Concept

Multiview drawing — where it appears

The drawing office's front, top and side views of a part, which together bound the solid between a hull and something smaller rather than determining it.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

front view · 32 filledtop view · 36 filledside view · 36 filledthe largest solid with these views — 192 cellsand a solid with the same views — 64 cells6 × 6 × 6 cellsthe three views are identical; the solids differ by 128 cells

Three views do not fix the solid

A stepped block on a six-cell grid draws a front, a top and a side view. So does a solid with a third of its material, and so does one with more than the block has — 192 cells against 64, every filled square in all three views identical. The drawing office's triple bounds a part between two solids and does not determine it, and the gap runs to a factor of n.

parallel · multiview
true length1.3928 mpoint viewthe edge is one pointtrue shape1.3232 m²one face, three ray directionseach step is a choice of direction, not a construction on the paper

The view that makes a line a point

Descriptive geometry's first drill is to look at an edge from a direction perpendicular to it, so it draws at true length, and then along it, so it draws as a point. Both are the same identity — the imaged length is the true length times the sine of the angle to the ray — and the sine holds to 1e-12 across the whole sweep of directions.

parallel · auxiliary
90°106°front view · 1.997 m²its own view · 2.900 m²area × 0.6886, the cosineworst corner out by 15.60°

The true shape of a cut

A plane through a box makes a hexagon of 2.8996 m². The front view draws it at 1.9966 m² — the true area times the cosine, 0.6886 — and gets its corners wrong as well, the worst by 15.60°, because a foreshortening scales one direction and not the other. The area is recoverable with one number and the angles are not, which is why a section gets a view of its own.

parallel · auxiliary

Named alongside it

The objects these essays reach for when they reach for this one.

Orthographic projectionAuxiliary viewDescriptive geometryElevationForeshorteningParallel projectionTrue lengthAffine mapAnisotropyArea scalenecessary, not sufficientpoint at infinity

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