# Top Front End (TFE) Intro Tutorial

AKA “What the heck do these lines mean???”

Top front end (TFE) is probably the hardest section to initially understand in the PAT, but fear not! Once you get a hang of it and what all the different lines mean it becomes an easy section to master. Take your time to read through this tutorial, as slow as you need to, re-read it, and refer back to it when you need to clarify something.

Before we get started, we need to get you caught up on all the terminology, and explain what the problem is really asking you to do. By the end of this tutorial you should be able to answer some easy TFE questions, and with practice, you’ll be able to answer the hard ones as well. Let’s get started!

Objective of TFE Section: Take the two 2D views, imagine the 3D shape they represent, and find the missing 2D view. It’s OK if that doesn’t make sense yet, just keep reading and keep this in the back of your mind.

# Explaining What Each View Means

Still learning the basics

Note: You will NOT be given the 3D object for real TFE questions, your job will be to imagine the 3D object from the 2D views. But, for the purpose of the tutorial, we’re going to show and use the 3D object to help ease you into solving TFE problems.

Imagine for the box pictured to the right, I asked you to draw me what the box would look like if you were looking from the top straight down, like so:

It would just look like a rectangle, as drawn below. This is known as the TOP view of the object.

What about the front view? Imagine what the box would look like if you were looking at it directly from the front, like this:

It would look similar to the top view, just a little thinner since the front is thinner than the top. This is known as the FRONT view of the object.

Finally, how would this object look from the right side of the object, like so:

It would look like the front view, only a little shorter this time. It would still retain the same height, since both the front and the right side share a common edge and are the same height in the 3D object. This right side view is also known as the END view. Whenever you see the END view, it’s synonymous with the right side view, remember that.

# Explaining What Solid and Dotted Lines Mean

We’re starting to get there…

Now we’re going to do the same thing, but this time our object is a little different. It has a hole in the middle of it. Let’s see how this affects our drawing of the box.

Starting with the TOP view, imagine what this box would look like if you were looking straight down at it from the top, as shown to the right:

It would look like a smaller rectangle placed within a larger rectangle. Notice we only see the highlighted edges of the shape from the TOP view.

Excellent. Now let’s move to the Front and End views. I want you to do the same thing, just draw what you directly see if you were looking at the object from the Front and End view, as shown to the right:

All we would see is a flat rectangular wall, similar to what we had in the previous problem with a solid box.

Wait a minute… but how can this object, which has a hole in the middle of it, have the exact same FRONT and END views as the previous solid object?

These two objects are fundamentally different. One of them has a giant hole in the middle of it. There has to be a way to tell them apart based on their views. Let’s look at the x-ray view of the shape with a hole in it.

If we look at the Front view now, what’s fundamentally different compared to the original solid box is the presence of the highlighted hidden edges in the object. There is a sharp change in the depth of the object on the highlighted edges, which we cannot see from the Front or End view in this case.

So for the edges of the object we could directly see, we used solid lines. For these new hidden edges we cannot directly see, because they are behind a solid piece of the object, we use dotted lines. Let’s apply that to the front and end views of our diagram.

To recap, the edges of the object we can directly see from our point of view are drawn as solid lines. The hidden edges of the object – sharp changes in the depth of the object that we CANNOT directly see from our point of view – are drawn as dotted lines.

# Superimposition of Solid and Dotted Lines

Here comes the tricky part

OK, we’re going to draw the top, front, and end views one more time, this time for a more complex shape.

Try drawing the Top view of this object yourself, imagine what it would look like:

Great, now let’s do the End view next. Remember, everything you can directly see will be drawn as a solid line, but the hidden edges you CANNOT see are drawn as dotted lines!

As you see from the End View, we see the solid blue lines, which is the outline of the shape, along with 3 green dotted vertical lines, which represent the hidden edges, or changes in depth we cannot see.

Now we’re going to move to the Front view of the object. Try it yourself, think about what it would look like, and continue reading. Be careful! Try to figure out what will be a solid line and dotted line (or if there are any dotted lines at all?)

Answer: Sure, those hidden edges are there, but they are superimposed (or directly covered) by the blue solid lines here:

These two directly visible edges from the Front view:

Are positioned directly over the two hidden edges, therefore you’ll only see solid lines here in the Front view.

So if there is a solid line on top of a dotted line in a particular point of view, the solid line will win out.

# Quick Lesson on Orientation

Learn how the different views relate to each other

Now that we’re familiar with the terminology and what the solid and dotted lines mean, I’m going to show you how each view relates with each other, and how you can find a unique feature in the 3D shape in all three views.

Remember, on the real TFE section, you won’t be given a 3D view of the model. You have to imagine the 3D model in your head, and figure out what the missing 2D view would look like. Sounds complicated, but once you get the hang of it, it gets much easier.

# Relating the TOP and FRONT Views

Making sense of the views

Let’s start off by relating the Top and Front views. These are the easiest views to relate, because they’re already stacked on top of each other. This means the Left and Right sides of the top and front views line up, as shown:

Therefore, if I wanted to know how the red dot in the Top view related to the Front view, I could just look for a feature in the same position.

Bonus lesson: If you only saw the red dot in the Top view, and were looking for that feature in the Front view, would you expect to find a solid or dotted line?

Well, if you were looking from the Front view at the Top view, you would directly see that sharp edge in that red dot, so you would expect to see a SOLID line from the Front view to represent this directly visible edge. This is the skill we will eventually develop to help beat this section.

# Relating the FRONT and END Views

Making sense of the views

Relating the Front and End views is pretty easy too. The top of the Front view is the same as the top of the End view. The bottom of the Front view is the bottom of the End view. Easy enough.

# Relating the TOP and END Views

Making sense of the views

OK, this one isn’t as easy at first, but there is a trick to it.

All you have to do is rotate the Top View 90 degrees clockwise to have it stacked on top of the End View, allowing you to compare and relate the two views.

With the Top and End Views stacked on top of each other, you can easily see how each feature in the Top View corresponds to the End View. Notice how all the features highlighted in red in the Top View corresponded with the lines in the End View.

Now on the real DAT, you won’t be able to flip the Top View 90 degrees to make it easy, this was just to show you how the two views relate with each other.

So how would you figure out how the feature highlighted in blue would match up with the End View?

Well, you know the blue dot is close to the back of the shape, since it’s close to the yellow line. Going from Back to Front in the Top View, it’s also the first feature seen. Therefore, going from Back to Front in the End View, it should be just to the left of the Back yellow line, as shown.

# Summary of Relating the Top, Front, and End Views

Remember to head to the next part for a practice problem!