On the Computability of Rectifiable Simple Curve (Extended Abstract)

Robert Rettinger & Xizhong Zheng
In mathematics curves are defined as the images of continuous real functions defined on closed intervals and these continuous functions are called parameterizations of the corresponding curves. If only simple curves of finite lengths are considered, then parameterizations can be restricted to the injective continuous functions or even to the continuous length-normalized parameterizations. In addition, a plane curve can also be considered as a connected one-dimensional compact subset of points. By corresponding effectivizations, we will...