One source (with references) is the CGAL manual, Envelopes of Surfaces in 3D.
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Their software doesn't explicitly handle quadratic surfaces, however (aside from spheres).
This paper, and its citations, may help:
Boissonnat, Jean-Daniel, and Katrin TG Dobrindt. "On-line construction of the upper envelope of triangles and surface patches in three dimensions." Computational Geometry 5.6 (1996): 303-320. Journal link.