In the previous article, we were talking about building Scrollers — tools that would change a Global parameter (like Level, Color, Weight, and lots more) by incrementing/decrementing (+ and -) or scaling (* and /) an existing setting.

We found these tools pretty easy to build, and useful for everyday design tasks...

However, when we started to think about making changes like this to the Active Angle, things stopped working the way we figured they would. When we used a key-in like...

instead of bumping the current Angle up by 15, MicroStation simply set the Active Angle to 15°, and likewise in the second example, we ended up with an Active Angle of 315° (360° minus 45°)!

What gives?!

Well, it turns out that the reason MicroStation doesn't apply our scroller or scaler modifiers to the Active Angle is because it's different than our other global parameters (go figure.)

As it turns out — believe it or not — MicroStation maintains the Active Angle not in decimal degrees (as we would expect) but in Radians! (And if you think that's weird, check into how it maintains Cell Names!)

So now I suspect you wanna know what the heck a Radian is, 'eh? Well, I was just gonna make you take 'Ol Bubba's word for it, but I guess as long as we're here, we might as well learn something along the way...

As we know, the way Angles are usually represented (in MicroStation, and well, 'um, all over the place) is in Degrees. However, as just discussed, MicroStation — internally — saves the Active Angle in Radians.

A Radian, ahem...

 ...is defined in terms of an Arc whose length (along the Arc)
 is the same as its Radius.

Yeah, I know — so what... Well, maybe a picture will help...

In our little example (yeah, I drew it in MicroStation) the length of the Arc BC is the same as the length of its Radius AB.

Another way to put this is that the size of an Angle, in Radians, is equal to the length of the Arc it subtends (subtends — an eight dollar Math word) divided by its Radius.

So, all that said, one Radian equals just about 57.3° — and while we're in the neighborhood, it can't hurt to know that there are exactly 2 Radians in a Circle (that is, 2 Radians equal 360°).

Got all that??

Let's summarize what we really need to know about this Radian business, so we can get back to our original deal here (and build some tools)...

 there are 57.2958° per one Radian

 which means there are 0.01745329 Radians per degree

And although it makes no difference at the moment (but will in a little bit), let's also establish...

 there are 0.08726645 Radians in five degrees (5°)
 (0.01745329 * 5 = 0.08726645)

Now that we know about some of this Radian stuff, let's get down to business with the reason we started this excursion to begin with.