The Clock Variable: Key To It All

POV-Ray supports an automatically declared floating point variable identified as clock (all lower case). This is the key to making image files that can be automated. In command line operations, the clock variable is set using the +k switch. For example, \Clo{+k3.4} from the command line would set the value of clock to 3.4. The same could be accomplished from the INI file using\IFKINDEX{Clock}

Clock = 3.4

If we don't set clock for anything, and the animation loop is not used (as will be described a little later) the clock variable is still there - it's just set for the default value of 0.0, so it is possible to set up some POV code for the purpose of animation, and still render it as a still picture during the object/world creation stage of our project.

The simplest example of using this to our advantage would be having an object which is travelling at a constant rate, say, along the x-axis. We would have the statement

translate <clock, 0, 0>

in our object's declaration, and then have the animation loop assign progressively higher values to clock. And that's fine, as long as only one element or aspect of our scene is changing, but what happens when we want to control multiple changes in the same scene simulatneously?

The secret here is to use normalized clock values, and then make other variables in your scene proportional to clock. That is, when we set up our clock, (we're getting to that, patience!) have it run from 0.0 to 1.0, and then use that as a multiplier to some other values. That way, the other values can be whatever we need them to be, and clock can be the same 0 to 1 value for every application. Let's look at a (relatively) simple example

#include "" camera { location <0, 3, -6> look_at <0, 0, 0> } light_source { <20, 20, -20> color White } plane { y, 0 pigment { checker color White color Black } } sphere { <0, 0, 0> , 1 pigment { gradient x color_map { [0.0 Blue ] [0.5 Blue ] [0.5 White ] [1.0 White ] } scale .25 } rotate <0, 0, -clock*360> translate <-pi, 1, 0> translate <2*pi*clock, 0, 0> }

Assuming that a series of frames is run with the clock progressively going from 0.0 to 1.0, the above code will produce a striped ball which rolls from left to right across the screen. We have two goals here:

1.Translate the ball from point A to point B, and,
2.Rotate the ball in exactly the right proportion to its linear movement to imply that it is rolling -- not gliding -- to its final position.

Taking the second goal first, we start with the sphere at the origin, because anywhere else and rotation will cause it to orbit the origin instead of rotating. Throughout the course of the animation, the ball will turn one complete 360 degree turn. Therefore, we used the formula, 360*clock to determine the rotation in each frame. Since clock runs 0 to 1, the rotation of the sphere runs from 0 degrees through 360.

Then we used the first translation to put the sphere at its initial starting point. Remember, we couldn't have just declared it there, or it would have orbited the origin, so before we can meet our other goal (translation), we have to compensate by putting the sphere back where it would have been at the start. After that, we re-translate the sphere by a clock relative distance, causing it to move relative to the starting point. We've chosen the formula of 2*pi* r*clock (the widest circumference of the sphere times current clock value) so that it will appear to move a distance equal to the circumference of the sphere in the same time that it rotates a complete 360 degrees. In this way, we've synchronized the rotation of the sphere to its translation, making it appear to be smoothly rolling along the plane.

Besides allowing us to coordinate multiple aspects of change over time more cleanly, mathematically speaking, the other good reason for using normalized clock values is that it will not matter whether we are doing a ten frame animated GIF, or a three hundred frame AVI. Values of the clock are proportioned to the number of frames, so that same POV code will work without regard to how long the frame sequence is. Our rolling ball will still travel the exact same amount no matter how many frames our animation ends up with.

Clock Dependant Variables And Multi-Stage Animations

Okay, what if we wanted the ball to roll left to right for the first half of the animation, then change direction 135 degrees and roll right to left, and toward the back of the scene. We would need to make use of POV's new conditional rendering directives, and test the clock value to determine when we reach the halfway point, then start rendering a different clock dependant sequence. But our goal, as above, it to be working in each stage with a variable in the range of 0 to 1 (normalized) because this makes the math so much cleaner to work with when we have to control multiple aspects during animation. So let's assume we keep the same camera, light, and plane, and let the clock run from 0 to 2! Now, replace the single sphere declaration with the following...

