On the classification of views of piecewise smooth objects

摘要

Views of objects composed of smooth surface patches whose intersections form smooth space curves are classified. These views may he described algebraically by mappings and diagrams of mappings from the line to the plane (for the crease) or from the plane to the plane (for the apparent contour). It is possible to derive a finite catalogue of generic views and their transitions, so that every view is either (up to smooth coordinate changes in source and target) equivalent to one of those in the catalogue or is of sufficiently high codimension.