Recreating Grant Skinner's sphereTest Part 2 — almost figuring it out the hard way.
Working off the tests I did previously to try and recreate Grant Skinner's original sphereTest, I drew a bunch of discs, moved them out along the Z-axis randomly between min and max values, and distributed them randomly along the X and Y axes using the
rotationY attributes. Then I incremented each disc's
rotationY value with the onEnterFrame event.
Obviously, the stack order would be need to be worked on, but not a bad start. To get the stack order, I needed to find the relative position of each disc along the Z-axis. To do this, I used the Z position as a circle's radius, and derived approximately how many pixels of movement each degree of rotation along the X axis represented. Once I found that new value, I'd do the calculations again for the Y rotation. To cut down on per-frame math, I figured out the z-position relative to X rotation immediately, and stored it since it wouldn't change. I only did the position relative to Y when needed. Also, I only approximated the Z position by dividing the diameter values by 180 (or, multiplying by 0.005555555556, which is faster and results in the same value), instead of mucking about with the position along the arc. It wasn't exact, but it was a good enough value to sort on. once I had the relative position, Discs that were relatively "closer" to the viewer were then sorted to appear in front of ones that weren't. This involved iterating through the discs to change their Y rotation, sorting the disc array on their derived relative value, and re-iterating to do the stacking. Not great, performance-wise, and still a little jumpy at the poles, but it worked.
To make the stacking appear smoother I ensured that "closer" discs that had an initial maximum Z position were always stacked in front, of other discs, then worked back until the "farther" maximum Z discs were sorted to the back. Next, I made the entire sphere "follow" the mouse. I did this by calculating the angle of the line from the mouse's position and the center of the sphere relative to the x-axis (non-trivial math, to be honest -- at least for me) and rotating the entire sphere around its Z-axis to make the disc's Y rotation move towards the mouse.
This looked fairly good to me. Then I went back to Grant's sphereTest and noticed that his sphere wasn't roting along the Z-axis. Each individual disc simply moved towards the mouse regardless of it's position relative to the Y-axis "pole". It was as if the sphere's Y-axis was moving independently of the discs. Actually, it looked as if they were moving around fixed X and Y axes simultaneously. But using each disc's
rotationY attributes meant the discs' X-axes were all over the map. My initial thought on how to emulate this behaviour was, oddly enough, quite complex. I thought that I would need rotate the sphere towards the mouse around its Z-axis; then correct that Z-rotation by moving the discs in the opposite direction around their own z-axis; then spin the entire sphere around it's own y-axis. Once that was done I'd need to calculate the relative Z of each disc based not only on their internal rotations, but on also on the sphere's rotations as well.
In short, a metric shit-load of math.
For each disc.
For every frame.
Then I found the 3DMatrix object in Adobe's Flash CS4 documentation; Swore out loud; and threw out most of my work to this point. I'll let you know what I replaced it with in my next blog post.