In Teigha you can work with solids and shells using boundary representations, or B-Reps. In different Teigha products, Teigha Drawings (for working with both .dwg and .dgn files), Teigha PRC, and Teigha BIM, there are separate implementations of B-Rep interfaces, but you can work with them using the common class OdBrBrep.
COLLADA is short for Collaborative Design Activity. DAE files are based on the XML COLLADA format, and they are used by various graphics programs to exchange digital assets under the same format. Each file consists of a set of elements that are images, lights, geometries, effects, materials, cameras, etc.