How do we decide the boundary of such polygon when there are so many choices to bound?
keenan
@Arthas007 Good question---we didn't say anything about boundary conditions here. The simplest thing to do is to just leave the boundary vertices fixed to their original locations, and only apply the local smoothing procedure to interior vertices. Alternatively, you could allow the boundary vertices to "slide along the boundary," i.e., compute the average of the two neighbors, but stay on the line parallel to the difference between the two neighbors and passing through the original vertex.
How do we decide the boundary of such polygon when there are so many choices to bound?
@Arthas007 Good question---we didn't say anything about boundary conditions here. The simplest thing to do is to just leave the boundary vertices fixed to their original locations, and only apply the local smoothing procedure to interior vertices. Alternatively, you could allow the boundary vertices to "slide along the boundary," i.e., compute the average of the two neighbors, but stay on the line parallel to the difference between the two neighbors and passing through the original vertex.