begrenzingsvakje

Begrenzingsvakje is a term used in Dutch to refer to a bounding box, a geometric or numerical construct that encloses a set of points or a region with a rectangular box aligned to the coordinate axes. In two dimensions it is defined by the minimum and maximum x- and y-coordinates of the contained objects, yielding corners at (xmin, ymin) and (xmax, ymax). In three dimensions it extends to include z, with corners at (xmin, ymin, zmin) and (xmax, ymax, zmax). The primary purpose is to provide a simple, efficient enclosure for quick spatial queries, collision detection, rendering, and spatial indexing.

In optimization and numerical computing, the term can refer to box constraints: each decision variable x_i is restricted to an interval [l_i, u_i]. The feasible region is then a hyperrectangle, and many algorithms such as projected gradient methods or L-BFGS-B exploit this structure for efficiency.

Other contexts include computer vision and object detection, where bounding boxes indicate the location and size of detected objects in an image, typically using coordinates of the box edges or center and width/height. Variants include axis-aligned bounding boxes (AABB) and rotated bounding boxes (OBB); AABB is favored for simplicity and speed, while OBB can fit objects more tightly but requires more computation.

Limitations: a bounding box may contain substantial empty space if the object is non-rectangular or rotated. Tighter bounding volumes can be achieved with oriented boxes or convex hulls.