Konusform

Konusform is a term found mainly in German-language sources, composed of Konus (cone) and Form (shape). It is used to denote a conical form or surface, and may appear in geometry, architecture, and 3D modeling.

In geometry, a konusform refers to a surface generated by a straight line (generator) moving with a fixed apex and a base curve, yielding a cone when the base is a circle, or a more general conical surface for other base curves. The simplest example is the right circular cone.

Mathematically, a right circular konusform with apex at the origin and axis along the z-axis is described by x^2 + y^2 = (tan α)^2 z^2 for z ≥ 0, where α is the semi-vertical angle. The cone consists of all lines from the apex to points on the base curve. Cross-sections by planes through the axis yield conic sections.

Variants include the conical frustum, produced by truncating a cone with a plane parallel to the base, and the double cone, which has two nappes. Konusform shapes are common in architecture, industrial design, and computer graphics, where they are used for rendering, structural analysis, and form exploration.

See also: cone, conical surface, conic section, conical frustum.