Capsuleshaped

Capsuleshaped is an adjective used to describe objects with a capsule-like silhouette, a shape formed by a central body capped by two hemispheres. In two dimensions this silhouette is often called a stadium shape; in three dimensions it is the capsule. The term is widely used in geometry, design, and computer graphics to describe rounded-end forms.

In 2D, a capsuleshaped figure consists of a line segment of length L with two semicircles of radius r attached at its ends. The overall width is 2r and the total length is L+2r. Its area is A = 2 r L + π r^2, and its perimeter is P = 2 L + 2 π r. If L = 0 the shape becomes a circle; if r = 0 it degenerates to a line segment of length L.

In 3D, a capsuleshaped solid is the union of a cylinder of radius r and height L with two hemispherical end caps. It has volume V = π r^2 L + 4/3 π r^3 and surface area SA = 2 π r L + 4 π r^2. The bounding box measures 2r by 2r by L+2r, and the shape is convex.

Capsuleshaped figures are axisymmetric and convex, making them useful as bounding volumes and collision shapes in physics engines. In user interface design, capsule-shaped buttons or pills are common for their friendly rounded appearance. In 3D modeling and computer graphics, capsule shapes serve as lightweight proxies for elongated characters or instruments.

Related terms include capsule (geometry) and stadium shape; in 3D graphics some engines refer to CapsuleCollider.