Projetivo

Projetivo is a term used to describe concepts related to projection and projective geometry. In Portuguese, it functions as both an adjective (describing objects tied to projection) and a noun referring to objects or ideas associated with projection. The term appears across mathematics, computer graphics, art, and related disciplines.

In geometry, a projection is a map that assigns to each point a corresponding point in a lower-dimensional space according to a fixed rule, such as lines through a center meeting a plane (central or perspective projection) or lines that are parallel (orthographic projection). Projective geometry studies properties that remain invariant under projective transformations, such as incidence (which points lie on which lines) and the cross-ratio of four collinear points. A key feature is the inclusion of points at infinity, which allows a unified treatment of parallelism and enhances the notion of invariance under projection.

In computer graphics and technical drawing, projection is the process of mapping 3D coordinates to a 2D image. Perspective projection simulates human vision, producing depth cues as objects recede; it is typically implemented via projection matrices or equations using a focal length. Orthographic (or parallel) projection preserves relative sizes, useful for measurements and schematic representations.

In art, projection underpins perspective drawing, enabling the representation of three-dimensional scenes on two-dimensional surfaces. In mathematics, the study of spaces, mappings, and invariants under projective transformations—such as projective spaces and homogeneous coordinates—is central to the field.

Overall, projetivo encompasses a range of concepts connected by the idea of projecting or transforming structures while preserving certain relationships.