Abstract
Let us consider a curve u = u(t), v = v(t) in the parametric domain of a parametric surface r = r(u, v) as shown in Fig. 3.1. Then r = r(t) = r (u(t), v(t)) is a parametric curve lying on the surface r = r(u,v).The tangent vector to the curve on the surface is evaluated by differentiating r(t) with respect to the parameter t using the chain rule and is given by
Where subscripts u and v denote partial differentiation with respect to u and v, respectively. The tangent plane at point P can be considered as a union of the tangent vectors of the form (3.1) for all r(t) through P as illustrated in Fig. 3.2. Point P corresponds to parameters u p, v p.
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© 2010 Springer-Verlag Berlin Heidelberg
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Patrikalakis, N.M., Maekawa, T. (2010). Differential Geometry of Surfaces. In: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04074-0_3
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DOI: https://doi.org/10.1007/978-3-642-04074-0_3
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