Normal congruence of paraboloid. Demiquadrics

It is an important problem to build a family of lines on the paraboloid of rotation with certain properties convenient for metallic mesh tailoring upon designing and manufacturing a parabolic antenna. Namely, the lines of this family should be locally close to geodesic lines to a reasonable extent, and an algorithm relating the line of this family to the natural parameter is also necessary. The first and important step has been made in solving the problem: a class of surfaces whose intersection with the paraboloid generates a class of lines promising for the achievement of the declared goals is revealed. These surfaces are demiquadrics associated in a special way with the normal congruence of the paraboloid.

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