sidesfor

Sidesfor is a term used in computational geometry and computer-aided design to describe a family of methods for assigning side lengths to polygons under a set of global constraints. In its general use, sidesfor denotes the process of choosing a vector of n positive side lengths (s1, s2, ..., sn) that satisfy a constraint such as fixed perimeter, fixed area, or fixed circumradius, while optimizing a secondary objective that promotes regularity or symmetry among the sides.

Formal framework: Given n ≥ 3 and a constraint set C, a sidesfor solution is a sequence s with sum or area equal to the prescribed target and with an objective function F(s) minimized. Common objectives include minimizing the variance of side lengths or maintaining bounded edge ratios, and can be augmented with angular stability or triangulation quality in mesh contexts.

Properties: Solutions often trend toward equal side lengths as symmetry is favored, yielding shapes close to regular polygons. The method is compatible with iterative refinement and can be integrated with mesh generation pipelines to improve element quality.

Applications and notes: Sidesfor concepts appear in polygon synthesis, mesh generation, architectural modeling, and graphics optimization. The term emphasizes the role of the polygon's sides in shaping overall geometry and numerical stability.

See also: polygon, isoperimetric problem, polygonal mesh, optimization.