Geometric manipulation of modeling primitives, such as that performed by a Geometry Pipeline, is the first stage in computer graphics systems which perform image generation based on geometric models. While Geometry Pipelines were originally implemented in software, they have become highly amenable to hardware implementation, particularly since the advent of very large scale integration (VLSI) in the early 1980's. A device called the Geometry Engine developed by Jim Clark and Marc Hannah at Stanford University in about 1981 was the watershed for what has since become an increasingly commoditized function in contemporary image-synthetic raster display systems.
Geometric transformations are applied to the vertices of polygons, or other geometric objects used as modelling primitives, as part of the first stage in a classical geometry-based graphic image rendering pipeline. Geometric computations may also be applied to transform polygon or patch surface normals, and then to perform the lighting and shading computations used in their subsequent rendering.
Hardware implementations of the geometry pipeline were introduced in the early Evans and Sutherland Picture System, but perhaps received broader recognition when later applied in the broad range of graphics systems products introduced by Silicon Graphics. Initially the SGI geometry hardware performed simple model-space to screen space viewing transformations with all the lighting and shading handled by a separate hardware implementation stage, but in later, much higher performance applications such as the SGI Reality Engine, they began to be applied to perform part of the rendering support as well.
More recently, perhaps dating from the late 1990's, the hardware support required to perform the manipulation and rendering of quite complex scenes has become accessible to the consumer market. Companies such as nVidia and ATI (now a part of AMD) are two current leading representatives of the hardware vendors in this space. The Geforce line of graphics cards from nVidia were an early introduction of these functionalities in the consumer market.
This subject matter is part of the technical foundation for modern computer graphics, and is a comprehensive topic taught at both the undergraduate and graduate levels as part of a Computer Science education. The reader is referred to the seminal and current texts for further detail: Principles of Interactive Computer Graphics, by William Newman and Bob Sproull, Computer Graphics: Principles and Practice by J.D. Foley and Andries van Dam, etc.
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