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Az \(\mathbf{a}\left( u\right) ,~u\in\left[ u_{0},u_{1}\right]\) térgörbe érintőfelülete \[\mathbf{s}\left( u,v\right) =\mathbf{a}\left( u\right) +v{\frac{d}{du}}\mathbf{a}\left( u\right) ,v\in\mathbb{R}%\] alakban írható fel. A \(z\) tengelyű, \(p\) paraméterű, \(r\) sugarú \[\mathbf{h}\left( u\right) =\left[ \begin{array} [c]{c}% r\cos\left( u\right) \\ r\sin\left( u\right) \\ pu \end{array} \right] ,~u\in\mathbb{R}%\] hengeres csavarvonal érintőfelülete \[\begin{aligned} \mathbf{s}\left( u,v\right) & =\mathbf{h}\left( u\right) +v\mathbf{\dot {h}}\left( u\right) \\ & =\left[ \begin{array} [c]{c}% r\cos\left( u\right) \\ r\sin\left( u\right) \\ pu \end{array} \right] +v\left[ \begin{array} [c]{c}% -r\sin\left( u\right) \\ r\cos\left( u\right) \\ p \end{array} \right] \\ & =\left[ \begin{array} [c]{c}% r\left( \cos\left( u\right) -v\sin\left( u\right) \right) \\ r\left( \sin\left( u\right) +v\cos\left( u\right) \right) \\ p\left( u+v\right) \end{array} \right] ,~u,v\in\mathbb{R}\text{.}% \end{aligned}\] |