Many three-dimensional objects are rather homogeneous along some axis. A tree trunk is a prime example. When a tree is sawed into two pieces in a plane perpendicular to the long axis, the two surfaces seen are cross-sections of the tree at that point. Cutting the tree at other points produces sections that are qualitatively similar to one another, so one section is adequate. {dendrochronology, tree rings -- 1D cores - separate topic} Slicing a fruit such as a lemon or banana perpendicular to the axis through the stem produces a similar representative cross section. The purpose of all this is to reduce the structure of a 3D object to a representative and informative 2D object for viewing.

When an object does not have a high degree of symmetry, the sectioning plane is constrained in other ways if it is to be maximally informative. The constraints can involve both the orientation of the plane and its positioning within the object.

An ordinary wooden pencil is approximately cylindrically symmetric but is only partially represented by a single cross-section perpendicular to its long axis, Fig. 1, Section A, (a coronal or sagittal section in anatomy). This is because it is not homogeneous on the long axis since it has an eraser, a metal band to hold the eraser in place, the graphite "lead" and the tapering of the wood and lead near the tip, as shown in the cross section, Fig. 1, Section B, (an axial section in anatomy or simply a cross section).

Figure 1. Two section views of a pencil.

A hammer has mirror symmetry through a plane along the axis of the handle and bisecting the head, as shown in the cross-section of Fig. 2 (a sagittal section).

Figure 2. A section view of a hammer, showing it in its plane of mirror symmetry.

In standard three view technical drawings, an object is traditionally shown in exterior views of the top and two lateral views, comprising three orthogonal planes. The same can be done with sections and may be necessary when the 3D object has little symmetry.

A sequence of sections along an axis is sometimes used when there is important variation that needs to be illustrated. Only certain objects lend themselves to such sequences. The pencil and especially, the hammer example, don't lend themselves particularly to such an illustration.

A series of floor plans for a hotel which can host meetings, and showing different floors, is a conventional series of "slices". They can show the layout of the lobby, dining areas, auditoriums, meetings rooms, etc., as they are laid out on successive floors. Typically the upper floors are all of the same design and are not shown in such displays. On the other hand, it is not uncommon for a hotel to have a floor plan in each room to demonstrate the location of the stairs and elevators. This plan might be identical for a range of floors.

Slices through high-dimensional datasets are used in visualization. Geological strata are common cross sections. There are also specialized 1D strata that are created by taking cores in ice or sediments. In trees, such a core is used in dendrochronology to study tree ring growth to infer information about earlier periods of temperature and precipitation.

Geological strata. Cores as 1D strata (sep section?)

Notes: Figures 1 and 2 drawn by Bob Futrelle.

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