Surfaces
[ September 2011]
Surface of revolution (generated by rotating a curve about an axis).
Torus (a circle in meridian plane, no intersection with an axis).
Sphere (a circle rotates about any of its diametres).
Prolate rotational ellipsoid ( an ellipse rotates about its major axis).
Oblate rotational ellipsoid (an ellipse rotates about its minor axis).
Rotational paraboloid (a parabola rotates about its axis).
One-sheet rotational hyperboloid (a hyperbola rotates about its minor axis).
Two-sheet rotational hyperboloid (a hyperbola rotates about its major axis).
One-sheet rotational hyperboloid (generating straight line skew to a rotational axis).
Helical surface (generated by screwing a curve about an axis).
Helicoid (line generator orthogonally intersects an helical axis).
Helicoid (a part between a helical axis and one helix).
Ruled helical surface (line generator orthogonal to a helical axis, no intersection).
Ruled helical surface (line generator askew intersects an helical axis)
Ruled helical surface (a part between a helical axis and one helix).
Ruled helical surface (line generator skew to a helical axis, no intersection).
Ruled helical surface (a part between two helixes).
Cyclical helical surface (a circle in a plane orthogonal to an helical axis).
Cyclical helical surface (a circle in meridian plane).
Cyclical helical surface (a circle in a plane orthogonal to helix tangent).
Developable surface (the principle of development).
Developable surfaces (cylinders and cones and their developments).
Ruled surface (determined by three director curves).
Hyperbolic paraboloid (one family of generators).
Hyperbolic paraboloid (one family of generators).
Hyperbolic paraboloid (both families of generators).
One-sheet rotational hyperboloid (one family of generators).
One-sheet rotational hyperboloid (one family of generators).
Circular conoid.
Parabolic conoid.
Frezier's cylindroid.
Montpellier's arc.
Marseille's arc.
Ruled surface (oblique passage).