ovalflat

Ovalflat is a term used in geometry and design to describe a family of two-dimensional shapes that interpolate between an ellipse (oval) and a flat-sided form. An ovalflat shape is conceptually produced by flattening an oval along two opposite directions, creating a boundary that blends curved arcs with straight-like segments. The amount of flattening is governed by a parameter that ranges from 0 to 1.

Construction and description: For modeling, an ovalflat can be generated by combining an ellipse with a central rectangle or by taking the convex hull of two parallel line segments joined by curved arcs. A low flattening value yields a near-ellipse, while higher values approach a stadium-like shape with more pronounced flat sides. The boundary remains convex for all values below the extreme.

Applications: In graphic design, iconography, and user interface elements, ovalflat forms are used to achieve a balance between the softness of curves and the clarity of straight edges. They appear in logo design, button shapes, and badges where a mid-range radius is desired. Some vector graphics tools offer morphing between ellipse and rounded-rectangle forms via an ovalflat parameter.

Terminology and usage: The term ovalflat is informal and not standardized in mathematics. Different authors may describe the same shape with varying constructions, and practical definitions are tool-dependent. The concept is closely related to ellipses, rounded rectangles, and stadium shapes.

Related shapes include ellipse, rounded rectangle, and stadium (racetrack) shapes.