core modeling kernels

Two major geometric kernels available on the market today :
1. Parasolid - developed and owned by UGS. (Unigraphics - they use it in their products Unigraphics, SolidEdge) and also license to other customers. Development is in UK.
2. ACIS - developed by Spatial, boulder, colorado company owned by Dessault systems.

There are other propreity kernels used by other CAD companies.

Autodesk - has Autodesk ShapeManager used in Inventor, AutoCAD ,etc.
Think3
VX - varimetrix corporation
PTC - Granite

The interesting thing is competitors are heavily dependent on each other for their kernel and other libraries. For example, Solidworks (owned by Dessault) uses its competitor's product, Parasolid. Autodesk owns Mechsoft, a functional modelling software- used by all UGS, Solidworks, etc.

More rambling later...