Lecture 8: Mesh Representations and Geometry Processing (41)
phoebeli23
How did the undesired edges (with one end at a vertex) get created in the first place?
CalArsen
Yeah, I'm also a little confused as to how the edges were initially split, since they seem to split differently from the earlier slides, where they were shown to split at some initial midpoint between two triangles?
xinwei-zhuang
why can't we just split triangles with three middle points connected in the beginning?
adityaramkumar
Do we always need exactly 3 splits? To me, it seems that the split + flip is equivalent to just doing a different type of split (as a triangle). Unless of course, the contents of the triangle are also being shifted.
sinood
@phoebeli23 @CalArsen This slide doesn't show the steps of the splitting; but these undesired edges happen naturally if you simply split every black (original edge). I made this graphic with the steps of the subdivision to see how this occurs:
https://drive.google.com/file/d/1CFMFwRsxC_Qo0aqrkHtG4668RwP-FiMz/view?usp=sharing
ML2000-LT
To be exact, the very first split on any original edge, would give us these undesired new edge, therefore such undesired edge is not avoidable. Reason is simple, with the first split, we create only one new vertex and all other vertices are old, therefore these newly created edge must be a connection between new and old vertex, hence, we need a flip. And that explains why we need to flip the edges that touched new & old, since we only want new & new new edges, and want the old & old unscathed
melodysifry
This diagram was incredibly helpful to me when understanding how splits and flips can result in subdivision- at first it was unclear to me how splitting the edges of the original mesh resulted in the diagram in the upper right, but after realizing that the splits aren't just taking account the original edges but also considering any newly created edges to be a part of the triangles when splitting, the algorithm made much more sense.
How did the undesired edges (with one end at a vertex) get created in the first place?
Yeah, I'm also a little confused as to how the edges were initially split, since they seem to split differently from the earlier slides, where they were shown to split at some initial midpoint between two triangles?
why can't we just split triangles with three middle points connected in the beginning?
Do we always need exactly 3 splits? To me, it seems that the split + flip is equivalent to just doing a different type of split (as a triangle). Unless of course, the contents of the triangle are also being shifted.
@phoebeli23 @CalArsen This slide doesn't show the steps of the splitting; but these undesired edges happen naturally if you simply split every black (original edge). I made this graphic with the steps of the subdivision to see how this occurs: https://drive.google.com/file/d/1CFMFwRsxC_Qo0aqrkHtG4668RwP-FiMz/view?usp=sharing
To be exact, the very first split on any original edge, would give us these undesired new edge, therefore such undesired edge is not avoidable. Reason is simple, with the first split, we create only one new vertex and all other vertices are old, therefore these newly created edge must be a connection between new and old vertex, hence, we need a flip. And that explains why we need to flip the edges that touched new & old, since we only want new & new new edges, and want the old & old unscathed
This diagram was incredibly helpful to me when understanding how splits and flips can result in subdivision- at first it was unclear to me how splitting the edges of the original mesh resulted in the diagram in the upper right, but after realizing that the splits aren't just taking account the original edges but also considering any newly created edges to be a part of the triangles when splitting, the algorithm made much more sense.