Tracing the border of a surface patch deals with arranging the border locations in such an order that a closed line which does not intersect itself is obtained, when the ordered border points are connected in the x1,y1,z1 coordinate system. The question is how to trace if the patch has support on more than one domain.
The case of a merged planar patch is considered in [22]. If the neighboring patches are also planar, the border of the patch is a poly-line consisting of vertices and non-occluded or occluded edges. The corresponding vertices and edges between the original patches that have been merged are first determined by matching vertex angles, edge lengths, and edge labels. The border of the merged patch is then traced out by following both borders around. ``When neither edge is occluded then both edges are followed, when one edge is occluded the other is followed, and when both edges are occluded the outermost is followed'' [22].
Our contribution is to propose a general algorithm for tracing the border of a merged patch applicable to patches of any type [IV]. The border locations are first determined independently on each map. Then the locations given by different maps are compared and the locations are removed which are actually inside the patch when all the views are considered. In case the same piece of the border has been measured from several viewpoints, only single border locations are stored for the tracing. The locations left are then traced on multiple domains by switching between the domains whenever the border locations end on a domain and continue on another one. The results given by the tracing algorithm are illustrated in [IV, Fig. 6].
After [IV], we have improved the definition of a border location so that there has to be at least one truly inside location also in the neighborhood of the border location. This makes the border smoother so that the tracing does not get stuck into thin ledges having the width of a single location. It is also checked that the new piece of line does not intersect the line traced so far. We may also take a couple of steps backwards during the tracing and select another location than previously.