spherocylinderiksi

A spherocylinder is a three-dimensional geometric shape formed by the union of a sphere and a cylinder. It can be visualized as a sphere with a cylinder passing through its center, or alternatively, as a cylinder with hemispherical caps at each end. The defining characteristic of a spherocylinder is its combination of a curved spherical surface and a straight cylindrical surface.

The shape is often used in various fields, including optics and computer graphics. In optics, lenses with a spherocylindrical shape, known as spherocylinders, are employed to correct astigmatism. These lenses have different refractive powers in perpendicular meridians, allowing them to focus light onto a single point on the retina, thereby improving vision. In computer graphics, spherocylinders can be used as simplified models for objects that possess both rounded and elongated features, such as capsules or certain types of bolts.

Mathematically, a spherocylinder can be described by its radius, which is the same for both the spherical and cylindrical components, and its length, which refers to the length of the cylindrical portion. The volume and surface area of a spherocylinder can be calculated by summing the volumes and surface areas of its constituent sphere and cylinder. The formula for the volume of a spherocylinder with radius r and cylinder length L is (4/3)πr³ + πr²L, and its surface area is 4πr² + 2πrL.