Lesson plan
Axis-aligned object
In geometry, an axis-aligned object (axis-parallel, axis-oriented) is an object in n-dimensional space whose shape is aligned with the coordinate axes of the space. Examples are axis-aligned rectangles (or hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding boxes are often implicitly assumed to be axis-aligned. A more general case is rectilinear polygons, the ones with all sides parallel to coordinate axes or rectilinear polyhedra. Many problems in computational geometry allow for faster algorithms when restricted to (collections of) axis-oriented objects, such as axis-aligned rectangles or axis-aligned line segments. A different kind of example are axis-aligned ellipsoids, i.e., the ellipsoids with principal axes parallel to the coordinate axes.
Article summary
In geometry, an axis-aligned object (axis-parallel, axis-oriented) is an object in n-dimensional space whose shape is aligned with the coordinate axes of the space. Examples are axis-aligned rectangles (or hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding boxes are often implicitly assumed to be axis-aligned. A more general case is rectilinear polygons, the ones with all sides parallel to coordinate axes or rectilinear polyhedra. Many problems in computational geometry allow for faster algorithms when restricted to (collections of) axis-oriented objects, such as axis-aligned rectangles or axis-aligned line segments. A different kind of example are axis-aligned ellipsoids, i.e., the ellipsoids with principal axes parallel to the coordinate axes.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.