minimalne1.nb

definicije funkcija Gaussove i srednje zakrivljenosti

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

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

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

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

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

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

In[79]:=

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

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

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

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Created by Mathematica (April 30, 2004)