Missions of the Reliant: Math is fun, or why I wish I hadn’t flunked geometry

At last, an update!

  1. Absolutely nothing visible to the user has changed whatsoever.
  2. The internal structure of the code has been significantly reorganized.

As with the lament of all programmers faced with the demands of the technologically disinclined, I’ve accomplished a great deal, but since it can’t be seen, it might as well be nothing at all. Wasted time, the hypothetical slave driver- I mean, boss- would say. But it isn’t, I swear to all two of you who read this blog!

And now, another math rant.

Once again, as with so many things, the way Mike did things in the original code was correct and logical for the time he did it, but doesn’t fit into the object-oriented model I’m cramming his code into, despite its pitiful cries for mercy from such rigid structure. There are days I wish we were living in times when code could be so freeform as his was and still be comprehensible, but you can’t do that in Cocoa. Oh sure, I could port all the Pascal functions 1-to-1, but the Toolbox calls would be sticky at best. Anyway, in this particular case, I was trying to wrestle with the radar range calculation.

The original code reads something vaguely like: screenPos = Planetabs - (Playerabs - Playerscreen)  inRadarRange = n <= screenPos / 16 <= m. Translating, this means that whether or not a given entity (a planet in this case) is within radar range of the planet is dependant upon the Player’s position in screen coordinates, as well as in the game’s absolute coordinate system.

In the old days, this design made a certain amount of sense. He already had the screen coordinates immediately handy, so why take the hit of indirecting through A5 to touch a global for the absolute position? However, my design makes the screen coordinates a bit dodgy to use. So I had to recalibrate n and m to represent distances in game coordinates.

Algebra to the rescue. The code above, reduced and replacing the inequalities, becomes the algebraic equation (x - (y - z)) / 16 = a, where a is the radar range coordinate. The only screen coordinate term in this equation is z, so solve to eliminate z:

Pygmentize not found.

But, because both a (the radar range) and z (the player’s position on screen) are actually constants, all I had to do was take Mike’s original numbers (let’s use 64 for a and 268 for z) and calculate 16*64 - 268 = 756. Then, retranslating, the equation becomes the inequality inRadarRange = (myPosition - playerPosition) <= 756;. Repeat for the lower and upper bounds of x and y coordinates, and boom, no screen coordinates at all and I can calculate whether or not an object's in radar range based on nothing but its offset from the player.

To be clear, what I did up there was to eliminate a term from the inequalities so that they could be evaluated based on the position of the given entity in game space, rather than on the position of the entity's sprite on the screen.

I can't believe it took me a week to doodle out that bit of math.

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