Incenter centers known to the ancient Greeks, and the only one that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers. For polygons with more than three sides, the incenter only exists for tangential polygons—those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant from all sides. It is a theorem in Euclidean geometry that the three
Geometry pipelines 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 repair 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 & Sutherland Picture System, but perhaps received broader recognition when later applied in the broad range of graphics systems products introduced by Silicon Graphics (SGI). Initially the SGI geometry hardware performed simple model space