Axisparallelen

Axisparallelen, or axis-parallel elements, describe geometric objects whose edges or directions align with the coordinate axes. In a two-dimensional plane, an axisparallele line is either horizontal (parallel to the x-axis) or vertical (parallel to the y-axis). In three dimensions, axisparallele objects include planes and boxes whose faces are parallel to the coordinate planes, and whose edges run parallel to the x, y, or z axes. The common instance is the axis-aligned bounding box (AABB), a rectangular prism aligned with the axes used to enclose a set of points or another object.

Properties of axisparallelen shapes are they have simple mathematical descriptions and straightforward intersection tests. In 2D, rectangles with sides parallel to the axes are defined by minimum and maximum coordinates, such as [xmin, xmax] × [ymin, ymax]. In 3D, boxes are defined by [xmin, xmax] × [ymin, ymax] × [zmin, zmax]. This simplicity makes calculations efficient, especially for containment checks (whether a point lies inside a shape) and for detecting intersections between shapes.

Applications span multiple fields. In computer graphics and simulations, axisparallele bounding volumes are used for quick culling and collision detection. In GIS and spatial databases, axis-aligned boxes assist in indexing and queries. They also serve as convenient approximations for more complex oriented shapes when performance is prioritized.

Variants include axis-aligned polygons, where all sides are parallel to axes, and axis-aligned bounding volumes in higher dimensions. The concept contrasts with oriented or arbitrarily rotated shapes, which require more complex mathematics for intersection and containment tests.