From the Greek orthos "right" and optikos "relating to sight".

The orthoptic surface of a surface is the locus of the points through which pass 3 planes tangent to the surface and perpendicular 2 by 2.

Examples:
    - the orthoptic surface of a sphere with radius R is a concentric sphere with radius .

    - more generally, the orthoptic surface of a centered quadric is a sphere called orthoptic sphere or Monge sphere ; for example, for the ellipsoid of half-axes a, b, c, the Monge sphere has same center that the ellipsoid and radius .

    - The orthoptic surface of the elliptic paraboloid :  is a plane called Monge plane, of equation .
A similar notion, bearing the same name, is that of orthoptic surface of a subset of the space: locus of the vertices of the right trihedra that circumscribe X (i.e. "containing" X, and the three faces of which meet X).

Example: the orthoptic of a circle with radius R is a sphere with the same center and radius .
 

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© Robert FERRÉOL  2022