Skills Needed to Design either: Quake, Quake II, Q3A, Unreal,  oUnreal 2003

I'm wondering, what kinds of skills do you need to design first person shooter games like those? For any of you who have designed them, would you need to be very familiar with linear algebra/abstract math/matrix theory type things? How advanced would you need to be in physics? Would you have to be a genius to design those kinds of games, or could you just do it with hard work and a little bit of help from the API? What are your thoughts.

To design the games or to actually write them?
You probably need lots of playing experience and some creativity, as well as knowledge of the limits on your 3D engine in order to design a good game on paper.
To actually write one, you'd probably need:
- 2D, 3D and sound editors, as well as code to load those files
- A system for representing the world and the various objects (enemies, powerups, misc. objects) within it, and a level editor to create these worlds easily; probably you'll also need a simple trigger-based scripting system for scripted missions where things happen after the player completes a goal
- Knowledge of general 3D graphics theory: the rendering pipeline, transformation matrices, multitexturing, various types of light sources, vertex shaders (?), special effects (fog, shadows, water waves, transparent bitmaps for fire/rain/explosions, etc)
- A good enough representation of physical objects that you can prevent them from going through each other (this is harder if they are arbitrary 3D meshes), and calculate their new velocity and position each frame based on gravity, friction, and interactions with other objects (probably using conservation of momentum or kinetic energy)
- An AI system for enemies: probably a finite state machine which can give them various goals/missions, and pathfinding and weapon targetting routines
- Miscellaneous user interface features: a minimap/radar, a way of selecting weapons, a main menu and level selector/loader, code to serialize/deserialize the game state for saving a game, code for networking (probably using UDP).
A good book on creating games would probably contain most of the things you'd need. I've seen many of these. Check Amazon or your local book store maybe.
I don't think a simple first person shooter with most of the main features of Quake or Unreal would be hard to make. However those designers had two things that made the games successful and would be very hard for a single person to do alone:
1) Time. Lots of it to add details, fix bugs, create artwork/sound, design challenging levels, and even write and document all the basic routines and object libraries that make up the game.
2) Heavy optimization. Those games look good because almost everything is optimized to go the fastest it can, so there can be more polygons, larger textures, more special effects, more objects and particles, larger levels, and so on. A game with the same gameplay/strategy features as Quake or Unreal but with 3-4 times lower polygon count, blurrier textures, many of the particle effects gone, and smaller levels would be a lot less successful.

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