In this paper, we propose a quick threshold-free algorithm, which computes the angular shape of a 2D object from the points of its contour. For that, we have extended a method [Debled & al 03] defined in a previous paper to a multiorder analysis. It is based on the arithmetical definition of discrete lines with variable thickness. We provide a framework to analyse a digital curve at different levels of thickness. The extremities of a segment provided at a high resolution are tracked at lower resolution in order to refine their location. The method is threshold-free and automatically provides a partitioning of a digital curve into its meaningful parts.