For starters, let's take a look at OpenGL. OpenGL is mainly a cross platform API (useable on multiple computers), made by Silicon Graphics. OpenGL is also a open source API, meaning that developers do not have to pay to use it, they can use and modify it to their own needs. While the PS3 uses the OpenGL API, the Wii uses a modified OpenGL API called GX. OpenGL however is mainly used to create programmes that can display and edit graphics.
Direct3D is a part of Microsofts DirectX API, and as such, is only useable on microsoft platforms, unless others pay for it's use (ex. Dreamcast). Since Direct3D came out, it has been OpenGL's main competitor. Direct3D was however, often criticized for having complicated means for performing simple task. While Direct3D is designed to utilize and graphics acceleration device is installed on a machine, OpenGL is specifically designed for machines that don't have a graphics accelerator.
Both API's do follow the system know as the Graphics Pipeline, which is the process of rasterization-based rendering, which is essentially taking a 3D scene, and creates a 2D raster image from it. OpenGL and Direct3D are two pipeline models, which are seen as industry standard.
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| The Graphics Pipeline. |


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