Scallop hull and its offset (Q1335433)

Engineers have long studied offset curves and surfaces, the same sets that mathematicians usually call parallel curves and surfaces. These offset curves are the paths of machine tools shaping a given surface. What the authors call scallop hull of a set \(A\) can be described in mathematical terms as the parallel set, in Hadwiger's notation, \((A_ \varrho)_{-\varrho}\). This clearly is a regularization process that eliminates narrow concavities. They present a linear time algorithm for the computation of the scallop hull. For a mathematical study of inward parallel sets see the book by \textit{H. Hadwiger} [Altes und Neues über konvexe Körper (1955; Zbl 0064.165)] and some of Hadwiger's papers.