Date: 2010-11-17 00:00 Speaker: Gema Quintana Abstract: A rotation-minimizing adapted frame (RMF) $(f_1,f_2,f_3)(f\_1,f\_2,f\_3)$ on a given space curve $rr$ is characterized by the fact that the frame vector $f_{1}f\_1$ coincides with the tangent $\frac{r\text{’}}{\mathrm{\parallel }r\text{’}\mathrm{\parallel }}\backslash frac\{r’\}\{\backslash |r’\backslash |\}$, while the frame angular velocity $\omega \backslash omega$ maintains a zero component along it. Its minimal twist makes RMFs be widely used in computer graphics . This includes sweep of blending surface modeling, motion design and control in computer animation and robotics, streamline visualization, and tool path planning in CAD/CAM. After introducing basic definitions, I will present a method to construct low degree rational curves with RMFs.This method is based on the use of rational spatial Pythagorean-Hodograph curves (rational curves with rational hodograph) and some classical results from Geometry of Curves and Surfaces in ${\mathbb{R}}^3\backslash mathbb\; R^3$.