Global Optimization Method to Comprise Rotation-Minimizing Euler-Rodrigues Frames of Pythagorean-Hodograph Curve

The rotation-minimizing frame is the main research object for a spatial curve. Although mathematical description not complicated, it easy to directly make an exact minimizing-rotation Euler-Rodrigues frame. condition non-normalized of Pythagorean-Hodograph curve become given in this article, which ordinary differential equation with rational form, analytical solution that does always exist. To avoid calculating equations, global optimization algorithm conditions proposed, has weight function objective function. quintic analyzed concretely method, and its constraint are clarified. example by using method different functions contrasting approach value.