Vertikalprojizierte

Vertikalprojizierte refers to the image of a geometric object obtained by a vertical projection, i.e., projecting along lines parallel to a fixed vertical axis onto a chosen projection plane. The most common instance is projection onto a horizontal plane, producing a plan or top view of a three-dimensional object. In general, the exact form of the projected figure depends on the orientation of the projection plane and the chosen vertical direction, but the defining feature is that the projection direction is aligned with the vertical axis.

In a typical setting with the vertical axis as z and a horizontal projection plane z = 0, a point (x, y, z) projects to (x, y) on the plane. If the projection is onto a vertical plane instead, the result would be a 2D representation formed by collapsing the vertical coordinate along the chosen plane, while the other coordinates are preserved as viewed. The operation is dimensionality-reducing and usually not invertible, since information along the projection direction is lost.

Vertikalprojizierte plays a central role in descriptive geometry and technical drawing, where multiple orthogonal views (including vertical projections) are used to convey three-dimensional shapes in two dimensions. It also finds applications in architecture, engineering, computer graphics, and mapping, for tasks such as generating building plans, side elevations, or silhouettes from 3D models.

The concept is closely related to other projection types, such as horizontal projections and oblique projections, but is specifically defined by the projection direction being fixed in the vertical sense.