#if ( clock <= 1 ) sphere { <0, 0, 0> , 1 pigment { gradient x color_map { [0.0 Blue ] [0.5 Blue ] [0.5 White ] [1.0 White ] } scale .25 } rotate <0, 0, -clock*360> translate <-pi, 1, 0> translate <2*pi*clock, 0, 0> } #else // (if clock is > 1, we're on the second phase) // we still want to work with a value from 0 - 1 #declare ElseClock = clock - 1 sphere { <0, 0, 0> , 1 pigment { gradient x color_map { [0.0 Blue ] [0.5 Blue ] [0.5 White ] [1.0 White ] } scale .25 } rotate <0, 0, ElseClock*360> translate <-2*pi*ElseClock, 0, 0> rotate <0, 45, 0> translate <pi, 1, 0> } #end

If we spotted the fact that this will cause the ball to do an unrealistic snap turn when changing direction, bonus points for us - we're a born animator. However, for the simplicity of the example, let's ignore that for now. It will be easy enough to fix in the real world, once we examine how the existing code works.

All we did differently was assume that the clock would run 0 to 2, and that we wanted to be working with a normalized value instead. So when the clock goes over 1.0, POV assumes the second phase of the journey has begun, and we declare a new variable Elseclock which we make relative to the original built in clock, in such a way that while clock is going 1 to 2, Elseclock is going 0 to 1. So, even though there is only one clock, there can be as many additional variables as we care to declare (and have memory for), so even in fairly complex scenes, the single clock variable can be made the common coordinating factor which orchestrates all other motions.

The Phase Keyword

There is another keyword we should know for purposes of animations: the phase keyword. The phase keyword can be used on many texture elements, especially those that can take a color, pigment, normal or texture map. Remember the form that these maps take. For example:

color_map { [0.00 White ] [0.25 Blue ] [0.76 Green ] [1.00 Red ] }

The floating point value to the left inside each set of brackets helps POV-Ray to map the color values to various areas of the object being textured. Notice that the map runs cleanly from 0.0 to 1.0?

Phase causes the color values to become shifted along the map by a floating point value which follows the keyword phase. Now, if we are using a normalized clock value already anyhow, we can make the variable clock the floating point value associated with phase, and the pattern will smoothly shift over the course of the animation. Let's look at a common example using a gradient normal pattern

#include "" #include "" #background { rgb<0.8, 0.8, 0.8> } camera { location <1.5, 1, -30> look_at <0, 1, 0> angle 10 } light_source { <-100, 20, -100> color White } // flag polygon { 5, <0, 0>, <0, 1>, <1, 1>, <1, 0>, <0, 0> pigment { Blue } normal { gradient x phase clock scale <0.2, 1, 1> sine_wave } scale <3, 2, 1> translate <-1.5, 0, 0> } // flagpole cylinder { <-1.5, -4, 0>, <-1.5, 2.25, 0>, 0.05 texture { Silver_Metal } } // polecap sphere { <-1.5, 2.25, 0>, 0.1 texture { Silver_Metal } }

Now, here we've created a simple blue flag with a gradient normal pattern on it. We've forced the gradient to use a sine-wave type wave so that it looks like the flag is rolling back and forth as though flapping in a breeze. But the real magic here is that phase keyword. It's been set to take the clock variable as a floating point value which, as the clock increments slowly toward 1.0, will cause the crests and troughs of the flag's wave to shift along the x-axis. Effectively, when we animate the frames created by this code, it will look like the flag is actually rippling in the wind.

This is only one, simple example of how a clock dependant phase shift can create interesting animation effects. Trying phase will all sorts of texture patterns, and it is amazing the range of animation effects we can create simply by phase alone, without ever actually moving the object.

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