regular smooth curve - Penn Math
regular smooth curve - Penn Math
regular smooth curve - Penn Math
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To produce the �-tube about this <strong>curve</strong>, we define<br />
by<br />
F: {0 � s � L} � {�� < t < �} � R 2<br />
F(s, t) = x(s) + t N(s) .<br />
Then the partial derivatives of F are given by<br />
Fs = x'(s) + t N'(s) = T(s) + t (��(s) T(s))<br />
Ft = N(s) .<br />
= (1 � t �(s)) T(s)<br />
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