Intro
Out of the many cool new features in Lightwave 6, Expressions is one that I was quite interested in.  Sure, its got a severe lack of documentation, is a bit buggy, tends to crash a lot if you make mistakes and 3.29 of the Motion manual suggests it as the domain of Maths Gurus, but even a moron such as myself can use it using some simple analysis of the situation, an incling of common sense and some basic mathematics...

To prove the point, I used expressions to create a real-time analogue clock animation to test this new tool. Because of the lack of explanation for all the functions in the manual, it took me a lot more work then I had expected initially, but by the time I had managed to crash Layout 10 or so times, I realised I was going way too far with my calculations and the solution was so simple, even a 5 year old could have solved it!
 

My clock scene, comprised of 4 simple models.

Here you go.  A clock comprised of 4 simple models to demonstrate how to use expressions. There are 3 objects we will be concentrating on here - An hours, minutes and seconds hand that I will be animating.  The 'hour markings' object around the edge was simply added in to check the the expressions were working I'll leave the modelling up to you - Its fairly straight forward - Each hand is simply a long rectangular box with the pivot point at one end...  The important part of this tutorial will be how we animate the objects using the Expressions tool! :)

To set up an Expression, select the Graph Editor As you can see in the image on the left here, once you have the graph editor selected, click on the channel you want to modify (for the clock, I used the Heading rotation (Rotation.H) for all hands) for the selected object and then select Modifiers / Add modifier / LW_Expressions to add in the expressions tool. To set the expression, double-click on the modifier name to get the settings box.  The Expression must appear in the top box, but you can assign 4 variables in lines A,B,C and D for more complex stuff! Now you know the basics, I'll quickly run through the expressions I used to animate the three hands of the clock model...

Seconds are ticking...
We'll start our clock with the smallest measure of time - and that's the second.  So, where do we start - well, we know a few things -

• A clocks hands rotate a full circle - That's, um, yeh, 360 degrees! :)
• There are 60 seconds per minute - And a minute is a complete rotation of 360 degrees.

Just to make things easier to understand then long mathematical equations, I've used the A,B,C & D scratch variables to break the maths up. (even though they are incredibly simple!) First, I've placed the 360/60 calculation for the angle inside the A variable.  If you wanted to be clever, you could just avoid this altogether and enter the answer 6 in the expression! To calculate the correct rotational angle, we simply calculate the A variable (6 degrees, or 360/60) multiplied by the Time value.

The value must be multiplied by the Time - The Time acts as the value that will animate our clock hand by giving the corrrect angle at each frame.  ie. Assuming that we were rendering for 30 fps, then if we were at frame 30 (Time = 1s) then 6*1 = 6 degrees, or the first 'second' on the clock face.  If we were at frame 45 (Time = 1.5s) then the angle would be 6*1.5 = 9 degrees and so on.

I also set Additive to be active.  Why?  When Additive is off, the value in the expression will be passed as the absolute value for the rotation.  Hence, at frame 0 (Time = 0s), the seconds hand would always start at the 12o'clock position (or a rotation of 0 degrees!)

Using additive, the expression value is added to the rotational value of the object.  That is, we can set up the starting position of the clock hand at frame 0  ie. Setting the correct time on the clock

Well, we've got the seconds hand animated (Yep, that's it!).  You can play the animation to check it out...
 

Minutes away...
The Minutes hand is our next object we want to animate using our newly-found expressions.  For this we know a few more facts...

• There are 60 seconds per minute.
• There are 60 minutes per hour.

We know that a second hand rotates 360/60 degrees every second.  To move 1/60th of the clock face every 60 seconds, we need to rotate slower, or in this case adjust the angle of the Minutes hand by a smaller angle. Easy - Since it takes 60 seconds, that means every second we only move 1/60th of the angle of the seconds hand. Again we need to multiply it by the time to animate it, and don't forget to set additive on so that we can set our clock by keyframing the hands at the correct 'time' in our animation!

You can play the animation to check it out...  Though you're gonna need a LOT of frames to see the minutes hand move (at 30 fps, that's 1800 frames per minute!)
 

The Hour is nigh...
W'eve conquered the seconds and minutes by using some pretty simple mathematics so far.  The hour hand is no different (well, not too much anyway!).  So, what do we know from looking at our real-life example?

• There are 60 minutes per hour.
• There are 12 hours in the 360 degrees

Yep, that's right - Because we know every 60 minutes we need to move 1/12 of the 360 degrees, we can simply calculate that value by dividing the minutes angle by 12!  Simple! Again, multiply the value by the time for animation and activate the Additive option.

Now that you've seen how easy Expressions can be, have a go yourself.  I'd suggest if your not a keen mathematician to avoid complex ideas and try for basics like this clock project - Try to invisage situations where the relationships between values, or objects are easy to understand and you'll be on your way!  There's a whole tonne of things you can do with expressions - The only limit is your imagination (oh, and mathematics plays a big part too!)

Well, hope that was of use to some of you out there!

Kevin 'kevman' Phillips
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