Counting External Features

Take a census before you compare

A census is a count. Before you judge whether an opening is the right size, count what sits on its outline: every protrusion, every notch, every step, every curve. Then count the same list on the view of the object you are matching. If the two counts disagree, the opening is out, and you never had to measure anything.

Read that outline as a loop. A foot runs along the bottom, an upright rises at one end, a tab juts out of the upright partway up, and a slot is cut into the upright's end. Three features — and the corners keep the books for you. A protrusion or a notch adds two inward corners to an outline; a step adds one. One step plus one tab plus one slot predicts five inward corners, and the outline has exactly five, out of fourteen corners in all.

The census belongs to a view, not to the object. The same object's top outline is a plain rectangle: four corners, nothing inward, no features at all. Census each view separately.

Why counting comes first

Counting is faster than measuring, and it is stubborn in a way that measurements are not. Openings are drawn at assorted rotations and flips, so which side a notch sits on tells you nothing — but how many notches there are is the same number whichever way the drawing is turned over. A count is also all-or-nothing. An outline with two inward corners cannot be an opening with three, however the proportions happen to work out, so a disagreement in the census is a decision, not a suspicion.

That is the order of operations: census the whole field first, then measure only what survives.

A worked elimination

Here is a real item from the practice generator. Count the inward turns on each opening before you read on.

A

B

C

D

E

Inward turns are the quickest census there is, because you can run them without deciding what any feature is. Going around the five openings: one of them never turns inward at all, two turn inward twice, and two turn inward three times.

The answer is the object's front outline, and that outline turns inward three times. The bookkeeping from the figure above says how to spend them: a lobe protruding from one side accounts for two, and a single step accounts for the third. Two features.

Now the eliminations. The opening whose outline never turns inward is convex from end to end — it carries no features whatsoever, where the object's outline carries two. Out. The two openings that turn inward exactly twice are each one feature short of the object; measuring cannot add a feature to a shape that does not have one. Out, and out.

That leaves two openings, and they agree with each other on everything the census can see: three inward turns apiece, a protruding lobe and a step on each. The count has taken five options down to two in a few seconds and can do no more. What separates them is that one is drawn about three-quarters the size of the other, and the five openings are drawn at one shared scale, so that difference is real rather than an artifact of fitting each shape to its own box. Turning it into a decision is the next topic.

A ✓

lobe + step, full size

B

C

D

E

The correct opening is the object's front outline.

The takeaway

Count the features on each of the object's view outlines — protrusions, notches, steps, curves — and count them again on every opening. Inward corners make the count reliable: two for a protrusion or a notch, one for a step. Any opening whose census disagrees with all three views is eliminated outright, which on most items is the majority of the field. Drill this on real items in the keyholes practice generator.