Piiripinnal

Piiripinnal is a Finnish term used in mathematics and computer graphics to describe the boundary surface of a three-dimensional object or region. The word is a compound of piir- (related to edge or boundary) and pinnal (surface). In standard usage, piiripinnal corresponds to the exterior surface that encloses a volume.

In geometry, if V is a solid region, its piiripinnal is the boundary set ∂V. For polyhedra, the piiripinnal is the union of its faces; for smooth bodies, it is a smooth two-dimensional manifold that bounds the interior. The concept is distinct from the interior itself, which lies on one side of the surface.

In computer graphics and CAD, the piiripinnal is often approximated by meshes (such as triangle or quad meshes) to enable rendering, shading, collision detection, and physical simulation. The visual appearance and physical behavior of a shape are largely determined by how its piiripinnal is represented and sampled.

Relation to other concepts: the piiripinnal is a two-dimensional boundary of a three-dimensional object. It is related to but distinct from the concept of volume, interior, and from the mathematical idea of a manifold that locally resembles a plane. Understanding the piiripinnal is essential for tasks such as surface parameterization, texture mapping, and surface-based analysis in engineering and graphics.

Examples: the piiripinnal of a sphere is the spherical surface; the piiripinnal of a cube is the union of its six square faces.

See also: boundary, surface, manifold, mesh, CAD, finite element method.

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