(* Freeware 1992 Loki_Demsey *)
(* :Version: Mathematica 2.0 *)
(* :Name: `Surfaces` *)
(* :Title: Parametric Equations For Common 3-Space Surfaces *)
(* :Author: Matthew (Loki) Demsey, This is Release 1.1 - April, 1992
Department of Mathematics, University of Arizona *)
(* :Keywords: differential geometry, surfaces *)
(* :Requirements: none. *)
(* :Warnings: none. *)
(* :Summary:
Originally intended for a supplement to the differential geometry package -
`DiffGeo` written by the author of this package.
*)
(* :Authors notes:
example usage: FirstForm[Sphere, u, v]
Please mail all criticisms, bugs, and suggestions to :
BitNet : norton@rsconvex.geo.arizona.edu - put "TO: Loki" in subject, please.
SnailMail: M.L. Demsey, c/o Dr. Denis Norton, Department of GeoSciences,
University of Arizona, Tucson, AZ 85721
*)
BeginPackage["Surfaces`"]
Sphere :=
Return[
{Sin[u] Cos[v], Sin[u] Sin[v], Cos[u]}
]
Parabaloid :=
Return[
{u^2, v^2, u^2 + v^2}
]
Ellipsoid :=
Return[
{a Sin [u] Cos[v], b Sin[u] Sin[v], c Cos[u]}
]
Cone :=
Return[
{a Sinh[u] Sinh[v], b Sinh[u] Cosh[v], c Sinh[u]}
]
HyperboloidTwo :=
Return[
{a Sinh[u] Cos[v], b Sinh[u] Sin[v], c Cosh[u]}
]
EllipticParaboloid :=
Return[
{a u Cos[v], b u Sin[v], u^2}
]
HyperbolicParaboloid :=
Return[
{a u Cosh[v], b u Sinh[v], u^2}
]
EndPackage[ ] (* Surfaces *)