definicije funkcija Gaussove i srednje zakrivljenosti

Koeficijenti 1. osnovne diferencijalna forme

ee[x_][u_, v_] := FullSimplify[D[x[uu, vv], uu] . D[x[uu, vv], uu]]/.{uuu, vvv}

ff[x_][u_, v_] := FullSimplify[D[x[uu, vv], uu] . D[x[uu, vv], vv]]/.{uuu, vvv}

gg[x_][u_, v_] := FullSimplify[D[x[uu, vv], vv] . D[x[uu, vv], vv]]/.{uuu, vvv}

Vektor normale

N0[x_][u_, v_] := FullSimplify[Cross[D[x[uu, vv], uu], D[x[uu, vv], vv]]/Sqrt[Cross[D[x[uu, vv ... , uu], D[x[uu, vv], vv]] . Cross[D[x[uu, vv], uu], D[x[uu, vv], vv]]]]/.{uuu, vvv}

Koeficijenti 2. osnovne diferencijalna forme

ll[x_][u_, v_] := FullSimplify[D[x[uu, vv], uu, uu] . N0[x][uu, vv]]/.{uuu, vvv}

mm[x_][u_, v_] := FullSimplify[D[x[uu, vv], uu, vv] . N0[x][uu, vv]]/.{uuu, vvv}

nn[x_][u_, v_] := FullSimplify[D[x[uu, vv], vv, vv] . N0[x][uu, vv]]/.{uuu, vvv}

Gaussova zakrivljenost

GZ[x_][u_, v_] := FullSimplify[(ll[x][uu, vv] * nn[x][uu, vv] - mm[x][uu, vv] * mm[x][uu, vv])/(ee[x][uu, vv] * gg[x][uu, vv] - ff[x][uu, vv] * ff[x][uu, vv])]/.{uuu, vvv}

Srednja zakrivljenost

SZ[x_][u_, v_] := FullSimplify[1/2 (ee[x][uu, vv] * nn[x][uu, vv] - 2mm[x][uu, vv] * ff[x][uu, ... vv])/(ee[x][uu, vv] * gg[x][uu, vv] - ff[x][uu, vv] * ff[x][uu, vv])]/.{uuu, vvv}

Created by Mathematica  (May 4, 2004)