Generating Top, Front, and End Views

One direction at a time

You already know what a silhouette is. The working question is how to produce the three of them reliably, in your head, without losing track of which is which.

Do them one at a time, and name the direction before you start. Each view is defined by the direction you look along, and each keeps exactly two of the object's three dimensions:

View	You look	The outline records
Top	straight down	width and depth
Front	horizontally, at the face toward you	width and height
End	horizontally, from the side	depth and height

The dimension missing from each row is the one you are looking along — the one the shadow throws away. Height never appears in a top view, because height is the direction you are looking.

Build the three views

The object below is a rectangular block with two edits: a notch cut out of one corner, and a thin bar sticking out of one end. Step through the directions and watch which edits reach the outline. The tinted faces are the ones facing you in that direction.

Showing the top view.

Faces pointing up — what you see looking straight down.

TOP VIEW

The top view: width and depth survive.

Looking down: the outline is 8 wide by 3 deep. Both edits show — the notch as a bite out of one corner, the bar as a thin tongue.

Which features survive

The two edits behave differently, and the reason generalizes:

The bar shows in the top and front views, not the end view. It sticks out past the block along the width direction, so it lengthens the outline in both views that record width. Across its depth and height it stays inside the block, so from the side it is swallowed.
The notch shows in the top view only. It is cut into the back of the block. From above there is nothing left to fill it, so the boundary steps inward. From the front and the side you are looking through solid material that sits in front of the cut, and the outline closes over it.

A feature reaches a view only when nothing else of the object covers it along that line of sight. An added piece changes the outline where it pokes out past everything else; a cut changes the outline only where no material is left behind it. A bore is the sharp case: the object's projection genuinely does have a hole in it, but only in the view whose direction the bore passes all the way through. Be careful carrying that across to the answer options, though — a drawn opening is a hole cut in a plate and cannot contain a floating island, so the openings fill such a hole back in, and the outline traced with the bore left in is a designated wrong answer. Matching outlines to options is the next topic's job.

The three views share their dimensions

The three views are not independent drawings. They are three pairings of the same three numbers, so each dimension appears in exactly two of them:

Top and front share width.
Front and end share height.
Top and end share depth.

TOP VIEW

FRONT VIEW

The same width, measured on two different views of one object — the bars are the same length because the number is the same.

This is worth more than bookkeeping. It halves the work — once you have the top view you already know the width of the front view and the depth of the end view — and it is a free error check. If the front view you just built is wider than the top view you built a moment ago, you have made a mistake in one of them. Two drawings of the same object cannot disagree about its width.

Doing it without a pencil

The PAT's own instructions tell you the job is mental: first imagine how the object looks from all directions, rather than the single direction shown. So practice building views the way you will have to use them — held in your head, not drawn.

Start from the biggest block. Fix its outline in that view first, then edit it. Most objects are one slab plus a short list of additions and removals.
Say the outline in words. "Rectangle, one corner bitten out, thin tongue on the right" is far easier to hold for twenty seconds than a remembered picture, and it survives being interrupted by looking back at the object.
Go top, then front, then end. Each view hands you one dimension of the next, so the numbers carry forward instead of being re-read.
Name the two numbers before you draw the shape. Settling "8 by 3" first stops the outline from drifting out of proportion as you add features.

Build these on easy items in the keyholes practice generator until the three views arrive without effort. Choosing among five drawn openings is the next topic's problem; this one is finished when you can produce the three outlines from the picture alone.

The takeaway

Take the views one at a time, naming the direction you are looking along and the two dimensions that survive it: top keeps width and depth, front keeps width and height, end keeps depth and height. A feature reaches the outline only where nothing else of the object covers it in that direction, which is why one edit can show in two views and another in only one. Because every dimension appears in exactly two views, each view you finish gives you a head start on the next — and a way to catch yourself when one of them is wrong.

Generating Top, Front, and End Views

Summary

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