CADability/OffsetSurface.max.txt at master · Syntaxrabbit/CADability · GitHub

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load("vect");

/* Definiere die allgemeine Vektorfunktion f(u, v) */
f(u, v) := [x(u, v), y(u, v), z(u, v)];

/* Definiere die partiellen Ableitungen */
dfdu : diff(f(u, v), u);
dfdv : diff(f(u, v), v);
dfduu : diff(f(u, v), u, 2);
dfdvv : diff(f(u, v), v, 2);
dfduv : diff(f(u, v), v, 1, u, 1);
dfduuu : diff(f(u, v), u, 3);
dfdvvv : diff(f(u, v), v, 3);
dfduvv : diff(f(u, v), v, 2, u, 1);
dfduuv : diff(f(u, v), v, 1, u, 2);

subst_d : [df_du=dfdu, df_dv=dfdv];

/* Berechne das Kreuzprodukt und normiere es */
n : dfdu ~ dfdv;
norm_n : sqrt(n[1]^2 + n[2]^2 + n[3]^2);
N : n / norm_n;

/* Definiere die neue Funktion o(u, v) */
o(u, v) := f(u, v) + d * N;

/* Berechne die partiellen Ableitungen von o(u, v) */
dod_u : diff(o(u, v), u);
dod_v : diff(o(u, v), v);
dod_uv: diff(o(u,v),u,1,v,1);
dod_uu: diff(o(u,v),u,2);
dod_vv: diff(o(u,v),v,2);

subst(df_du,dfdu,
subst(df_dv,dfdv,
subst(df_duu,dfduu,
subst(df_dvv,dfdvv,
subst(df_duv,dfduv,dod_u)))));

subst(df_du,dfdu,
subst(df_dv,dfdv,
subst(df_duu,dfduu,
subst(df_dvv,dfdvv,
subst(df_duv,dfduv,dod_v)))));

subst(df_du,dfdu,
subst(df_dv,dfdv,
subst(df_duu,dfduu,
subst(df_dvv,dfdvv,
subst(df_duv,dfduv,
subst(df_duuu,dfduuu,
subst(df_duuv,dfduuv,
subst(df_duvv,dfduvv,
subst(df_dvvv,dfdvvv,dod_uu)))))))));

subst(df_du,dfdu,
subst(df_dv,dfdv,
subst(df_duu,dfduu,
subst(df_dvv,dfdvv,
subst(df_duv,dfduv,
subst(df_duuu,dfduuu,
subst(df_duuv,dfduuv,
subst(df_duvv,dfduvv,
subst(df_dvvv,dfdvvv,dod_vv)))))))));

subst(df_du,dfdu,
subst(df_dv,dfdv,
subst(df_duu,dfduu,
subst(df_dvv,dfdvv,
subst(df_duv,dfduv,
subst(df_duuu,dfduuu,
subst(df_duuv,dfduuv,
subst(df_duvv,dfduvv,
subst(df_dvvv,dfdvvv,dod_uv)))))))));