The hyperbolic paraboloid carries two families of straight lines. One may express this as: the surface is a “doubly ruled” surface. This animation starts with an almost flat example and stretches the z-ccordinate. - Note that each tangent plane intersects the surface in the two straight lines through the point of contact.
A growing piece of the surface emphasizes the two straight line families.
An anaglyph view of the saddle shaped hyperbolic paraboloid.
Rotation of the surface around one of its lines, cross-eyed rendering.
Conic Section Surfaces
Hyperboloid of One Sheet
Hyperboloid of Two Sheet
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3DXM Surface Gallery