One source (with references) is the CGAL manual, Envelopes of Surfaces in 3D.

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            [![TwoTriangles][1]][1]
            ^{CGAL figure.}

Their software doesn't explicitly handle quadratic surfaces, however (aside from spheres).

These twos papers, and their 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.

Meyerovitch, Michal. "Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces." ESA: European Symposium on Algorithms. 2006. Springer link. PDF download.

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            [![Meyerovitch][2]][2]
            ^{Meyerovitch figure.}

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Here I respond concerning envelopes of surfaces in $\mathbb{R}^3$ (not necessarily higher dimensions).

One source (with references) is the CGAL manual, Envelopes of Surfaces in 3D.

---

            [![TwoTriangles][1]][1]
            ^{CGAL figure.}

Their software doesn't explicitly handle quadratic surfaces, however (aside from spheres).

These twos papers, and their 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.

Meyerovitch, Michal. "Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces." ESA: European Symposium on Algorithms. 2006. Springer link. PDF download.

---

            [![Meyerovitch][2]][2]
            ^{Meyerovitch figure.}

---

One source (with references) is the CGAL manual, Envelopes of Surfaces in 3D.

---

            [![TwoTriangles][1]][1]

---

  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.

One source (with references) is the CGAL manual, Envelopes of Surfaces in 3D.

---

            [![TwoTriangles][1]][1]  
            ^{CGAL figure.}

Their software doesn't explicitly handle quadratic surfaces, however (aside from spheres).

These twos papers, and their 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.

Meyerovitch, Michal. "Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces." ESA: European Symposium on Algorithms. 2006. Springer link. PDF download.

---

            [![Meyerovitch][2]][2]
            ^{Meyerovitch figure.}

---