Learning Curve: All the Right Angles

6 Jul, 2006 By: Bill Fane

Perpendicular may mean more than you think it does.

It was a beautiful warm spring evening -- May 13, 2006, to be precise. Captain LearnCurve's 1937 Rolls Royce limousine was running flawlessly as his son-in-law Rod drove it to deliver Jenn Claydon to the church to marry the Captain's son Trevor. They were a little late, but that was a traffic problem and no fault of the car or driver.

The Captain sat upright in his rented tuxedo, alongside his gorgeous wife, waiting for the ceremony to begin. While waiting, he tried to think of a topic for his now overdue column (hey, it had been a busy couple of weeks!) when suddenly an inspiration hit him. "Upright! That's it! The Perpendicular Object Snap!"

One of the main differences between old-fashioned paper and pencil drafting and CAD drafting is the extreme accuracy that is possible when CAD is used properly. One of the tools used to obtain this accuracy is the Object Snap functionality.

Most of AutoCAD's Object Snap modes are quite straightforward. Let's face it, once you say that AutoCAD can snap precisely to the end of an arc or the center of a circle or the midpoint of a line, then you have just about said it all.

Perpendicular Power
One object snap in particular, however, is much more powerful and versatile than most people suspect. Would everyone please take their places and pay attention as we explore the thrilling possibilities of the Perpendicular Object Snap?

"Yeah, right, this should be about as thrilling as watching grass grow."

Trust me: it is more entertaining than that. For starters, most people don't even know the full definition of perpendicular. For example, if I asked 1,000 people to draw two perpendicular lines, the vast majority of them would produce something like figure 1.

 Figure 1. A typical example of two perpendicular lines.

Indeed, figure 1 is the typical geometry textbook illustration. The vertical line is perpendicular to the horizontal line because the little square in the corner tells you so. The problem is that you have seen such an illustration so many times, you have come to assume that a perpendicular line is always vertical and is perpendicular upward from a horizontal line and the lines touch at their ends.

Reinforcing this, my Shorter Oxford Dictionary defines perpendicular as

"1. Situated at right angles to the plane of the horizon or directly up and down."

So far so good. Now let's move on to the next part of the dictionary definition:

"2. Geom. Of a line or plane: Having a direction at right angles to a given line, plane or surface."

Wait a minute! There's no reference to horizontal or vertical!

Bingo! Now look at figure 2. Once again, one line is perpendicular to the other, but neither is horizontal nor vertical, nor do they touch at their ends. In fact, it is not even correct to refer to one line as the perpendicular one; strictly speaking, two lines are perpendicular to each other if they form a right angle. See where the traditional textbook diagram has gotten us? We have a much narrower mental image of the subject, even if we remember the words of the definition.

 Figure 2. Perpendicular lines are not restricted to horizontal and vertical.

Let's explore this a little further. Notice that the definition did not say that the lines actually had to meet: figure 3a shows two lines that are perpendicular to each other. The dashed lines in figure 3b indicate that the lines are indeed perpendicular. AutoCAD's perpendicular object snap will yield the theoretical point in space where the lines would meet if they were extended.

 Figure 3. These lines are perpendicular even though they do not touch each other.

Now let's look outside the lines. Specifically, whoever said that perpendicular was limited to straight lines? The line in figure 4 is perpendicular to the arc at the contact point, and hence the line is the shortest possible one between point A and the arc. Point B lies on the straight line that connects point A to the center of the arc. To draw it, I simply started the line at point A, invoked the Perpendicular Object Snap and then selected the arc. It also works with circles or if the line starts inside the arc or circle and radiates outward.

 Figure 4. The line is perpendicular to the arc.

It gets better. You can draw a line that is perpendicular to two circles or arcs (figure 5) or between a line and an arc or circle. AutoCAD can hold a pending object snap, so I used the following command sequence to create this illustration:

```	LINE
From point:
PER  (pick the first circle. Note the "elastic line"
will not appear because AutoCAD doesn't know
where to start it yet).
To point:
PER  (pick the second circle, and AutoCAD will
draw the line).```

 Figure 5. The line is perpendicular to the arc and to the circle.

As you may have guessed by now, this possibility is not the only one. You also can draw a perpendicular line between two nested arcs or circles, providing they are not concentric.

As you can see, we have wandered a long way away from your original preconception of exactly what constitutes perpendicular. Next, I will cause yet another significant jump in your thinking.

But Wait, There's More!
AutoCAD does not even restrict use of the Perpendicular Object Snap to the Line command. Like all other object snaps, you can use it at almost any time that AutoCAD is asking for a point and will result in the action taking place at the theoretical perpendicular point. Consider figure 6a, which shows a line and a circle. You can use the Perpendicular Object Snap during the Move command (figure 6b). Figure 6c shows the result of moving the center of the circle to the point that is perpendicular to the extension of the line.

 Figure 6. You can use the Perpendicular Object Snap while moving objects.

You can use the Perpendicular Object Snap during almost any editing command, such as Stretch (figure 7), Mirror, Copy and so on. You also can use it during inquiry commands such as Distance and to obtain a distance for the Offset command or for the Array command. In every case, it will return the point where two perpendicular objects would meet, even if it has to extend either or both objects to produce a theoretical meeting point. Next comes another interesting bit: like the other object snaps, it even works in 3D.

 Figure 7. The Perpendicular Object Snap works with editing commands such as Stretch.

The Perpendicular Object Snap is one of the most powerful and versatile of all the object snap modes. The others all pretty well behave as advertised; what else would you expect from modes such as CENter, MIDdle, END, INTersection, NEAr and so on? The perpendicular mode, however, can take some interesting twists when you start to play with it.

"Wow, you did it. One whole column on a single snap mode, and it was marginally more interesting than watching grass grow."

And Now For Something Completely Different . . .
It has been said that the shortest sentence in the English language is "I am," and the longest one is "I do."

As Captain LearnCurve and his gorgeous wife celebrate their 40th wedding anniversary, he has decided that the secret to a long and happy marriage resides in just two little words: "Yes, dear."