How the Engine works

The 3D engine was one of the few projects where I actually had to contemplate the mathematical complexities of the engine before I sat down and programmed. My usual practise in these matters is to lay down as much code as I can, and then to fiddle, pretty much at random, until something clicks and the engine starts to work. This was my main strategy for Trooper II, where the engine could be contructed in pieces, and has led to a very polished and refined finishing product; however, designing a 3D engine requires much more thought, since the rules of perspective are fixed; unlike the imaginary conditions I imposed on the fictional physical world of Trooper II. The pain the engine has caused me; writing reams of code, only to find the perspective just doesn't look right; despit my calculations; was quite intense, and I thought that to spare anyone else undergoing the same ordeal, I would construct a simple guide to the design of a general 3D engine. It's also an oportunity to explore my own thought process as I desgined the things, and analyssis of your own code is never a bad thing.
First things first; how are objects in a 3D world represented? Well, in the purest sense, objects in 2D can be contructed by vectors. You can also, of course, use sprites, but there is no room for processing there: you can plonk an image anywhere you like, but it always looks the same. Good for a simple engine, but no good if we want stuff to move in 3D. A real object in 2D can be represented by a line; just one vector. In 3D, a plane must be used to represent a real thing; how many strings of infinite fineness do you see in real life? These planes are best modelled as polygons, flat shapes that exist as planes in 3D space. It's easy to store a polygon, using 3D cartesian coordinates: all the polys used in my engine are four sided (optimum speed whilst easy to draw), and I suggest you do the same, so store all your polys in an array with 4 entries for each vertex (corner), each of those represented by an x, a y and a z value. In my world, the z-axis extends into the monitor, which may vary from other treatments of cartesian coords. Now we have a series of planes suspended in 3D space. If the correct transformations are applied to these, then they can be moved about as if they are real 3D objects. When the time comes to display your world on the monitor, the 3D objects must be reduced onto the 2D screen; and to make this realistic the correct perspective algorithm must be used.

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