廣琴Sheffer, Spanning Tree Seams""Sheffer detects extremaby searchingforvertices withhighcurvature(曲率)Shefferapproximates Steiner tree by the minimumspanning tree (MST)2009.3.30TsinghuaUniversity
• Sheffer, “Spanning Tree Seams ” – Sheffer detects extrema by searching for vertices with Sheffer detects extrema by searching for vertices with high curvature(曲率). – Sheffer approximates Steiner tree by the minimum Sheffer approximates Steiner tree by the minimum spanning tree (MST). Tsinghua University 2009. 3.30
廣翠Two points concerned in existing methodsGreedymethod:This incremental method dependsheavilyonthe sequenceof adding extremal vertices-MsT method:can't introduce steinerpointswhosedegree are greater than 2, then seam will pass throughmost extrama multipletimes.This will lead tobadresult。2009.3.30Tsinghua University
• Two points concerned in existing methods: – Greedy method Greedy method：This incremental method depends This incremental method depends heavily on the sequence of adding extremal vertices. – MST method：can’t introduce steiner points whose de gg , p g ree are greater than 2, then seam will pass throu gh most extrama multiple times. This will lead to bad result。 Tsinghua University 2009. 3.30
廣琴3.Outline:The Skeleton-basedmethodIdea:-Let'slookatthehorseModel,themostobviousextremaarelocatedattheendsof the four legs and the head, The seamcomputed using theMST method ispooras theMST passes throughmostextremamorethanonceTsinghua University
3 Outline: The Skeleton 3. Outline: The Skeleton -based method based method • Idea: – Let s’ look at the horse Model the most look at the horse Model, the most obvious extrema are located at the ends of the four legs and the head The seam of the four legs and the head, The seam computed using the MST method is poor as the MST passes thro gh most poor as the MST passes thro ugh most extrema more than once. Tsinghua University 2009. 3.30
廣琴-However,extremal vertices are always atthe ends ofprotrusions(突出), and so it is reasonable to require thattheseam should passthrougheachextremal vertexasfew times as possible. It will be best if all extremalverticesareleavesontheseam2009.3.30TsinghuaUniversity
– However, extremal vertices are always at the ends of p ( rotrusions (突出), q and so it is reasonable to re quire that the seam should pass through each extremal vertex as few times as possible. It will be best if all extremal vertil h ces are leaves on t he seam. Tsinghua University 2009. 3.30
廣琴-For thisreason,we constrainthe Steiner treeto bea“full component"ofthemesh,andSuggestanewmethod tocomputean approximationtothe minimal full component Steiner tree, deriving itfrom the straight skeletonAfull component is a subtree in which eachterminal is a leaf.2009.3.30Tsinghua University
– For this reason, we constrain the Steiner tree to be a “full com p , onent” of the mesh, and – Suggest a new method to compute an approximation to the minimal full component Steiner tree, deriving it from the straight skeleton. A full component is a subtree in which each terminal is a leaf. Tsinghua University 2009. 3.30