论文标题
四面体网状的tutte嵌入
Tutte Embeddings of Tetrahedral Meshes
论文作者
论文摘要
Tutte的嵌入定理指出，如果外部脸部处于凸位位置，并且内部顶点是邻居的凸组合，则每3个连接的图形没有$ k_5 $或$ k_ {3,3} $ minor（即平面图）。 We show that this result extends to simply connected tetrahedral meshes in a natural way: for the tetrahedral mesh to be embedded if the outer polyhedron is in convex position and the interior vertices are convex combination of their neighbors it is sufficient (but not necessary) that the graph of the tetrahedral mesh contains no $K_6$ and no $K_{3,3,1}$, and all三角形在三个边界顶点上的三角形是边界三角形。
Tutte's embedding theorem states that every 3-connected graph without a $K_5$ or $K_{3,3}$ minor (i.e. a planar graph) is embedded in the plane if the outer face is in convex position and the interior vertices are convex combinations of their neighbors. We show that this result extends to simply connected tetrahedral meshes in a natural way: for the tetrahedral mesh to be embedded if the outer polyhedron is in convex position and the interior vertices are convex combination of their neighbors it is sufficient (but not necessary) that the graph of the tetrahedral mesh contains no $K_6$ and no $K_{3,3,1}$, and all triangles incident on three boundary vertices are boundary triangles.
