Explicit stereographic projections for ellipsoids and elliptic paraboloids are derived, and horizontal-section ellipses are shown to project to homothetic ellipses with preserved eccentricity and simple scaling laws for curvature, arc length, and area.
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Stereographic Projections on Some Quadric Surfaces
Explicit stereographic projections for ellipsoids and elliptic paraboloids are derived, and horizontal-section ellipses are shown to project to homothetic ellipses with preserved eccentricity and simple scaling laws for curvature, arc length, and area.