I'm a self-taught 3D Game Developer and Programmer of 15 years. I have freelanced on game projects as a 3D artist and programmer for about 8 years, I've worked some 6-figure salary jobs in San Francisco on Social Games, and have been independent for the past 3 years developing Unity 3D Multiplayer Games for my own game portal MartianGames.com.
If my career path interests you, send me some questions! :D
Good question! This was exactly my first curiosity when I first encountered Arcade games back in the 80s. The good news is there are softwares available to handle most of the under-the-hood mechanics involved with assembling and rendering 3D content. My favorite is 3D Max, but a very popular free 3D modeling/animating program is called Blender. After the model is assembled in a 3D program, it's then imported into a "Game Engine" like Unreal or Unity. From there, most of the programming involved is for playing and blending animations (by name) according to what is happening in the game, per user input, (such as a walk-cycle, or a punch, or a swim cycle.) The numbers which form the 3D mesh are organized in vertices and corresponding triangles (3 vertices each). These are auto-generated by 3D software during the modeling process which is more similar to molding clay than actually entering in data values by hand. Analogously PhotoShop let's you manipulate pixels with a paint brush without the artist needing to bother with individual pixel data values. If the process of modeling and animation interests you, there are hordes of excellent tutorial videos on YouTube covering this topic. ;)
Everyone has their own personal hero in this area, but mine would have to be John Carmack: founder of id Software, the game engine Quake, pioneered video games Wolfenstein, Doom, and the foundational tech for Half-Life. He has a real passion for 3D / VR innovation which continues on to this day. For most questions containing words like "Where did all this 3D magic get started?" would have to be answered with John Carmack.
I am in love with, fascinated with, the magic that happens when giving a computer a list of instructions, it gives a responsive feedback, like a living breathing life form. To give life to art is the complete reward.
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