The direct application of the two-dimensional shape measurements described in the previous chapters to three-dimensional objects is often difficult, incomplete, or ambiguous. Reducing a three-dimensional object to a two-dimensional shape that can be measured using the various procedures illustrated does not produce a meaningful result in most cases. A projected image of the outline or silhouette of a three-dimensional object does not fully reveal the shape and may even be quite misleading (see Figure 1.5). Even with multiple views there will often be missing information. Indentations in the surface are covered up in the projected outline, which presents a smoother appearance as hills cover valleys. For a particle ...
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