Eikonveksit

Eikonveksit is a term used in geometry and visual design to describe a family of convex representations derived from icon-like shapes. The word combines eikon, from Greek for image or icon, with a form related to convexity, and eikonveksit denotes the plural. In this usage, an eikonveksi refers to the convex hull or related convex envelope constructed around an icon’s sampled points, emphasizing the link between iconography and convex geometry.

Definition and construction: Given an icon modeled as a finite set of points (for example, boundary pixels of a bitmap), the eikonveksi is the convex hull that contains those points. The collection of hulls produced from a set of icons forms the eikonveksit. Construction typically involves sampling boundary or salient points, computing the convex hull by a standard algorithm (such as Graham scan), and optionally applying normalization to allow comparison across scales and orientations.

Properties and interpretation: Each eikonveksi is a convex polygon (or polytope in higher dimensions) that contains the original icon. The hull preserves the overall silhouette at a coarse level while discarding interior detail. The fidelity of the hull depends on the sampling density and method; different sampling strategies yield different members of the eikonveksit.

Applications: The concept appears in discussions of icon design, digital typography, and pattern recognition. Potential uses include generating bounding shapes for rendering at small sizes, simplifying complex icons for vector representations, and analyzing how icon shapes relate to their convex outlines.

History and status: Eikonveksit is a niche term that appears in a small subset of design and computational-geometry discussions, and it is not yet a standardized term in mainstream literature. See also convex hull, shape analysis.