Flip Graphs of Pseudo-Triangulations With Face Degree at Most 4
CoRR(2024)
摘要
A pseudo-triangle is a simple polygon with exactly three convex vertices, and
all other vertices (if any) are distributed on three concave chains. A
pseudo-triangulation 𝒯 of a point set P in ℝ^2 is a
partitioning of the convex hull of P into pseudo-triangles, such that the
union of the vertices of the pseudo-triangles is exactly P. We call a size-4
pseudo-triangle a dart. For a fixed k≥ 1, we study k-dart
pseudo-triangulations (k-DPTs), that is, pseudo-triangulations in which
exactly k faces are darts and all other faces are triangles. We study the
flip graph for such pseudo-triangulations, in which a flip exchanges the
diagonals of a pseudo-quadrilatral. Our results are as follows. We prove that
the flip graph of 1-DPTs is generally not connected, and show how to compute
its connected components. Furthermore, for k-DPTs on a point configuration
called the double chain we analyze the structure of the flip graph on a more
fine-grained level.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要