projectieomtrek

Projectieomtrek, or projection perimeter, is the length of the boundary of the image of a geometric object after it is projected onto a plane along a specified viewing direction. It depends on the projection method (orthogonal or perspective) and on the orientation of the object relative to the projection direction.

In an orthogonal projection, rays are parallel to a fixed direction, and the projectieomtrek is the perimeter of the planar region obtained by projecting every point of the object onto the projection plane along lines parallel to this direction. In a perspective projection, lines emanate from a viewpoint, and the resulting region can be nonuniformly scaled and foreshortened, affecting its boundary length.

For polyhedral objects, the projection boundary is formed by the projection of the silhouette edges that separate visible from hidden regions. The projected perimeter is not invariant under rigid motion and can vary with rotation of the object or with changes in projection direction. Computing it generally involves projecting boundary points and determining the boundary of the projected shape, or, for convex objects, computing the convex hull of projected vertices and summing the lengths of the hull edges.

Applications of the projectieomtrek appear in computer graphics, computer vision, and CAD, where the apparent boundary length influences rendering decisions, object recognition, and measurement tasks. Related concepts include projection, orthogonal projection, perspective projection, silhouette, and convex hull.