualization support. The term circlesin is used both as a technical descriptor in geometry work and as a project or library name in some educational and research contexts.

Related topics include circle packing, inradius, tangency, Apollonian gaskets, and Voronoi diagrams, all of which intersect with the study and application of circles inscribed within shapes and arrangements.